Hand scores

The backbone of the game is that each poker hand has its own point value, as given in this table:

One pair – 1 point.
Two pair – 2 points.
Three of a kind – 3 points.
Straight – 4 points.
Flush – 5 points.
Full House – 6 points.
Four of a kind – 7 points (but see Variations below).
Straight flush – 8 points (but see Variations below).

Basic rules

Chicago is played with a standard 52-card deck. Each player is dealt five cards. The objective is to reach 52 points.

Exchanges and hand scoring

The players are allowed to exchange any number of their cards. If a player chooses to exchange one card only, he may choose “one up”, meaning that he is dealt one card faced up, which he can either accept, or instead take the next card unseen. After the exchanges, the player with the best hand (and only one player) gets points for his hand. Then follows another round of exchanges, but no hand scoring.

The game

Now, the first player begins by playing one card. Ordinary whist rules apply, but the players keep their cards collected by themselves. The player who wins the last trick gets 5 points. Also, the player with the best hand (whether it is the same player or not) gets points for his hand.

Chicago

After the second exchange, any player can choose to play Chicago. In this case, he pledges himself to win all the tricks of the game. If he does, he is awarded 15 points, but if he fails, the penalty is just as harsh: -15 points.

Variations

• Sometimes, a player given five cards below ten (either inclusive or exclusive) is allowed to replace them before the exchanges begin.
• Some play with 3 exchanges instead of 2. Then of course, scoring for hands will be made after both the first and the second exchange.
• Some do not use the “one up” rule.
• Often, one wants to give higher rewards than 7 or 8 points for Four of a kind and Straight flush respectively. There are several ways to achieve this, most notably by elevating the player immediately to 52 points, or lowering either all players or one player of the holder’s choice to 0 points, or a combination of these. Holding a Royal flush usually means immediate victory.
• The confusion is great as to what scores are appointed in the case of Chicago. Some will argue that no player will get any points at all besides the +15 or -15, whilst others will allow almost any points. The +5 for the game, however, can never be stacked with the +15 for Chicago.
• Some prescribe that any player with 45 points or more is not allowed to replace any cards.
• Some require that after (and not in the same hand as) a player reaches 52 points, he must win the game once more before he actually wins. This handles the possibility that more than one player reach 52 points in the same hand.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

WinHoldEm is an online Texas hold ‘em bot, created by Ray Bornert. Bots of this kind can sometimes be used in online poker play, but this is considered cheating by poker rooms, and grounds for account termination. The bot is loaded, and will play in lieu of a real human, calculating pot odds and making betting decisions based on these calculations. There is no way to accurately estimate the extent to which these bots are used.

The bot works through installing client software on your machine which interfaces with the poker room, i.e. it is able to read what cards have been dealt, what bets have been made, etc. The bot’s ‘intelligence’ ends there. Whether the bot wins, or no

Links

• Official site
• Wired 13.09 article with Bornert interview

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Rules

• The game is played with a standard 52 card deck.
• Each player makes an ante bet of 1 unit and may make an optional bonus bet.
• The player and dealer are both delt 2 cards (face down).
• After checking his/her cards, the player may decide to fold with no further play losing the ante bet or make a flop bet of 2 units.
• 3 cards are then dealt to the board.
• The player may decide to check or make a turn bet of 1 unit.
• Another card is dealt to the board (making 4 cards in total on the board).
• The player may decide to check to make a river bet of 1 unit.
• One more card is dealt to the board(making 5 in total).
• The player and dealer make their best 5 card poker hand from their own hand and 5 board cards.

• If the dealer’s hand is better than the player’s hand the player loses all bets.
• If the dealer’s hand is equal to the player’s hand, all bets are a push.
• If the player’s hand is better than the dealer’s hand, the player wins even money on the flop, turn and river bets. The player also wins even money on the ante bet if his best hand is a straight or better, otherwise the ante bet pushes.
• If a players hole cards are a pair, A-K, A-Q, or A-J, the player wins the bonus bet according to the paytable. This bet pays even if the player does not beat the dealers hand.

Player Strategy

The optimal strategy for the flop bet is to call all hands except for 2-3 offsuit, 2-4 offsuit, 2-5 offsuit, 2-6 offsuit and 2-7 offsuit.

Because of the large number and variety of combinations, it is impossible to list a basic strategy for the turn and river bets.

Links

• Mikohn Gaming official site
• Wizard of Odds detailed analysis
• Optimal Strategy Calculator

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

There is a way to compute the Skalansky Malmuth table for those people who have trouble memorizing. The results are almost identical to those generated using the Chen Point Count.^[1] To compute the point count the following formula should apply:

1. Take the high card and score it. A=10,K=8,Q=7,J=6,T-2 = 1/2 value shown.
2. If the 2nd card pairs the first the value is either twice the high card point or 5 which ever is greater.
3. If they are not paired then calculate the gap for the lower card and subtract off a gap penalty:.
   1. For a 0 gapper subtract 0,
   2. For a 1 gapper subtract 1
   3. For a 2 gapper subtract 2
   4. For a 3 gapper subtract 4
   5. For a 4 gapper or more subtract 5 (includes A2,A3,A4).
4. If the cards are of the same suit apply a flush bonus of +2 pts.
5. If the cards are a 0 or 1 gap and the top card is a J or lower apply a +1 straight bonus
6. Round 1/2 point up

Then 12 – Chen Point Count in general is the SM hand grouping. Examples:

• 8♣ 8♠: 4 pts for the first 8, double for the pair is 8 Chen points. This puts it in S&M group 4.
• 9♣ 7♣: 4.5 points for the 9, -1 for the 1 gapper, +2 for the same suit and +1 for the straight bonus. Round up to 7 Chen points which is in S&M group 5.

The following hands are the exceptions (off by 1): 55, AQs, A9, AX, 96s, 32s, 98, 97, 76.

Notes

1. ^ Lou Krieger, Hold’em Excellence, ch Power Rating ISBN 1886070148

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

David Sklansky and Mason Malmuth ^[1] assigned each hand to a group, and proposed all hands in the group could normally be played similarly. Stronger starting hands are identified by a lower number. Hands without a number are the weakest starting hands.

• Note: Unsuited on the bottom left, suited on the top right.

Chen Point Count

There is a way to compute the Skalansky Malmuth table for those people who have trouble memorizing. The results are almost identical to those generated using the Chen Point Count.^[2] To compute the point count the following formula should apply:

1. Take the high card and score it. A=10,K=8,Q=7,J=6,T-2 = 1/2 value shown.
2. If the 2nd card pairs the first the value is either twice the high card point or 5 which ever is greater.
3. If they are not paired then calculate the gap for the lower card and subtract off a gap penalty:.
   1. For a 0 gapper subtract 0,
   2. For a 1 gapper subtract 1
   3. For a 2 gapper subtract 2
   4. For a 3 gapper subtract 4
   5. For a 4 gapper or more subtract 5 (includes A2,A3,A4).
4. If the cards are of the same suit apply a flush bonus of +2 pts.
5. If the cards are a 0 or 1 gap and the top card is a J or lower apply a +1 straight bonus
6. Round 1/2 point up

Then 12 – Chen Point Count in general is the SM hand grouping. Examples:

• 8♣ 8♠: 4 pts for the first 8, double for the pair is 8 Chen points. This puts it in S&M group 4.
• 9♣ 7♣: 4.5 points for the 9, -1 for the 1 gapper, +2 for the same suit and +1 for the straight bonus. Round up to 7 Chen points which is in S&M group 5.

The following hands are the exceptions (off by 1): 55, AQs, A9, AX, 96s, 32s, 98, 97, 76.

Notes

1. ^ David Sklansky and Mason Malmuth (1999). Hold ‘em Poker for Advanced Players. Two Plus Two Publications. ISBN 1880685221
2. ^ Lou Krieger, Hold’em Excellence, ch Power Rating ISBN 1886070148

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

One can replace any round of (or add a round to) a stud poker game with a twist round, in which each player is offered the option to replace exactly one card in his hand with a new one from the remaining deck stub. This is similar to the draw phase of draw poker, differing in the following way: if the player chooses to replace a downcard, he discards it and is dealt a replacement card also face down; if he wishes to replace an upcard, he discards it and receives the replacement face up. On a twist round, players make the decision of which card to replace in turn starting with the player who bet first on the preceding round (usually the player whose upcards make the best hand), discarding the card they choose to replace, if any. After everyone has made their decision, the replacement cards are dealt starting at the dealer’s left as usual.

Sometimes replacement cards are “bought” by requiring a player to add a fixed amount to the pot to be able to get a replacement.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

• Pairs, (or “pocket pairs”), which consist of two cards of the same rank (e.g. 9♠9♣). One hand in 17 will be a pair, each occurring with individual probability 1/221 (P(pair) = 3/51 = 1/17).

• Suited hands, which contain two cards of the same suit (e.g. A♠6♠). Four hands out of 17 will be suited, and each suited configuration occurs with probability 2/663 (P(suited) = 12/51 = 4/17).

• Offsuit hands, which contain two cards of different suit and rank (e.g. K♠J♥). Twelve out of 17 hands will be nonpair, offsuit hands, each of which occurs with probability 2/221 (P(offsuit non-pair) = 3*(13-1)/51 = 12/17).

It is typical to abbreviate suited hands in hold ‘em by affixing an “s” to the hand, as well as to abbreviate non-suited hands with an “o” (for offsuit). That is,

QQ represents any pair of queens,

AK (or, sometimes, AKo) represents any ace and king of different suits, and

JTs represents any jack and ten of the same suit.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

In the poker game Texas hold ‘em, a player’s hand consists of two hole cards, which belong solely to the player and remain hidden from the other players. Five community cards are also dealt into play. Betting begins before any of the community cards are exposed, and continues throughout the hand.

The player’s “playing hand”, which will be compared against that of each competing player, is the best 5-card poker hand available from his two hole cards and the five community cards.

Unless otherwise specified, here the term hand applies to the player’s two hole cards, or starting hand.

Links

• Percentage of Pots Won with Hold’em Hands Ranked by Percent
• More Detailed look at Starting Hand Statistics
• Essay discussing the different hand groups
• Texas Hold’em Poker

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Common outs

Drawing to a flush is an example of drawing from a common set of outs. Both the turn and river need to be the same suit, so both outs are coming from a common set of outs—the set of remaining cards of the desired suit. After the flop, if x is the number of common outs, the probability P of drawing runner-runner outs is

P = (x/47) x ((x – 1)/46).

Since a flush would have 10 outs, the probability of a runner-runner flush draw is (10/47) x (9/46) = (90/2162) ~ 0.04163. Other examples of runner-runner draws from a common set of outs are drawing to three or four of a kind. When counting outs, it is convenient to convert runner-runner outs to “normal” outs. A runner-runner flush draw is about the equivalent of one “normal” out.

The following table shows the probability and odds of making a runner-runner from a common set of outs and the equivalent normal outs.

Likely drawing to	Common outs	Probability	Odds	Equivalent outs
Four of a kind (with pair) Inside-only straight flush	2	0.00093	1080 : 1	0.02
Three of a kind (with no pair)	3	0.00278	359 : 1	0.07
	4	0.00556	179 : 1	0.13
	5	0.00925	107 : 1	0.22
Two pair or three of a kind (with no pair)	6	0.01388	71.1 : 1	0.33
	7	0.01943	50.5 : 1	0.46
	8	0.02590	37.6 : 1	0.61
	9	0.03330	29.0 : 1	0.78
Flush	10	0.04163	23.0 : 1	0.98

Disjoint outs

Two outs are disjoint when there are no common cards between the set of cards needed for the first out and the set of cards needed for the second out. The outs are independent of each other if it does not matter which card comes first, and one card appearing does not affect the probability of the other card appearing except by changing the number of remaining cards; an example is drawing two cards to an inside straight. The outs are conditional on each other if the number of outs available for the second card depends on the first card; an example is drawing two cards to an outside straight.

After the flop, if x is the number of independent outs for one card and y is the number of outs for the second card, then the probability P of making the runner-runner is

P = (x/47) x (y/46) x 2 = (xy/1081).

For example, a player holding J♦ Q♦ after the flop 9♥ 5♣ 6♠ needs a 10 and either a K or 8 on the turn and river to make a straight. There are 4 10s and 8 kings and 8s, so the probability is (4×8)/1081 ~ 0.0296.

The probability of making a conditional runner-runner depends on the condition. For example, a player holding 9♥ 10♥ after the flop 8♦ 2♠ A♣ can make a straight with {J, Q}, {7, J} or {6, 7}. The number of outs for the second card is conditional on the first card—a Q or 6 (8 cards) on the first card leaves only 4 outs (J or 7, respectively) for the second card, while a J or 7 (8 cards) for the first card leaves 8 outs ({Q, 7} or {J, 6}, respectively) for the second card. The probability P of a runner-runner straight for this hand is calculated by the equation

P = ((8/47) x (4/46)) + ((8/47) x (8/46)) = 96/2162 ~ 0.0444.

The following table shows the probability and odds of making a runner-runner from a disjoint set of outs for common situations and the equivalent normal outs.

Drawing to	Probability	Odds	Equivalent outs
Outside straight	0.04440	21.5 : 1	1.04
Inside+outside straight	0.02960	32.8 : 1	0.70
Inside-only straight	0.01480	66.6 : 1	0.35
Outside straight flush	0.00278	359 : 1	0.07
Inside+outside straight flush	0.00185	540 : 1	0.04

The preceding table assumes the following definitions.

Outside straight and straight flush

Drawing to a sequence of three cards of consecutive rank from 3-4-5 to 10-J-Q where two cards can be added to either end of the sequence to make a straight or straight flush.

Inside+outside straight and straight flush

Drawing to a straight or straight flush where one required rank can be combined with one of two other ranks to make the hand. This includes sequences like 5-7-8 which requires a 6 plus either a 4 or 9 as well as the sequences J-Q-K, which requires a 10 plus either a 9 or A, and 2-3-4 which requires a 5 plus either an A or 6.

Inside-only straight and straight flush

Drawing to a straight or straight flush where there are only two ranks that make the hand. This includes hands such as 5-7-9 which requires a 6 and an 8 as well as A-2-3 which requires a 4 and a 5.

Compound outs

The strongest runner-runner probabilities lie with hands that are drawing to multiple hands with different runner-runner combinations. These include hands that can make a straight, flush or straight flush, as well as four of a kind or a full house. Calculating these probabilities requires adding the compound probabilities for the various outs, taking care to account for any shared hands. For example, if P_s is the probability of a runner-runner straight, P_f is the probability of a runner-runner flush, and P_sf is the probability of a runner-runner straight flush, then the compound probability P of getting one of these hands is

P = P_s + P_f − P_sf.

The probability of the straight flush is subtracted from the total because it is already included in both the probability of a straight and the probability of a flush, so it has been added twice and must therefore be subtracted from the compound outs of a straight or flush.

The following table gives the compound probability and odds of making a runner-runner for common situations and the equivalent normal outs.

Drawing to	Probability	Odds	Equivalent outs
Flush, outside straight or straight flush	0.08326	11.0 : 1	1.98
Flush, inside+outside straight or straight flush	0.06938	13.4 : 1	1.65
Flush, inside-only straight or straight flush	0.05550	17.0 : 1	1.30

Some hands have even more runner-runner chances to improve. For example, holding the hand J♠ Q♠ after a flop of 10♠ J♥ 7♦ there are several runner-runner hands to make at least a straight. The hand can get two cards from the common outs of {J, Q} (5 cards) to make a full house or four of a kind, can get a J (2 cards) plus either a 7 or 10 (6 cards) to make a full house from these independent disjoint outs, and is drawing to the compound outs of a flush, outside straight or straight flush. The hand can also make {7, 7} or {10, 10} (each drawing from 3 common outs) to make a full house, although this will make four of a kind for anyone holding the remaining 7 or 10 or a bigger full house for anyone holding an overpair. Working from the probabilities from the previous tables and equations, the probability P of making one of these runner-runner hands is a compound probability

P = 0.08326 + 0.00925 + (2×6)/1081 + (0.00278 x 2) ~ 0.1092

and odds of 8.16 : 1 for the equivalent of 2.59 normal outs. Almost all of these runner-runners give a winning hand against an opponent who had flopped a straight holding 8, 9^[3], but only some give a winning hand against A♠ 2♠ (this hand makes bigger flushes when a flush is hit) or against K♣ Q♦ (this hand makes bigger straights when a straight is hit with 8 9). When counting outs, it is necessary to adjust for which outs are likely to give a winning hand—this is where the skill in poker becomes more important than being able to calculate the probabilities.

Notes

1. ^{^} In the example, if the opponent is holding either 8♥ 9♥ or 8♦ 9♦, then the opponent wins with a flush if the player makes a straight using two hearts or two diamonds, respectively. If the opponent is holding 8♦ 9♦, then the opponent wins with a straight flush if the player makes a full house with 10♦ J♦.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

The sample deal below assumes that a game is being played by four players: Alice, who is dealing in the examples; Bob, who is sitting to her left; Carol to his left; and David to Carol’s left.

All players ante $.25. Alice deals each player two downcards and one upcard, beginning with Bob and ending with herself. Bob is dealt the 4♠, Carol the K♦, David the 4♦, and Alice the 9♣. Because they are playing with a $1 bring-in, David is required to start the betting with a $1 bring-in (his 4♦ is lower than Bob’s 4♠ by suit). He had the option to open the betting for more, but he chose to bet only the required $1. The bring-in sets the current bet amount to $1, so Alice cannot check. She decides to call. Bob folds, indicating this by turning his upcard face down and discarding his cards. Carol raises to $3. David folds, and Alice calls.

Alice now deals a second face-up card to each remaining player: Carol is dealt the J♣, and Alice the K♥. Alice’s two upcards make a poker hand of no pair, K-9-high, and Carol has K-J-high, so it is Carol’s turn to bet. She checks, as does Alice, ending the betting round. Another face up card is dealt: Carol gets the T♥, (T = 10) and Alice gets the K♣. Alice now has a pair of kings showing, and Carol still has no pair, so Alice bets first. She bets $5, and Carol calls. On the next round, Carol receives the T♦, making her upcards K-J-T-T. Alice receives the 3♠. Alice’s upcards are 9-K-K-3; the pair of kings is still higher than Carol’s pair of tens, so she bets $5 and Carol calls. Each player now receives a downcard. It is still Alice’s turn to bet because the downcard did not change either hand. She checks, Carol bets $10, and Alice calls.

That closes the last betting round, and both players remain, so there is a showdown. Alice shows her cards: 9♥ 5♦ 9♣ K♥ K♣ 3♠ 5♠. The best five-card poker hand she can play is K-K-9-9-5, making two pair, kings and nines. Carol shows Q♠ 2♥ K♦ J♣ T♥ T♦ A♦. She can play A-K-Q-J-T, making an ace-high straight, and so Carol wins the pot.

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.