§ 1 Introduction

1.1 About the FAQ. Redistribution. How to submit updates and suggestions.

1.2 Who pays for the FAQ? How do I get the best online poker sign-up bonus? And why are those questions related?

1.3 What is the best way to access RGP?

1.4 Useful poker links.

§ 2 Poker games and rules

§ 2.1 How to play

2.1.1 What are the basic rules of poker? What are the hand rankings?

2.1.2 What happens if two players have the same hand? How do you divide the pot?

2.1.3 What should I expect the first time I play poker in a casino or card room? What etiquette should I follow?

2.1.4 What is a poker tournament? How does one work? What is a chip race? What is a satellite?

2.1.5 What are some good books about poker?

2.1.6 What are some good magazines about poker?

2.1.7 What are some good poker-related software programs?

2.1.8 What do all these poker terms mean? Table stakes, no limit, all-in, the nuts, drawing dead, and a thousand more...

§ 2.2 Popular poker games

2.2.1 What are some fun home poker games?

2.2.2 How do you play Texas Hold'em?

2.2.3 How do you play Omaha?

2.2.4 How do you play Chowaha?

2.2.5 How do you play no-limit seven-card stud? What is Mississippi Stud?

§ 2.3 More advanced topics

2.3.1 What are the betting and raising rules in No Limit?

2.3.2 What does pot-limit mean?

2.3.3 What does half-pot-limit mean?

2.3.4 What is a kill pot? What is a game with a kill? What is a half kill?

2.3.5 What is a straddle bet?

2.3.6 What is Hi-Lo declare? What if someone declares both ways but ties?

2.3.7 What is a burn card and why is it dealt?

2.3.8 What happens if there aren't enough cards in the deck to deal the final card in 7-card stud?

§ 2.4 Odds and probabilities

2.4.1 Why are poker hands ranked the way they are?

2.4.2 What is the correct ranking for 3-card poker hands?

2.4.3 Why are ace-hi flushes ranked highest, when it's much harder to get a seven-hi flush? And similarly for two pairs?

2.4.4 What are my chances of sucking out on my opponent in Hold'em?

2.4.5 What are my chances of sucking out on my opponent in Stud?

2.4.6 How many fundamentally different Omaha or Omaha-8 starting hands are there?

§ 2.5 Miscellaneous

2.5.1 What is the difference between a shill and a proposition player? What skills are needed to be one?

2.5.2 What is the Dead Man's Hand?

§ 3 Poker strategy

3.1 What skills are important for Texas Hold'em?

3.2 What is a good preflop strategy for limit Texas Hold'em?

3.3 How does tournament strategy differ from that of regular games?

3.4 Is "checking it down" in a tournament implicit collusion?

3.5 Why is position so important in poker?

3.6 Can one overcome the rake at low limit poker games?

§ 4 Poker community

4.1 When can I meet and play poker with fellow r.g.pers? What are BARGE, FARGO, etc?

4.2 What the hell is Rumple Mintz?

4.3 What is the World Series of Poker?

4.4 What is IRC poker and how can I play?

§ 5 Online poker

5.1 Where can I play online poker against real people for real money? Is it legal? Is it safe?

5.2 What are some advantages of online poker over cardroom poker?

5.3 How do I play online poker on a Mac computer?

5.4 How can I best use Player Notes to track my online opponents?

5.5 How do I find out what games are available and how many tables are active at each online site?

5.6 What is the online "cash-out curse"? Is the curse evidence that the sites are rigged?

1 Introduction

1.1 About the FAQ. Redistribution. How to submit updates and suggestions.

This is the rec.gambling.poker Frequently Asked Questions (FAQ) list. It is officially hosted in two locations:

• http://www.rgpfaq.com
• http://www.conjelco.com/faq/poker.html

A text version is posted to rec.gambling.poker once per month. There is also a single-page HTML version.

Copying. This document contains material copyrighted by various authors. If you want to redistribute or copy the FAQ, you have these options:

1. You may freely link to either of the URLs above.
2. You may copy or redistribute the FAQ in its entirety and without modifications, either in HTML or text form. You must retain the authorship and copyright notices as they are.
3. You may request permission to copy or redistribute a portion of the FAQ by writing to either info@rgpfaq.com or to the individual copyright holder.

Updates. Changes or additions to the FAQ should be submitted to: info@rgpfaq.com. Include the word "FAQ" in the subject to avoid being lost amid the spam.

1.2 Who pays for the FAQ? How do I get the best online poker sign-up bonus? And why are those questions related?

The rec.gambling.poker FAQ is a volunteer effort. It's a lot of work to update articles with fresh information, maintain old links and add new ones, and keep abreast of the rapidly changing world of poker. If you have an update or want to submit a new article, send mail to info@rgpfaq.com. We'll give you full credit for your article (you retain the copyright) and help you become famous among the r.g.p. community!

(Almost) no ads! You'll notice that rgpfaq.com doesn't distract your eye with a dozen flashing banner ads on every page. Instead we try to keep the site as plain as possible to make it easy for you to find the information you need. We figure if you wanted to be on another site you'd go there yourself.

But there is a way you can help the FAQ financially if you are thinking about opening up an online poker account. By taking advantage of the system of online poker sign-up bonuses, you can receive a bonus deposit (usually $20 to $100) when you open a new account and help fund the FAQ at the same time. How's that? By using the bonus code of our sponsor site, who receives a referral fee from the poker site, and then donates many hours of volunteer time to the FAQ (and also pays for our web hosting bandwidth).

How do these referrals work? When you open up an online poker account, you have a few choices:

1. No bonus code or referral ID. If you surf directly to a poker site by typing in their URL and then download the software, the account you open won't be associated with any referrer. You may receive some sort of sign-up bonus from the site, or not, depending on what promotions they happen to be running.
2. Sneaky referral ID. If you ever click on a banner ad that takes you to a poker site and then, perhaps much later, you download the software, your new account will be tagged with the referral ID of the site with the banner ad (unless you use a bonus code, explained next). You can usually see the ID in the landing page URL. Sometimes the referring site offers a sign-up bonus that you will get when you open your account, but sometimes not. In any case, the referring site receives credit for helping the poker site find you, even if you don't get a bonus.
3. Sign-up bonus code. No matter how you download the software, if you enter a sign-up bonus code in the account registration form then you will receive the bonus and the promoter of the bonus code will receive credit for sending a new customer. By using a bonus code, you can be sure of getting the best bonus currently available and also know who will benefit from the opening of your account. Rather than helping some random banner advertiser or spammer, you can choose a more deserving recipient.

Now, there is no question that you want to receive a sign-up bonus when you open a new online poker account. The only decision is who you want to receive the referral fee. In the hope that you find this FAQ a worthy cause, we refer you to a constantly updated list of the best sign-up bonuses offered by the top sites. You can find the latest codes in the bonus code center.

1.3 What is the best way to access RGP?

Since RGP is a Usenet Newsgroup, the best way to access any Usenet Newsgroup is through a newsreader. Usenet and Newsreaders have been around since long before the Internet was created. However, due to the success of the Internet, there are now several other ways to access RGP, although none of them as flexible as the least capable of the newsreaders.

Below, I have grouped the access methods into three types, listing only the free solutions. There are also a number of paid Usenet access websites and news servers.

1. Free Poker-Only Web Interfaces: The following is a list of poker-related web interfaces for reading and posting to RGP. If one of these sites is ever down, you should be able to quickly setup an account at another site.

• Recpoker
• Live Action Poker
• Pokeritis
• Pokerhelper

2. Free Multi-Group Web Interfaces: The following is a list of free websites that offer access to RGP plus many other Usenet groups:

• Google Groups
• Talk About Gambling

3. Free Newsreader Access: The best way to find out if your computer is already setup to access RGP via a newsreader is to click on this link: news:rec.gambling.poker (if you do not see a link above, then your Internet browser does not support this feature, but you can still setup a newsreader).

If clicking on the link above loads a news reader such as Outlook Express, you are halfway there. If not, you will probably need to install a newsreader on your computer. Below is a list of a couple of good free ones:

• Forte - the makers of Free Agent
• Newsreaders.com - a complete list of other newsreaders

If you have a newsreader setup, but it tells you that you need to setup the news server, you will need to get a username and password from a news provider. Most ISPs (the people who connect you to the Internet) offer free news servers as part of their package. Either call their support line (the best solution if you are new to computers) or go to their help page and search on "News Feed" or "News Server" or "Usenet" or "Newsgroups" for information on how to setup their news service.

If your ISP does not offer a news service, then send an email requesting a userid and password to access www.individual.net which is hosted by a University in Germany. It may take a week to get the user id, but you will have RGP access plus thousands of other Usenet groups. Visit www.individual.net for details on getting the userid and password setting up this news service on your computer.

1.4 Useful poker links.

Ways to access rec.gambling.poker:
See the FAQ item on RGP access for more details.
Usenet access to rec.gambling.poker
Google access to rec.gambling.poker
RecPoker — web gateway to rec.gambling.poker
Live ActionPoker — web gateway to rec.gambling.poker

Web sites - r.g.p related:
rgpfaq.com — home of the rec.gambling.poker FAQ
Conjelco — longtime bookstore for r.g.p. readers and hoster of this FAQ
BARGE — Big Annual Rec.Gambling Excursion (details)
World Rec.Gambling Poker Tournament — the famous annual email poker tournament
IRC Poker Database — over 10 million hands recorded on the IRC poker server

Web sites - maintained by r.g.p individuals:
Poker Portal — an amazing collection of poker links
Dan Kimberg's Poker Page
Ken Churilla's Poker Page
Jazbo's Poker Page
Abdul's Pos. E.V. Poker Page
Izmet Fekali's Playing With the Fish
Jim Geary's Poker Page
Steve Badger's PlayWinningPoker
Andy Bloch's WPT Fan Site
JohnnyD Poker
Lou Krieger Online
Daniel Negreanu's Full Contact Poker
HowardLederer.com
Wolf's Poker Page
David Zanetti's Mississippi Stud Page

Non-r.g.p poker forums:
Two Plus Two Forums — a very large community of poker players
United Poker Forum
The Poker Forum
Cardschat Poker Forums — friendly poker discussion, freeroll events
Neverwin Poker Forums — regular hangout for very high limit online pros
StoxPoker — a collection of poker blogs from some of the most successful players on the internet
Internet Texas Holdem
Poker In Europe Forums
See Poker Portal for more

Web sites - about online poker:
Online Poker FAQ — 55-page online guide to online poker (our sponsor)
Poker Site Scout — traffic rankings for online poker sites
The Poker Project — reviews of online poker sites
Poker Listings — reviews of online poker sites
Which Poker UK — reviews of online poker sites, especially in UK
Mac Poker — info about playing online poker from your Mac or Linux computer
See Poker Portal for many more

Web sites - other commercial:
Poker Pages — lots of good tournament info, articles and forums
Poker School Online — a learning community
Card Player Magazine — articles by top poker columnists
Home Poker — fun variations to spice up your home game
Home Poker Games — where to play in your neighborhood
Local Poker List — local and home poker games and tournaments, listings across US
Poker.net — articles plus a directory of real-life cardrooms
Poker Search — includes guide to US cardrooms
See Poker Portal for many more

Poker references:
Mike Caro University Library
Caro and Cooke's Rules of Real Poker
Bob Ciaffone's "Robert's Rules of Poker"
Tournament Directors Association (TDA) Rules
2004 World Series of Poker (WSOP) Rules
Tex's TEARS — poker tournament structure sheets

2 Poker games and rules

2.1 How to play

2.1.1 What are the basic rules of poker? What are the hand rankings?

Most variants of poker satisfy the following definition, but in a home game of course you are free to modify the rules as you see fit.

Poker is a card game in which players bet into a communal pot during the course of a hand, and in which the player holding the best hand at the end of the betting wins the pot. During a given betting round, each remaining player in turn may take one of four actions:

1. check, a bet of zero that does not forfeit interest in the pot
2. bet or raise, a nonzero bet greater than preceding bets that all successive players must match or exceed or else forfeit all interest in the pot
3. call, a nonzero bet equal to a preceding bet that maintains a player's interest in the pot
4. fold, a surrender of interest in the pot in response to another player's bet, accompanied by the loss of one's cards and previous bets

Betting usually proceeds in a circle until each player has either called all bets or folded. Different poker games have various numbers of betting rounds interspersed with the receipt or replacement of cards.

Poker is usually played with a standard 4-suit 52-card deck, but a joker or other wild cards may be added. The ace normally plays high, but can sometimes play low, as explained below. At the showdown, those players still remaining compare their hands according to the following rankings:

1. Straight flush, five cards of the same suit in sequence, such as 76543 of hearts. Ranked by the top card, so that AKQJT is the best straight flush, also called a royal flush. The ace can play low to make 5432A, the lowest straight flush.
2. Four of a kind, four cards of the same rank accompanied by a "kicker", like 44442. Ranked by the quads, so that 44442 beats 3333K, and then ranked by the side card, so that 4444A beats 4444K(*).
3. Full house, three cards of one rank accompanied by two of another, such as 777JJ. Ranked by the trips, so that 44422 beats 333AA, and then ranked by the pair, so that 444AA beats 444KK(*).
4. Flush, five cards of the same suit, such as AJ942 of hearts. Ranked by the top card, and then by the next card, and so on for all five cards, so that AJ942 beats AJ876. Suits are not used to break ties.
5. Straight, five cards in sequence, such as 76543. The ace plays either high or low, making AKQJT and 5432A. "Around the corner" straights like 32AKQ are usually not allowed.
6. Three of a kind, three cards of the same rank and two kickers of different ranks, such as KKK84. Ranked by the trips, so that KKK84 beats QQQAK, and then ranked by the two kickers, so that QQQAK beats QQQA7(*).
7. Two pair, two cards of one rank, two cards of another rank and a kicker of a third rank, such as KK449. Ranked by the top pair, then the bottom pair and finally the kicker, so that KK449 beats any of QQJJA, KK22Q, and KK445.
8. One pair, two cards of one rank accompanied by three kickers of different ranks, such as AAK53. Ranked by the pair, followed by each kicker in turn, so that AAK53 beats AAK52.
9. High card, any hand that does not qualify as one of the better hands above, such as KJ542 of mixed suits. Ranked by the top card, then the second card and so on for all five cards, as for flushes. Suits are not used to break ties.

(* Such matchups are only possible in games where there are wild cards or where community cards are shared, such as Texas Holdem.)

Suits are not used to break ties, nor are cards beyond the fifth; only the best five cards in each hand are used in the comparison. In the case of a tie, the pot is split equally among the winning hands. For a more detailed explanation, see the section on splitting the pot.

Several variations are possible when playing for low. Some games permit the ace to play low and ignore straights and flushes, making 5432A the best possible low, even if it makes a straight flush. Other games just reverse the order used for high hands, making 75432 of mixed suits the best possible low. Still others count straights and flushes against you but let the ace play low, making 6432A best. Note that in most games in which the ace plays low, a pair of aces is lower than a pair of deuces, just as an ace is lower than a deuce.

When a joker is in play, it usually can only be used as an ace or to complete a straight or flush. It cannot be used as a true wild card, for example, as a queen to make QQ43X play as three queens. When playing for low, the joker becomes the lowest rank not already held, so 864AX is played as 8642A, with the joker used as a deuce.

Although true wild cards are rarely seen in a casino, they are a popular way to add excitement to a home game. Wild cards introduce an additional hand, five of a kind, which normally ranks above a straight flush. They can also cause confusion when two players hold the same hand composed of different wild card combinations. The standard rules of poker do not distinguish between such hands, but some players prefer to rank hands using fewer wild cards above less "natural" versions of the same hand.

You may find these comprehensive poker rulebooks helpful:
Caro and Cooke's Rules of Real Poker
Bob Ciaffone's "Robert's Rules of Poker"
Tournament Directors Association (TDA) Rules
2004 World Series of Poker (WSOP) Rules

If you are interested in learning all about online poker in particular, try the Beginners' Guide to Online Poker. It goes way beyond the basics to topics like record keeping software, site integrity, the law and taxes.

2.1.2 What happens if two players have the same hand? How do you divide the pot?

In some forms of poker it is fairly common for two or more players to end up with the same best hand. In that case, the players with equal hands split the pot equally between them. Remember that only the best five cards of a player's hand are considered in the showdown. If the best five cards yield a tie, you do not use additional cards to break the tie. Also, you don't look at the suits to break a tie. It's simply a tie. Here are some examples:

• In Holdem, one player has [Ah Jc] and another player has [As Jd]. The final board is Ad Ts 8s 4h 2d. Both players have a pair of aces with J-T-8 kickers. They split the pot.
• In Holdem, one player has [Ah Jc] and another player has [As 2d]. The final board is Ad Kc Ts Th 2c. Both players have two pair, aces and tens, with a king kicker. They split the pot.
• In Holdem, one player has [Ah Ac], a second player has [8s 7s], and a third player has [5s 4h]. The final board is Th 9h 8d 7d 6c. All three players have a straight, ten high. This is called "playing the board". They split the pot three ways.
• In Omaha high/low split, one player has [Ac 3d Th Td] and another player has [As 3s 4c 5d]. The final board is 2c 4d 8s Ts Jc. Remember that in Omaha, each player must play exactly two cards from his hand and three from the board, but can use a different two cards for the high and low halves of the pot. For the high half of the pot, the first player plays [Th Td] for three of a kind, tens, with J-8 kickers, while the second player plays [As 4c] for a pair of fours, A-J-T kickers. The first player wins all of the high half of the pot. For the low half of the pot, the first player plays [Ac 3d] for an 8-4-3-2-A low, while the second player plays [As 3s] for an 8-4-3-2-A low. They have the same hand for low, so they split the low half of the pot. All told, the first player wins three quarters of the pot and the second player wins one quarter.
• In Seven-card Stud, one player has [Ac Ad Tc Td Js 8s 4s] and another player has [As Ah Ts Th 5s 5h Jd]. Both players have two pair, aces and tens, with a jack kicker. You don't consider the sixth or seventh cards. You can see this is pretty unusual for stud and happens mostly with straights.

What about the extra chip? If you split the pot and there is an extra chip left over, the usual rule is to award it to the first winning player in the clockwise direction from the dealer.

What about high-low declare? In high-low split declare games, the rules can be more complicated. See the special high-low declare section for more details.

2.1.3 What should I expect the first time I play poker in a casino or card room? What etiquette should I follow?

Many people are intimidated on their first visit to a public cardroom. Knowing what to expect and some simple rules of etiquette will help the first-time visitor relax and have a good time.

Any cardroom with more than a few tables will have a sign-up desk or board for the various games being played. Usually someone will be standing here to take your name if a seat is not immediately available. This person can explain what games are offered, the betting limits, special house rules and so on. This is the moment of your first decision: which game and for what stakes?

Choosing a game is fairly easy; you already know which game is most familiar to you. You may be surprised to find that your favorite home games are not spread in public cardrooms. Most will offer one or more of Texas Hold'em, Seven-Card Stud, and Omaha Hold'em (usually hi/lo split, 8-or-better for low). Sometimes you will find California Lowball (5-card draw for low), Seven-Card Stud hi/lo, or Hold'em variations like Pineapple. You will rarely find High Draw (5-card draw for hi), and will never find home game pot-builders like Anaconda, Follow-the-Queen, 7-27 or Guts. Except for the joker in draw poker, cardrooms never use wild cards.

Choosing a betting limit is a bit harder. It is best to start playing at a limit so small that the money is not important to you. After all, with all the excitement of your first time playing poker there is no need to be worried about losing the nest egg to a table full of sharks. Betting limits are typically expressed as $1-$5 or $3-$6, and may be "spread-limit" or "structured-limit". A spread-limit means one can bet or raise any amount between the two numbers (although a raise must be at least as much as a previous bet or raise). For example, in $1-$5 spread-limit, if one person bets $2 the next person is free to call the $2 or raise $2, $3, $4, or $5, but cannot raise just $1. On the next round, everything is reset and the first bettor may bet anything from $1 to $5. In structured-limit like $3-$6 (usually recognizable by a factor of two between betting limits), all betting and raising on early rounds is in units of $3, and on later rounds is in units of $6. One only has a choice of *whether* to bet or raise; the amount is fixed by the limit. One usually doesn't have a choice between spread and structured betting at a given limit. Keep in mind that it is quite easy to win or lose 20 "big bets" (the large number in the limit) in an hour of play. Also, since your mind will be occupied with the mechanics of the game while the regular players consider strategy, you are more likely to lose than win. In other words: choose a low limit.

If the game you want is full, your name will go on a list and the person running the list will call you when a seat opens up. Depending on the cardroom, you may have trouble hearing your name called and they may be quick to pass you over, so be alert. Once a seat is available, the list person will vaguely direct you toward it, or toward a floorman who will show you where to sit.

Now is the time for you to take out your money and for the other players to look you over. A good choice for this "buy-in" is ten to twenty big bets, but you must buy-in for at least the posted table minimum, usually about five big bets. Most public poker games are played "table-stakes", which means that you can't reach into your pocket for more money during the play of a hand. It also means that you can't be forced out of a pot because of insufficient funds. If you run out of money during a hand you are still in the pot (the dealer will say you are "all-in"), but further betting is "on the side" for an additional pot you cannot win. Between hands, you are free to buy as many chips as you want, but are not allowed to take any chips off the table unless you are leaving. This final rule gives opponents a chance to win back what they have lost to you. If you bust out, you may buy back in for at least the table minimum or leave.

Once you have told the dealer how much money you are playing, the dealer may sell you chips right away or call over a chip runner to do so. You may want to tell the dealer that you are a first-time player. This is a signal to the dealer to give a little explanation when it is your turn to act, and to the other players to extend you a bit of courtesy when you slow down the game. Everyone will figure it out in a few minutes anyway, so don't be bashful. You may even ask to sit out a few hands just to see how it all works.

There are three ways that pots are seeded with money at the beginning of the hand. The most familiar to the home player is the "ante", where each player tosses a small amount into the pot for the right to be dealt a hand. The second way, often used in conjunction with an ante, is the "forced bring-in". For example, in seven-card stud, after everyone antes and is dealt the first three cards, the player with the lowest upcard may be forced to bet to get things started. The third way, often used in games without upcards like Hold'em or Omaha, is a "forced blind bet". This is similar to the bring-in, but is always made by the person immediately after the player with the "button". The "button" is a plastic disk that moves around the table and indicates which player is acting as dealer for the hand (of course, the house dealer does the actual dealing of cards, but does not play). A second or even third blind may follow the first, usually of increasing size. Whichever seed method is used, note that this initial pot, small as it is, is the only reason to play at all.

If the game has blinds, the dealer may now ask you if you want to "post". This means, "do you want to pay extra to see a hand now, in bad position, and then pay the blinds, or are you willing to sit and watch for a few minutes?" Answer "no, I'll wait" and watch the game until the dealer tells you it's time to begin, usually after the blinds pass you.

Finally, it is your turn to get cards and play. Your first impression will probably be how fast the game seems to move. If you are playing stud, several upcards may be "mucked" (folded into the discards) before you even see them; if you are playing hold'em, it may be your turn to act before you have looked at your cards. After a few hands you should settle into the rhythm and be able to keep up. If you ever get confused, just ask the dealer what is going on.

When playing, consider the following elements of poker etiquette:

Acting in Turn

Although you may see others fold or call out of turn, don't do it yourself. It is considered rude because it gives an unfair advantage to the players before you who have yet to act. This is especially important at the showdown when only three players are left. If players after you are acting out of turn while you decide what to do, say "Time!" to make it clear that you have not yet acted.

Handling Cards

You may find it awkward at first to peek at your own cards without exposing them to others. Note that the other players have no formal obligation to alert you to your clumsiness, although some will. Watch how the other players manage it and emulate them. Leave your cards in sight at all times; holding them in your lap or passing them to your kibitzing friend is grounds for killing your hand. Finally, if you intentionally show your cards to another player during the hand, both your hands may be declared dead. Your neighbor might want to see *you* declared dead :) if this happens!

Protecting Cards

In a game with "pocket cards" like Hold'em or Omaha, it is your responsibility to "protect your own cards". This confusing phrase really means "put a chip on your cards". If your cards are just sitting out in the open, you are subject to two possible disasters. First, the dealer may scoop them up in a blink because to leave one's cards unprotected is a signal that you are folding. Second, another player's cards may happen to touch yours as they fold, disqualifying your hand and your interest in the pot. Along the same lines, when you turn your cards face up at the showdown, be careful not to lose control of your cards. If one of them falls off the table or lands face-down among the discards your hand will be dead, even if that card is not used to make your hand.

Accidentally Checking

In some fast-paced games, a moment of inaction when it is your turn to act may be interpreted as a check. Usually, a verbal declaration or rapping one's hand on the table is required, but many players are impatient and will assume your pause is a check. If you need more than a second to decide what to do, call "Time!" to stop the action. While you decide, don't tap your fingers nervously; that is a clear check signal and will be considered binding.

String Bets

A "string bet" is a bet that initially looks like a call, but then turns out to be a raise. Once your hand has put some chips out, you may not go back to your stack to get more chips and increase the size of your bet, unless you verbally declared the size of your bet at the beginning. If you always declare "call" or "raise" as you bet, you will be immune to this problem. Note that a verbal declaration in turn is binding, so a verbal string bet is possible and also prohibited. That means you cannot say "I call your $5, and raise you another $5!" Once you have said you call, that's it. The rest of the sentence is irrelevant. You can't raise.

Splashing the Pot

In some home games, it is customary to throw chips directly into the pot. In a public cardroom, this is cause for dirty looks, a reprimand from the dealer, and possibly stopping the game to count down the pot. When you bet, place your chips directly in front of you. The dealer will make sure that you have the right number and sweep them into the pot.

One Chip Rule

In some cardrooms, the chip denominations and game stakes are incommensurate. For example, a $3-$6 game might use $1 and $5 chips, instead of the more sensible $3 chip. The one-chip rule says that using a large-denomination chip is just a call, even though the chip may be big enough to cover a raise. If you don't have exact change, it is best to verbally state your action when throwing that large chip into the pot. For example, suppose you are playing in a $1-$5 spread-limit game, the bet is $2 to you, and you have only $5 chips. Silently tossing a $5 chip out means you call the $2 bet. If you want to raise to $4 or $5, you must say so *before* your chip hits the felt. Whatever your action, the dealer will make any required change at the end of the betting round. Don't make change for yourself out of the pot.

Raising Forever

In a game like Hold'em, it is possible to know that you hold "the nuts" and cannot be beaten. If this happens when all the cards are out and you get in a raising war with someone, don't stop! Raise until one of you runs out of chips. If there is the possibility of a tie, the rest of the table may clamor for you to call, since you "obviously" both have the same hand. Ignore the rabble. You'll be surprised how many of your opponents turn out to be bona fide idiots.

The Showdown

Hands end in one of three ways: one person bets and everyone else folds, one person bets on the final round and at least one person calls, or everybody checks on the final round. If everybody folds to a bet, the bettor need not show the winning cards and will usually toss them to the dealer face down. If somebody calls on the end, the person who bet or raised most recently is *supposed* to immediately show, or "open", their cards. They may delay doing so in a rude attempt to induce another player to show their hand in impatience, and then muck their own hand if it is not a winner. Don't do this yourself. Show your hand immediately if you get called. If you have called a bet, wait for the bettor to show, then show your own hand if it's better. If the final round is checked down, in most cardrooms everyone is supposed to open their hands immediately. Sometimes everyone will wait for someone else to show first, resulting in a time-wasting deadlock. Break the chain and show your cards.

Most cardrooms give every player at the table the right to see all cards that called to a showdown, even if they are mucked as losers. (This helps prevent cheating by team-play.) If you are extremely curious about a certain hand, ask the dealer to show it to you. It is considered impolite to constantly ask to see losing cards. It is even more impolite if you hold the winning cards, and in most cardrooms you will forfeit the pot if the "losing" cards turn out to be better than yours.

As a beginner, you may want to show your hand all the time, since you may have overlooked a winning hand. What you gain from one such pot will far outweigh any loss due to revealing how you played a particular losing hand. "Cards speak" at the showdown, meaning that you need not declare the value of your hand. The dealer will look at your cards and decide if you have a winner.

As a final word of caution, it is best to hold on to your winning cards until the dealer pushes you the pot. If the dealer takes your cards and incorrectly "mucks" them, many cardrooms rule that you have no further right to the pot, even if everyone saw your winning cards.

Raking in the Pot

As you win your first pot, the excitement within you will drive you beyond the realm of rational behavior, and you will immediately lunge to scoop up the precious chips with both arms. Despite the fact that no other player had done this while you watched, despite the fact that you read here not to do it, you WILL do it. Since every dealer has a witty admonition prepared for this moment, maybe it's all for the best. But next time, let the dealer push it to you, ok?

Touching Cards or Chips

Don't. Only touch your own cards and chips. Other players' chips and cards, discards, board cards, the pot and everything else are off-limits. Only the dealer touches the cards and pot.

Tipping

Dealers make their living from tips. It is customary for the winner of each pot to tip the dealer 50 cents to a dollar, depending on locale and the stakes. Sometimes you will see players tip several dollars for a big pot or an extremely unlikely suckout. Sometimes you will see players stiff the dealer if the pot was tiny or split between two players. This is a personal issue, but imitating the other players is a good start.

Correcting Mistakes

Occasionally the dealer or a player may make a mistake, such as miscalling the winning hand at the showdown. If you are the victim of such a mistake, call it out immediately and do not let the game proceed. If your opponent is the victim, let your conscience be your guide; many see no ethical dilemma in remaining silent. If you are not involved in the pot, you must judge the texture of the game to determine whether to speak up. In general, the higher the stakes, the more likely you should keep your mouth shut.

Taking a Break

You are free to get up to stretch your legs, visit the restroom and so on. Ask the dealer how long you may be away from your seat; 20 or 30 minutes is typical. It is customary to leave your chips sitting on the table; part of the dealer's job is to keep them safe. If you miss your blind(s) while away, you may have to make them up when you return, or you may be asked to sit out a few more hands until they reach you again. If several players are gone from a table, they may all be called back to keep the game going; those who don't return in time forfeit their seats.

Color Change

If you are in the happy situation of having too many chips, you may request a "color change" (except in Atlantic City). You can fill up a rack or two with your excess chips and will receive a few large denomination chips in return. These large chips are still in play, but at least you aren't inconvenienced by a mountain of chips in front of you. Remember the one chip rule when betting with them.

Leaving

Leave whenever you feel like it. You never have an obligation to stay at the table, even if you've won a fortune. You should definitely leave if you are tired, losing more than you expect, or have other reasons to believe you are not playing your best game. Depending on the cardroom, you can redeem your chips for cash with a chip-runner or floorman or at the cashier's cage.

House Charges

Last but not least is the matter of the house take. Somebody has to maintain the tastefully opulent furnishings and pay the electric bill. The money taken by the house is called the "drop", since it is dropped down a slot in the table at the end of each hand. The house will choose one of three ways to charge you to play.

Time Charge

A simple "time charge" is common in higher limit games and at some small games: seats are rented by the half hour, at rates ranging from $4 to $10 or so, depending on the stakes. This method charges all players equally.

Rake

Other cardrooms will "rake" a percentage of the final pot, up to some maximum, before awarding it to the winning player. The usual rake is either 5% or 10%, capped at $3 or $4. If the pot is raked, the dealer will remove chips from the pot as it grows, setting them aside until the hand is over and they are dropped into a slot in the table. This method favors the tight player who enters few pots but wins a large fraction of them.

Button Charge

A simpler method is to collect a fixed amount at the start of each hand; one player, usually the one with the dealer button, pays the entire amount of the drop. Depending on house rules, this "button charge" of $2-$4 may or may not play as a bet. If the chips do play as a bet, this method also favors the tighter players, but not nearly as much as the rake does.

Regardless of the mechanism, a cardroom will try to drop about $80-$120 per hour at a $3-$6 table. The exact amount is most dependent on the local cost of doing business: Nevada is low, California and Atlantic City are high. Since there are 7-10 players at the table, expect to pay somewhere from $7 to $14 per hour just to sit down. Add $2-$4 per hour for dealer tips and you see why most low-limit players are long-run losers.

More information on cardroom play and etiquette can be found in George Percy's "Seven-Card Stud: The Waiting Game" and Lee Jones' "Winning Low-Limit Holdem". Beginning players may also want to watch for special cardroom promotions to draw new players; many offer free lessons followed by a very low-stakes game with other novices. Since everyone is a beginner, much of the tension is relieved.

Online Poker Etiquette

The Beginners' Guide to Online Poker has a brief section on online poker etiquette.

2.1.4 What is a poker tournament? How does one work? What is a chip race? What is a satellite?

Basics

A poker tournament is an event in which poker players compete for all or part of a prize pool. Each player pays an entry fee and initial buy-in for a set number of tournament chips. The chips are non-negotiable, having no cash value except at the end of the tournament. The contestants play until all but one or a few are busted; the top finishers divide up the prize pool according to the tournament rules. The game's stakes increase with time to hasten the tournament's end.

Variations

Within this framework is considerable room for variation. Many tournaments permit "rebuys", which allow a busted player to reenter the tournament by immediately posting additional money to the prize pool. The number of rebuys may be unlimited, limited to one or a few, or limited to an initial period of the tournament. Rebuys may also be available to players with short stacks or even to all active players. Some tournaments allow an "add-on", a one-time opportunity for all active players to buy a set number of additional chips, again increasing the prize pool. The add-on may be available at the end of the rebuy period, at the beginning of the tournament, or, rarely, at any time during the rebuy period. The exchange rate for rebuys and add-ons may be better than that for the initial buy-in. A tournament with no rebuys is called a "freezeout". The betting structure may be limit only, pot-limit, no-limit, or a mixture, usually limit in the early rounds and no-limit later. Whatever the betting structure, the blinds or betting limits increase regularly, perhaps doubling every twenty minutes in a small tournament, or more slowly in a large one.

The Chip Race

A confusing aspect of the increasing stakes is the way in which some tournaments get rid of the small denomination chips. At some point in the tournament, the dealer may "race off" all the red $5 chips. Each player puts all their red chips in front of them, and the dealer converts them to as many green $25 chips as possible. Whatever red chips remain are raced off: each player receives one card for each chip, and the player receiving the highest card (ace, king, etc) wins everybody's reds and converts them to greens. Bridge suits break ties for the high card (spades, hearts, diamonds, clubs). In other tournaments, the red chips may simply be rounded to green chips. Although rounding can change the total amount of money in play, it is better at preserving the players' relative chip positions.

Some tournaments use a new chip race technique that only awards one chip to the player with the highest card. Then that player is ineligible to receive more chips. If more chips remain, the player having the next highest card receives the next chip and becomes ineligible also, and so on until all chips are distributed.

Winning

The tournament usually continues until only one player remains. The winner may take all the money, or the top finishers may divide it up according to a set schedule. In most tournaments, tables are consolidated and seats redrawn when a certain number of players are eliminated, eventually resulting in a "final table" of contestants. Sometimes, each table plays until only one player remains, and then the survivors meet at a final table; this is called a "shootout". Since the betting stakes are large at the final table and payout schedules often favor first place, luck plays a major role and many players prefer cutting a deal to playing the tournament to its conclusion.

Satellites

A "satellite" is a tournament in which the prize is an entry to another tournament. Large tournaments like the $10,000 No-limit Hold'em event in the World Series of Poker generate a lot of satellites. Typically, the satellite buy-in is around 1/10 the tournament buy-in, so the top 10% of satellite finishers win a tournament buy-in. Sometimes a satellite will even have mini-satellites, in which the prize is an entry to the main satellite. A mini-satellite for the $10,000 event might have a $100 buy-in and award a $1,000 buyin to a satellite that is awarding a $10,000 buy-in to the main event.

A satellite format popular in the larger tournaments is the "super-satellite". This is a multi-table tournament that awards a number of entries into the main tournament. The buy-in to the super can be as little as 2% of the buy-in to the main tournament, with rebuys usually permitted. Depending on the number of entrants and rebuys, the top N finishers receive an entry into the main tournament. The strategy late in a super-satellite can be unusual because of the flat payout structure.

Schedules

Many small (under $100 buy-in) daily or weekly tournaments are listed in the back pages of Card Player magazine. Be sure to call the casino to see if they are having the tournament that day, since the magazine is sometimes out of date.

Tournament Strategy

See the special section on tournament strategy for more information.

Tournament Structures

See Tex's TEARS for widely used poker tournament structures (how the blinds and betting limits go up each round).

Online Tournaments

The Beginners' Guide to Online Poker has a section on online tournaments that explains the most commonly seen variations.

2.1.5 What are some good books about poker?

All thinking poker players should have this book on their shelf:

David Sklansky, "The Theory of Poker" (formerly titled "Winning Poker"), Two Plus Two Publishing, 1992, $30. ISBN 1-880685-00-0.

Beginners will benefit from the following:

Daniel Kimberg, "Serious Poker", ConJelCo, 2002, $20. ISBN: 1-886070-16-4

Lou Krieger and Richard Harroch, "Poker for Dummies", IDG Books Worldwide, 2000, $15. ISBN 0-764552-32-5.

Mason Malmuth and Lynne Loomis, "Fundamentals of Poker", Two Plus Two Publishing, 1992, $4. ISBN 1-880685-11-6.

This classic in the field is an advanced but slightly out-of-date work covering a wide range of games, including an excellent section on no-limit Hold'em:

Doyle Brunson et al., "Super/System: A Course in Poker Power", B & G Publishing, 1978/1989, $50. ISBN 0-931444-01-4.

The most recommended book for medium-limit Hold'em is

David Sklansky and Mason Malmuth, " Hold'em Poker for Advanced Players", Two Plus Two Publishing, 1988/1993, $30. ISBN 1-880685-01-9.

These works by fellow rec.gamblers have received favorable reviews:

Lee Jones, "Winning Low-Limit Holdem", ConJelCo, 1994, $25. ISBN 1-886070-15-6.

Lou Krieger, "Hold'em Excellence", ConJelCo, 2000, $20. ISBN 1-886070-14-8 .

Beginning Seven Card Stud players must read this small spiral-bound gem:

George Percy, "7 Card Stud: The Waiting Game", GBC Press, 1979, $9. ISBN 0-89650-903-6.

More experienced stud players may benefit from

David Sklansky, Mason Malmuth and Ray Zee, " Seven Card Stud for Advanced Players", Two Plus Two Publishing, 1992, $29.95. ISBN 1-880685-02-7.

Finally, in a different vein is the following book about reading your opponents and preventing them from reading you:

Mike Caro, "Caro's Book of Tells - The Body Language of Poker", Mike Caro University Press, 2000, $30 (paperback), $40 (hardback), ISBN 1-880069-01-6 (paperback), ISBN 1-880069-02-4 (hardback).

Many of these books are available to rec.gamblers with an Internet discount from ConJelCo.

Online reviews of poker books. The Online Poker FAQ has brief reviews in its essential poker readling list. See Dan Kimberg's Poker Reading Page for some unsolicited and independent reviews that have appeared on the net. And I don't know where Nick Christenson finds the time to read the dozens of books he has reviewed to date.

Ken's Poker Page has a comprehensive listing of poker-related books.

2.1.6 What are some good magazines about poker?

Card Player is the best established periodical for poker players. Each issue has several columns specifically about poker strategy, including regular features by well-known poker writers. It lists schedules for small daily and weekly tournaments in the U.S. and Europe and reports large tournament results. Other sections cover gambling and the law, cardroom management, sports betting and general gambling news. Because it is financed largely by casino industry advertisements, it does not print unfavorable casino news and is not a good place to find a balanced review of a cardroom. It is available free in most cardrooms and offers subscriptions at first-class and bulk-mail rates.

        The Card Player
        3140 S. Polaris #8
        Las Vegas, NV  89102
        (702) 871-1720
        (702) 871-2674 FAX
        http://www.cardplayer.com
    

All In Magazine is a monthly magazine with original articles on poker strategy, interviews with pro and celebrity players, special coverage of major tournaments and more. They also publish a free email newsletter.

        All In Magazine
        Subscriptions: https://www.allinmagazine.com/subscribe.asp
        More info: http://www.allinmagazine.com
    

Bluff Magazine, first published in October 2004, is a bimonthly glossy with original poker articles, tournament schedules, player rankings and more.

        Bluff Magazine
        5600 Roswell Road
        Suite East 250
        Atlanta, GA 30342
        Subscriptions: email subscriptions@bluffmedia.com
        or call 1-888-881-5861
        http://www.bluffmagazine.com
    

Ken's Poker Page has a comprehensive listing of poker-related magazines.

2.1.7 What are some good poker-related software programs?

Editor's note: Ken's Poker Page has a comprehensive listing of poker-related software. The Beginners' Guide to Online Poker has a special section on online tracking software for yourself and your opponents.

Commercial Programs

There are many poker programs available but the quality of them ranges from terrible to fairly good. The following are worth considering:

• Poki's Poker Academy This is the first commercially available computer program to incorporate both game theory and recent advancements in machine learning. Its use of game theory makes it a challenging heads-up opponent that is not afraid to bluff you with just the right frequency. The machine learning techniques include statistical opponent modeling that help it adapt to your game and exploit your weaknesses. This program is a strong learning tool, especially for heads-up play.
• Wilson Software Turbo Series Separate games are available for Texas Holdem, 7-card stud, Omaha-8 and Omaha High. There are both ring-game and tournament versions. Computer players are driven by large tables describing each decision point. These tables can be modified by the user to create new players. Play against the computer or let the computer players play each other in a fast mode. Check resulting statistics for the various strategies.
• Masque World Series of Poker Adventure Plays Texas Holdem, 7-card stud and Omaha. Also plays blackjack and other casino games. Runs under DOS. This is more of a fun simulation of playing in the World Series at Binions. Play ring games or other casino games to get enough money to enter a satellite. Win the satellite to get into the no-limit finals. Poker opponent play is pretty good, but not exactly World Champion level.
• iPoker Shareware for Macintosh, with nice graphics and GUI.
• Acespade.

Exact Enumeration Calculators

Several people have written software that computes exact showdown probabilities for poker matchups:

• Steve Brecher's Hold'Em Showdown.
• Andrew Prock's Pokerstove.
• Janne Raevaara's Poker Calculator.

Pokersource (Source Code)

If you want to write some of your own poker software, a fast poker hand evaluator is available as part of the Pokersource. package It is in C but uses some Gnu C extensions; it also has a Java interface. You can see it in action at Two Dimes Pokenum, which lets you enter multiple-hand matchups and computes exact win percentages for each hand.

Hotpoker (formerly Netpoker)

Hotpoker is a suite of programs for multi-player hold'em over the internet. C source for Netpoker used to be available; I'm not sure about Hotpoker.

2.1.8 What do all these poker terms mean? Table stakes, no limit, all-in, the nuts, drawing dead, and a thousand more...

Several good poker glossaries are available on the net:

John Hallyburton's compendium, compiled with the help of several rec.gamblers, is the oldest.

Lee Jones' book "Winning Low-Limit Holdem" includes a glossary.

Dan Kimberg's book "Serious Poker" also includes a glossary.

Michael Wiesenberg's incredibly thorough "The Official Dictionary of Poker" is online and is available in print (MGI/Mike Caro University, ISBN: 1880069520).

Bob Ciaffone's "Robert's Rules of Poker" includes a glossary at the very end of the rulebook. This purpose of this glossary is to clarify the meaning of the rules, rather than be a dictionary of poker terms, but it's a useful reference.

2.2 Popular poker games

2.2.1 What are some fun home poker games?

There are enough crazy home game poker variants to fill a book. You can find rules for games ranging from plain to insane at:

• Poker Mike
• Game Report
• Home Poker

Poker variants differ in the amount of skill they admit. Some, like 7-card stud high/low with declare (no qualifier), provide skilled players many opportunities to gain an edge. Others are a virtual crap shoot. In general, the crazier games are designed to discourage folding and minimize the influence of skill on the outcome. They accomplish this through a betting structure that requires a large investment before the value of one's hand is known. The level playing field that results is ideal for many informal social groups.

2.2.2 How do you play Texas Hold'em?

Texas Hold'em is a "community card" game, meaning that some cards are dealt face-up in the middle of the table and shared by all the players. Each player has two down cards that are theirs alone, and combines them with the five community cards to make the best possible five-card hand.

Play begins by dealing two cards face down to each player; these are known as "hole cards" or "pocket cards". This is followed by a round of betting. Most hold'em games get the betting started with one or two "blind bets" to the left of the dealer. These are forced bets which must be made before seeing one's cards. Play proceeds clockwise from the blinds, with each player free to fold, call the blind bet, or raise. Usually the blinds are "live", meaning that they may raise themselves when the action gets back around to them.

Now three cards are dealt face up in the middle of the table; this is called the "flop". A round of betting ensues, with action starting on the first blind, immediately to the dealers left. Another card is dealt face up (the "turn"), followed by another round of betting, again beginning to the dealer's left. Then the final card (the "river") is dealt followed by the final round of betting. In a structured-limit game, the bets on the turn and river are usually double the size of those before and on the flop.

The game is usually played for high only, and each player makes the best five-card combination to compete for the pot. Players usually use both their hole cards to make their best hand, but this is not required. A player may even choose to "play the board" and use no hole cards at all. Identical five-card hands split the pot; the sixth and seventh cards are not used to break ties. For a more detailed explanation of ties, see the section on splitting the pot.

2.2.3 How do you play Omaha?

The rules of Omaha are very similar to those of Texas Hold'em. There are only two differences:

• Each player receives four hole cards, instead of two.
• One must use *exactly* three community cards and two hole cards to make one's hand.

The second difference is confusing for most beginners. These examples show how it works.

    Board        Hole Cards     Best High Hand
    =====        ==========     ==============
As Kc Qc 8d 2d   Ac 2c Jd Th    Jd Th makes ace-hi straight.
As Kc Qc Jh Td   Ac 2c Jd 8h    Ac Jd makes ace-hi straight.
As Kc Qc Jh Td   3c 2c Jd 8h    Jd 8h makes pair of jacks.  No straight
                                is possible using two hole cards.
As Ks 8h 9d 2s   Qs 4h 4d 4s    Qs 4s makes AKQ42 "nut" flush.
As Ks 8s 9s 2s   Qs 4h 4d Qd    Qs Qd makes pair of queens.  No flush is
                                possible using two hole cards.
As Ts 8s 8h 4d   Td Tc Ad 9c    Td Tc makes TTT88 full house.
As Ts 8s 8h 4d   Td 8c Ad 9c    Ad 8c makes 888AA full house.
As Ac 8s 8h 4d   Ah 2h 3h 5h    Ah 5h makes trip aces AAA85.  No full
                                house is possible using two hole cards.
As Ac 8s 8h 4d   Ah 2h 3h 4h    Ah 4h makes full house AAA44.

Omaha is often played high/low, meaning that the highest and lowest hands split the pot. The low hand usually must "qualify" by being at least an 8-low (the largest card must be 8 or lower). One can use a different two cards to compete for the high and low portions of the pot, and the game is played "cards speak" rather than "declare". Aces are either low or high, and straights and flushes don't count for low. Since everybody must use two hole cards to make a hand, the board must have three cards 8 or lower for a low to even be possible. Players often tie for low, and the low half of the pot is divided equally among them. Some more examples:

    Board        Hole Cards     Best Low Hand
    =====        ==========     =============
As Kc Qc 8d 2d   8c Jc Jd Th    Jd Th makes the low hand JT82A, which
                                does not qualify as 8-or-better.
3d 5h 8d Tc Ts   Ac 2c Jd Th    Ac 2c makes the "nut low" 8532A.
3d 5h 8d Tc Ts   Ac 3c 4d Th    Ac 4d makes 8543A.
3d 5h 8d Ad Ts   Ac 3c 5d 8h    Any two make T853A, not qualifying.
Ac 2c 3d 4h 5s   Ad 2d Th Td    Ad 2d makes "nut low" 5432A.
Ac 2c 3d 4h 5s   4d 5d Th Td    4d 5d makes "nut low" 5432A.
5h 7h 8d Ac 2c   Ad 2d Th Td    Ad 2d makes 8752A, but the nut low is
                                5432A with a 3 and 4.  On the flop we
                                had the best possible low, but the turn
                                and river "counterfeited" us.

As in all split-pot games, the real goal of playing any hand is to win both halves of the pot, or "scoop". Thus, hands that have a chance to win both ways are far superior to those that can only win one way.

For more details on how to handle ties, see the section on splitting the pot.

2.2.4 How do you play Chowaha?

Wolf's poker page has a nice graphical display explaining how to play Chowaha, the popular BARGE game.

2.2.5 How do you play no-limit seven-card stud? What is Mississippi Stud?

It isn't practical to play classic seven-card stud with no-limit betting, but here is a game called mississippi seven card stud, which can. Deal the start cards as for conventional seven-card stud, two down, one up; then deal each active player two more upcards, then a fourth upcard, then a fifth upcard. In other words deal the cards 3-2-1-1 instead of 3-1-1-1-(1).

Mississippi is more suited to half-pot, pot-limit and no-limit betting than seven-card stud for two reasons: The four round structure is less crippling financially than five rounds, and the fact that only two hole cards out of seven are concealed means that hands as small as trips of the biggest card showing can be the absolute nuts at the end. Similarly, a straight or flush is the absolute nuts if none of your opponents have paired their board, and aren't showing three cards to a possible (bigger) straight or flush. In seven-card stud (with it's third hole-card) trips, straights and flushes can never be the nuts at the end because your opponent could have quads or a full house without showing a pair, or a (bigger) straight or flush if they have two cards to a straight or flush showing.

Mississippi also plays well as a limit game. It's faster and more active than seven-card stud because the two card individual flop not only speeds up the game, it is better value than taking the cards one at a time, and you get more callers at every round on average as a result. Mississippi can be dealt with the last card down for limit betting if you prefer it that way.

If you like mississippi, the layout also works very well with an extra hole-card, a form called murrumbidgee stud: the deal is the same as mississippi except everyone gets three hole-cards to start: only two of the hole cards can be used at the end. Hands like (3s,Kc,Ac)3c, have a lot of ways to improve: you'll make the flush 20% of the time by the end, and there are eight cards which give you at least kings up. (9s,Jc,Qc)10c will make either a straight or a flush over 40% of the time by the end, and if you flop Ko,8c or Kc, 8o, you have a twenty-three way straight and flush draw. A king or an eight on the flop, plus one club, gives you a twenty way straight and flush draw. There is plenty of action in murrumbidgee, making it an excellent short-handed game: it can be dealt for up to six players at time.

Disclosure: the writer invented mississippi in mid 1998 and murrumbidgee in early 1999.

2.3 More advanced topics

2.3.1 What are the betting and raising rules in No Limit?

For more by this author, visit pokercheckraise.com and Poker Gamer (at BlogSpot).

The initial call in No Limit poker must be at least as big as the big blind. For example, if you are playing in a No Limit game and the small blind is $5 and the big blind is $10 then you must call at least $10 to call the big blind. If you don't have enough chips to cover the big blind ($10 in our example) then you are eligible only to win the chips that you have matched in the pot.

In order to raise in No Limit the amount of chips that you wish to raise by must be at least as large as the last raise in the same round. In our $5-10 game that means if you are the first to enter the pot in order to raise you must put in $20. Since the big blind is $10 and you wish to raise then you must put in at least $20 (The $10 big blind is considered the raise that you must match).

If someone has already raised before you then your raise must be at least as large as his/her raise. This is not to be confused with the need to match the last bet with your raise. For example, if the blinds are $5-10 and player A sends in a bet of $50 he is raising by $40. If player B wishes to raise he/she must raise by at least $40 (total bet of $90). Many players and even dealers make the mistake of thinking that player B must raise by $50 (total bet of $100) thinking that player B must match the last bet. This is incorrect as the player need only match the raise ($40 in our example).

Now let us consider when a player has gone all in with a partial raise. Other players may not reraise on a player's all in raise unless (a) it is a full raise or (b) they have not yet acted since the most recent full bet or raise. This is complicated so let's use an example.

Suppose we have players A, B, and C in a game where the blinds are $5-10. Player A opens with a raise to $50 total chips (he matches the $10 blinds and raises by $40). Player B reraises all in for a total of $70 total chips (he calls the bet of $50 plus raises $20 more). Player C cold calls the $70. Player A can not reraise since Player B did not put in a legal raise. Player B raised by only $20 when he needed to match a raise of $40. Note that Player C could have raised if he desired, since he had not yet acted in response to the original bet.

Now let us consider an example of when player A could reraise. Again we have players A, B, and C with the blinds at $5-10. Player A raises to a total of $40 chips (he matches the blind of $10 and raises by $30). Player B pushes all in with $70 (calls the $40 and raises by $30). Player C then cold calls. Player A can reraise as much as he wants because Player B has made a legal raise. Player B has matched the original raise amount of $30.

[See this article for rules on pot-limit betting, including examples.]

2.3.2 What does pot-limit mean?

This is an explanation of bet size limits in pot limit poker.

In pot limit, as in all poker, you may fold, or call the previous bet -- which may be a forced blind, if there is no previous voluntary bet -- or you may raise. A raise, as in all poker, must be at least as large as the previous bet or raise. In pot limit, however, your raise may be no larger than the size of the pot after your call. If you are the opening bettor on a round for which no blinds are made, your bet can be no more than the size of the pot.

Say that the pot contains p units before a previous bettor bets (or blinds) b units. You wish to raise the maximum. What is the total amount that you should bet?

The size of the pot when it is your turn to act is p+b. Your action includes a call, making the pot p+2b, and thus the amount of your raise will be p+2b and your total bet will be p+3b. Therefore:

If you wish to raise the previous bettor (or big blind) the maximum amount, your total bet will be three times the previous bet plus the size of the pot before the previous bet was made. If you are the first to act on the first round, the size of the pot before the previous bet is the total of the small blind(s), and the previous bet is the big blind.

Sometimes the minimum betting unit is larger than the size of one or more blinds. E.g., it may be that only $5 chips play for betting, but one or more blinds are smaller than $5. In this case, the maximum initial bring-in is rounded to the betting unit.

Some people state the general rule that the maximum initial bring-in is "four times the big blind." This is correct only if the total of the small blinds, after rounding if appropriate, is equal to the big blind, and this is not always the case. E.g., in a tournament when the blinds are $100 and $200, the maximum bring-in is $700, not $800. The correct rule is "three times the big blind plus the total of the small blinds, rounded as appropriate."

Examples:

• 1, 2, and 5 blinds. 3 times 5 = 15; 15 + 1 + 2 = 18. Assuming that the minimum betting unit is 5, the maximum initial bring-in would be 18 rounded up to become 20 -- a raise of 15.
• With 1, 2, and 5 blinds, someone brings it in for 10. The maximum bet of the next to act would be 3 times 10 = 30, plus the total blinds of 7, rounded up to 40 -- a raise of 30.
• The pot contains, say, 1 unit. Suppose each successive bettor wishes to raise the maximum; how fast will the bets increase?

  size of pot before                   3 x previous bet
  previous bet         previous bet   + size of pot before
                                        previous bet
                                         = next bet
       1                   -                 1
       1                   1                 4
       2                   4                14
       6                  14                48
      20                  48               164
      68                 164               560
     232                 560              1912

So, if the initial pot size were $100, the seventh maniacal raiser would be making a total bet of $191,200. The action can escalate quickly.

2.3.3 What does half-pot-limit mean?

In half-pot betting the maximum bet is half of whatever is in the pot. In a head-to-head contest, HP pots and bets double with each additional bet or raise, so four bets or raises increase the pot by a factor of 2 x 2 x 2 x 2, or sixteen times. Pot-sized bets triple the pot, giving 3 x 3 x 3 x 3 or eighty-one times the original pot after four bets or raises, in a head-to-head contest.

Half-pot is the smallest of the big-bet games, and like its big brothers pot-limit and no-limit, it provides plenty of scope for using position and well timed bluffs to win with inferior hands, and the pot builds quickly when you are betting for value. At the same time the more moderate bet sizes mean that half-pot games last much longer than pot-limit or no-limit games with a given amount of money available. Half-pot games are much easier to keep alive than pot-limit and no-limit games, and this alone makes them worthy of consideration as a big-bet option.

Half-pot, like limit-betting, is a game which provides reasonable odds for a call -- 3/1 in a head to head contest, as opposed to 2/1 in pot-limit -- and as a result there is more action and multi-way pots than in pot-limit and no-limit. Because half-pot is a big-bet game, bets and bluffs do not decrease in effect as the hand progresses, as they do in limit, where a final round bet can be as little as two or three percent of the pot. In effect, half-pot combines the best features of pot-limit/no-limit, and limit-betting: it has multi-way action, favorable pot-odds and reasonable bankroll longevity, like limit-betting, and it's also an excellent bluffing form in which pots and bets build quickly, like PL and NL.

Here is a chart comparing half-pot and pot-limit pot sizes and bets in a 50-100 (cents or dollars, depending on your BR) game of holdem. In this example the opener raises, and then bets at every round, and one player (other than either of the blinds) calls at every round, and then raises and is called at the end. The pot size at the start of each round includes all bets and calls for the preceding round, so the pot at the start of the second round in the half-pot column is 150 (blinds) + 100 + 125 (call and raise) + 225 (call) = 600.

   Half-pot                                  Pot-limit
Start:  call 100, raise 125                       call 100, raise 250
Flop:   pot 600, bet 300                          pot 850, bet 850
Turn:   pot 1200, bet 600                         pot 2550, bet 2550 
River:  pot 2400, bet 1200                        pot 7650, bet 7650
        raise 2400, final pot 9600                raise 22,950, final pot 68,850

The rapid escalation of the bets means that a hand of PL in which there is serious action at every round of play is something of a rarity, because players with average bankrolls tap out after three or four bets. Four rounds of action, even multi-way action, is common in half-pot play.

Pot-limit is good, but half-pot lasts longer.

While it is perfectly understandable that some players will always prefer pot-limit to half-pot -- and if bankroll conditions and the players are right I like it myself -- I believe it is a mistake to dismiss half-pot as a big-bet game. A half-pot game can survive for years in a situation where a pot-limit game would quickly break many of the available players and revert to limit-betting. The situation in the USA and Canada -- where pot-limit games can be hard to find -- is a reflection of this tendency of limit games to push out pot-limit. Players who prefer big-bet poker but who spend most of their time playing limit because the pot-limit game folded again, (or because their own bankroll can't handle the big swings) might consider half-pot betting as an alternative, if not to pot-limit, at least to limit-betting.

2.3.4 What is a kill pot? What is a game with a kill? What is a half kill?

Big bet (no-limit or pot-limit) poker frequently allows a player to "kill the pot", by posting an amount equal to current to-go amount, and the amount to-go (to come into the hand, or call preflop) is now double the kill amount. In no-limit games, players are frequently allowed to kill for more than the to-go amount, but for no more than 1/2 of their stack. Some games allow overkills - after someone has killed the pot, someone else can kill it again, raising the amount to-go to double the new kill amount. There may be a limit to the number of kills allowed on a hand, even though the game is "no-limit". Killing the pot alters the order of action preflop/predraw. The killers act after the blinds in the order in which they killed the pot. After the flop or draw, action returns to its normal order.

To kill the pot in Hold'em or other flop games, the kill must be announced (either verbally or by placing the amount of the kill in the pot) before any cards are dealt. Draw lowball games frequently allow players to kill the after seeing two cards - and some places even allow a kill in lowball after the 3rd card is dealt. No-limit draw lowball also frequently allows the player with the big blind to place a blind which is larger than the normal amount, but still smaller than the to-go amount, and the new to-go amount is twice the big blind.

Example: In a 1-2-2, 5-to-go Hold'em game, the player on the button (who also has the $1 blind) decides to kill it for $5, rebuying his right to act last before the flop. The blinds now look like 5-2-2, and the game is now 10-to-go. After the player to the right of the button acts, the two $2 blinds act, then the killer acts.

Example: In a draw-lowball game, 1-1-2 blinds, 4-to-go, the player with the big blind puts out $3 before cards are dealt and it is now 6-to-go. After two cards are dealt, the player to the right of the button kills the pot for $10, and it is now 20-to-go. The player after the blinds is first to act. After the player in front of the killer acts, the button and other blinds must act, and then the killer acts.

Limit lowball games also frequently allow a player to kill the pot from any position. In this case, the killer makes a blind of the current limit, and the limit is doubled for that hand. As in no-limit games, the player who kills the pot acts last after the blinds before the draw, and action resumes to the normal order after the draw.

In addition, some limit games are played with a kill or a half kill. In these games, there is some condition which if met, raises the stakes of the game - doubling them in the case of a kill game, or increasing them by 50% in the case of a half kill. In addition to the normal blinds posted for the game, the player who met the kill condition must post a blind equal to the new small bet size. This blind is instead of the small or big blind if the player would have been in position to have one of those. In some clubs the killer gets to act last after the blinds; but in others the killer acts in normal turn order.

In a high only game, the condition is typically that someone wins two pots in a row. In a high-low split game, the condition is usually that someone takes the whole pot, and that the pot is some minimum size.

For example: in a 10-20 Omaha-8 game with a half kill that I've played in, if someone scoops a pot with $100 in it, then they must post a $15 blind and the next hand the game is 15-30.

2.3.5 What is a straddle bet?

In limit Hold'em and other flop games players are frequently allowed to make a bet called a straddle bet, sometimes known as a live blind, live raise, or live-<amount> where <amount> is the amount of the bet. The player who follows the big blind and would normally be under the gun can raise before cards before cards are dealt. Players that act after him must call the raise, fold, or raise the bet themselves. The straddler's raise is live - if no-one else raises, s/he has the option to reraise after the blinds have acted. If straddle bets are allowed, the player behind the straddler can also post a straddle by raising again, and so on until the maximum number of bets is reached.

For example: In a 6-12 game, the blinds are 3 and 6, the player after the small blind makes it live-12 by raising before the cards are dealt, and the player after him can make it live-18.

2.3.6 What is Hi-Lo declare? What if someone declares both ways but ties?

Hi-Lo declare is a popular variation in home games that can be applied to any game that can be played hi-lo. The betting proceeds normally to the end of the hand, then everyone still in the hand declares whether they are going high, low, or both ways.

There are many variations to the rules, so it is best to make sure that the rules used in your game are announced in advance and that everyone agrees to them.

There are several ways that the hand can be declared. One of the most popular is to declare simultaneously with chips. Each player secretly conceals chips in their hand; then at the same time all players open their hands to reveal their declaration. Common systems for chip declare include using number of chips (for instance, no chips means low, one chip means high, two chips means both ways), or using color of chips (for instance white chips in hand mean low, red chips mean high, both colors mean both ways). Another way of declaring is for the players to announce aloud in turn (either from dealer's left, from the high showing hand, or from the last bettor depending on what's been agreed upon in advance). This latter form of declare obviously has a huge positional advantage for the player who gets to declare last.

After the declare, there may be another betting round, depending on the house rules. If there is an additional betting round, a "lock" bettor may be allowed to bet or raise, or may be required only to check and call depending on the house variation being used. A "lock" bettor is a player who declares one way and no-one else declares that way.

After the declare and optional betting round is the showdown. At the showdown, the best high hand (of the hands that have been declared as going high) and the best low hand (of the hands that declared low) split the pot. If everyone has declared the same way, then the whole pot is awarded to the best hand that way. If more than one player has they same best hand in the way they've declared they split that share of the pot.

If someone declares "both ways" (also called a "hogger"), things get more complicated. If the "both ways" player has the best high and the best low hand, then they win the whole pot. If they are beat in either direction, however, they win none of the pot. What happens if they have the best high but are beat low, or have the best low but are beat high is a matter of house rules (and can be a matter of great dispute if the players have not agreed beforehand). In some houses if a player declares both ways and has the best high hand but is beat low, the second best high hand is allowed to win the high share of the pot (the same reasoning applies if the both ways declarer has the best low but is beat high). In other houses, if a player declares both ways and has the best high but is beat low, then no-one wins the high, and the entire pot is awarded to the best low hand.

Another important variation in the rules to know about for declaring both ways is whether a both ways declarer is allowed to tie on either side. In some houses, the both ways declarer must win both sides free and clear, or get none of the pot. For instance if player A declares both ways, and player B declares high, and they both have the same straight, then player A gets nothing. Other houses allow the both ways declarer to get shares if the pot if they tie on one side (as long as they win or tie on the other as well). For instance if Player A declares both ways, and player B declares high, and they both have they same straight, then A would get 3/4 of the pot (all of low and half of high), and B would get 1/4 (half of the high).

It leads to the least complications in extremely rare situations if "second best" hands are allowed to win if a both ways declarer is beat in the other direction. If second best hands are not allowed to win, then situations can arise where no-one is eligible for a share of the pot and a long argument is likely to ensue. For instance Players A, B, C and D declare hi, low, both and both respectively. Player C has the best high hand, but player D has the best low hand, if "second best" hands are not allowed a share of the pot, then no-one is allowed to win. If "second best" hands are allowed to win, then player A wins high, and player B wins low. If "second best" hands are not allowed to win in your game, it's probably best to have a house rule to allow them to win in the case where no-one would otherwise be eligible for any of the pot.

In the case where all players have declared both ways, but no-one wins both ways, it's best to treat it as if the hand had been played without declare, and the best high hand and the best low hand are allowed to split the pot.

Hi-Lo Declare Examples

Here are some showdown clarifications for Hi-Lo Declare under different rule sets. For illustration purposes, the game used will be 7 card stud (so that there can be ties on either the high or low sides), but the concepts apply to any game that can be played Hi-Lo.

Rule variation #1 - "Both ways" must win free and clear (cannot tie), and 2nd best hands cannot win. This is probably the most popular rule set used, but needs some extra rules to settle unusual situations.

Rule variation #2 - "Both ways" hands are allowed to tie, and 2nd best hands are allowed to win if they are only beat by hands that are otherwise ineligible to win. This is the most liberal set of rules, and is almost always clear about how the pot is divided. Even this needs clarification if everyone declares both ways.

Rule variation #3 - "Both ways" must win free and clear, but 2nd best hands are allowed to win. This set is included because at least one home game is currently known to use it.

In the cases where no-one is eligible to win, an extra rule needs to be invoked to handle the situation (the pot rides to the next hand, second best hand is allowed to win, both ways allowed to win just one way, etc.)

+-------------------------+----------------+----------------+----------------+
| Declaration and hands:  | Variation #1   | Variation #2   | Variation #3   |
+-------------------------+----------------+----------------+----------------+
| A: high with KQJT9      | A gets 1/2 the pot for high                      |
| B: low with an 8532A    | B gets 1/2 the pot for low                       |
+-------------------------+----------------+----------------+----------------+
| A: high with KQJT9      | A gets 1/2 the pot for high                      |
| B: low with an 7532A    | B gets 1/2 the pot for low                       |
| C: both ways with 76543 |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: low with an 7532A    | A wins the whole pot                             |
| B: both ways with 76543 |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with three 9s   | B wins the whole pot                             |
| B: both ways with 76543 |                                                  |
| C: low with 8532A       |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with flush      | A gets 1/2 the pot for high                      |
| B: both ways with 76543 | C gets 1/2 the pot for low                       |
| C: low with 6542A       |                                                  |
+-------------------------+----------------+----------------+----------------+
| A: high with three 9s   | C wins the pot | A gets 1/2 pot | A gets 1/2 pot |
| B: both ways with 76543 |                | C gets 1/2 pot | C gets 1/2 pot |
| C: low with 6 low       |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: high with 98765      | A wins the pot | A gets 1/4 pot | A gets 1/2 pot |
| B: high with 98765      |                | B gets 3/4 pot | C gets 1/2 pot |
|     and low with 7653A  |                |                |                |
| C: low with 76542       |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | A gets 1/2 pot | C wins the pot |
| B: both ways with 76543 |                | B gets 1/2 pot |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | B wins the pot | A gets 3/4 pot | B wins the pot |
| B: high with 76543      |                | B gets 1/4 pot |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | B wins the pot | A gets 3/4 pot | B gets 1/2 pot |
| B: low with 76543       |                | B gets 1/4 pot | C gets 1/2 pot |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | A gets 1/2 pot | none eligible* |
| B: both ways with 76543 |                | B gets 1/2 pot |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | B wins the pot | none eligible* |
| B: both ways with flush |                |                |                |
|      and 76543          |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | B wins the pot | C wins the pot |
| B: both ways with flush |                |                |                |
|      and 76543          |                |                |                |
| C: high with KKJJ9      |                |                |                |
+-------------------------+----------------+----------------+----------------+
| A: both ways with 76543 | none eligible* | none eligible* | none eligible* |
| B: both ways with flush |                |                |                |
|      and 8543A          |                |                |                |
+-------------------------+----------------+----------------+----------------+

In summary, Hi-Lo declare is popular and can add fun and variety to your home game, but arguments are best avoided by clarifying the particular house rules and unusual situations in advance.

2.3.7 What is a burn card and why is it dealt?

A burn card is a card dealt face down at the beginning of a round, before any other cards are dealt. This card is not used in the play of the hand. The main reason for this custom is to guard against marked cards. If the cards are marked, a player who can read the backs will know what the top card on the deck is. In a flop-game like Hold'em or Omaha, knowledge of the next board card is extremely profitable. Knowledge of which card it will *not* be is slightly useful, but much less so.

2.3.8 What happens if there aren't enough cards in the deck to deal the final card in 7-card stud?

The burn cards will be shuffled into the remaining deck. If there are still not enough cards, a single community card will be dealt face-up and used by all the players.

2.4 Odds and probabilities

2.4.1 Why are poker hands ranked the way they are?

The standard poker hands are ranked based on the probability of their being dealt pat in 5 cards from a full 52-card deck. The following table lists the hands in order of increasing frequency, and shows how many ways each hand can be dealt in 3, 5, and 7 cards.

Hand                  3 cards           5 cards           7 cards
====                  =======           =======           =======
Straight Flush             48                40            41,584
Four of a Kind              0               624           224,848
Full House                  0             3,744         3,473,184
Flush                   1,096             5,108         4,047,644
Straight                  720            10,200         6,180,020
Three of a Kind            52            54,912         6,461,620
Two Pair                    0           123,552        31,433,400
One Pair                3,744         1,098,240        58,627,800
High Card              16,440         1,302,540        23,294,460
=================================================================
TOTALS                 22,100         2,598,960       133,784,560

Notes:

1. The standard rankings are incorrect for 3-card hands, since it is easier to get a flush than a straight, and easier to get a straight than three of a kind. See the entry on three-card rankings.

2. For 7-card hands, the numbers reflect the best possible 5-card hand out of the 7 cards. For instance, a hand that contains both a straight and three of a kind is counted as a straight.

3. For 7-card hands, only five cards need be in sequence to make a straight, or of the same suit to make a flush. In a 3-card hand a sequence of three is considered a straight, and three of the same suit a flush. These rules reflect standard poker practice.

4. In a 7-card hand, it is easier for one's *best* 5 cards to have one or two pair than no pair. (Good bar bet opportunity!) However, if we changed the ranking to value no pairs above two pairs, all of the one pair hands and most of the two pair hands would be able to qualify for "no pair" by choosing a different set of five cards.

5. Within each type of hand (e.g., among all flushes) the hands are ranked according to an arbitrary scheme, unrelated to probability. See the explanation of flush and two-pair rankings.

2.4.2 What is the correct ranking for 3-card poker hands?

The standard ranking of poker hands is based on their frequency of occurrence in a five card hand. In three card hands the relative frequency of hands is different, so different in fact that three of a kind beats a straight, and a straight beats a flush.

The following is a break down of all three card poker hands. They can be used for certain three card games, such as Guts or 3-card-6. They can also be used to analyze starting hands for games like 7-Card Stud.

Hand Type      Kinds   Each   Total     Cuml   Rating
---------      -----   ----   -----     ----   ------
straight flush   12      4       48       48   0.9978
trips            13      4       52      100   0.9955
straight         12     60      720      820   0.9629
flush  **       274      4     1096     1916   0.9133
pair  ***       156     24     3744     5660   0.7439
Ace high         64     60     3840     9500   0.5701
King high        54     60     3240    12740   0.4235
Queen high       44     60     2640    15380   0.3041
Jack high        35     60     2100    17480   0.2090
Ten high         27     60     1620    19100   0.1357
Nine high        20     60     1200    20300   0.0814
Eight high       14     60      840    21140   0.0434
Seven high        9     60      540    21680   0.0190
Six high          5     60      300    21980   0.0054
Five high         2     60      120    22100   0.0000


** More on Flushes           
------------------           
High Card       Kinds Percent  Total    Cuml   Rating
---------       ----- -------  -----    ----   ------
Ace high         64    23.4     256     1076   0.9513
King high        54    19.7     216     1292   0.9415
Queen high       44    16.1     176     1468   0.9336
Jack high        35    12.8     140     1608   0.9272
Ten high         27     9.9     108     1716   0.9224
Nine high        20     7.3      80     1796   0.9187
Eight high       14     5.1      56     1852   0.9162
Seven high        9     3.3      36     1888   0.9146
Six high          5     1.8      20     1908   0.9137
Five high         2     0.7       8     1916   0.9133


*** More on Pairs
-----------------
Hand Type      Kinds   Each    Total    Cuml   Rating
---------      -----   ----    -----    ----   ------
   AAx           12     24      288     2204   0.9003
   KKx           12     24      288     2492   0.8872
   QQx           12     24      288     2780   0.8742
   JJx           12     24      288     3068   0.8612
   TTx           12     24      288     3356   0.8481
   99x           12     24      288     3644   0.8351
   88x           12     24      288     3932   0.8221
   77x           12     24      288     4220   0.8090
   66x           12     24      288     4508   0.7960
   55x           12     24      288     4796   0.7830
   44x           12     24      288     5084   0.7700
   33x           12     24      288     5372   0.7569
   22x           12     24      288     5660   0.7439

In the preceding tables, "Kinds" refers to the number of card combinations in each class, while "Each" is the number of non-distinct hands of each Kind. The product of these two numbers gives the total number of hands in that class. "Cuml" is the cumulative total of all hands, and "Rating" is a percentile ranking of the lowest hand in the class.

Note that "Rating" is only an estimate of the probability of beating a random hand. To compute the exact probability, a given hand must be compared to the (49 choose 3) combinations of the remaining cards in the deck.

2.4.3 Why are ace-hi flushes ranked highest, when it's much harder to get a seven-hi flush? And similarly for two pairs?

[Michael Maurer's original answer:] Only the classes themselves (flush, straight, etc) are ranked by the probability of getting them in five cards. Within each class we use an arbitrary system to rank hands of the same type. For example, our arbitrary system ranks four aces higher than four deuces, even though the hands occur with the same frequency. Similarly, flushes are ranked by the highest card, with the next highest card breaking ties, and so on down to the fifth card. This has the curious effect of creating many more ace-hi flushes than any other kind, because any flush that contains an ace is "ace-hi", regardless of the other cards. Thus, although 490 of the 1277 flushes in each suit contain a seven, only four of them are seven-hi flushes: 76542, 76532, 76432, and 75432. The median flush turns out to be KJT42.

A similar situation occurs for two pair hands. There are twelve times as many ways to make two pair with aces being the high pair ("aces up") as there are to do it with threes as the high pair ("threes up"). While the aces can go with another other rank of pair, the threes must go with twos, or we would reverse the order and call them, for instance, "eights up". Note that it is fruitless to alter the relative rankings to try to account for this imbalance, since as soon as we do the cards will be reinterpreted to make the best hand under the new system. For example, if we decide to make "threes up" the best possible two pair hand, now all the hands like "eights and threes" will be interpreted as "threes and eights", and the population of "threes up" hands will soar twelve-fold. The median two pair hand turns out to be a tie between JJ552 and JJ44A.

[Giancarlo DiPierro suggests a fresh interpretation:] You've figured it out. Flushes are not correctly ranked according to their mathematical probability. The ranking of flushes and no-pair hands by the highest card (hence the term "high-card" for no-pair hands) that is commonly used around the world today is an arbitrary system that likely dates back to when someone first started betting on poker hands.

The correct way to rank these hands according to how hard they are be dealt becomes clear if you have ever played lowball or any high-low split game. In those games, low hands are ranked by the worst card, not the best card. Any 6-high low hand is ranked higher than any 7-high low hand because a 6-high is dealt three times less frequently than a 7-high. It doesn't matter if the lowest card in the 7-high hand is an ace and the lowest card in the 6-high hand is only a deuce, the 6-high wins.

Applying that principle to flushes and no-pair hands in high poker, a 9-low hand is dealt about three times less frequently than an 8-low and about seven times less frequently than a 7-low. So the 9-low should ranked higher, even if the 7-low contains an ace and the 9-low does not. In any situation where unpaired cards are determining the ranking of