Pineapple hold ‘em exists halfway between Texas hold ‘em and Omaha hold ‘em. Players are initially dealt three cards. Each player then discards one of the three cards, and the game proceeds exactly as in Texas hold ‘em. In Crazy Pineapple, the players discard their third card after the flop betting round, before the fourth community card is dealt. In Tahoe, players keep all three cards through showdown, but may not use all three of them to make a hand. Each player may use none, one, or two cards from his hand, combined with those on the board, to make his final five-card hand.
Crazy Pineapple and Tahoe are usually played high-low split.
Chinese poker is a card game that has been played in the Asian community for many years. It has begun to gain popularity in the broader world of game players because it has all the features of a good gambling game:
It is easy to learn.
Anyone who knows the rank of Poker hands can begin playing after a few minutes of instruction.
There is a large element of luck, so that a beginner has a real chance of winning, even against experienced opponents. Also, it is plausible for poor players to attribute bad results to their cards rather than their plays.
There is still enough skill in the game that experts have a significant advantage when playing poor players.
Although it is basically a four player game, it can be played with 2 or 3 players. It is fun to play. Unexpected results and interesting hands are common.
Playing a Hand
In Chinese Poker, each player receives a 13 card hand from a standard 52 card deck. He then has to divide his cards into three Poker hands, two containing five cards each and one three card hand. The only restriction is that both five card hands must outrank the three card hand (Note: straights and flushes do not count in the three card hand). The higher ranking of the five card hands, called the Back hand, is placed face down on the table in front of the player. Then the other five card hand, called the Middle hand, is placed face down in front of the Back hand. Finally, the three card hand, called the Front hand, is placed (again face down) in front of the middle hand. When all four players have set their hands, the cards are turned face up and the deal is scored.
Variant
The game can be played with the middle hand being low, rather than high.
Scoring
The basic scoring rule is that comparisons are done head-to-head and that a player wins one unit for each hand (of the three) which outranks the corresponding hand of each opponent. Thus, unlike most poker games, being second-best at the table is good enough to win money. Also, due to the head-to-head nature of the comparisons, it’s possible for different players to play for different stakes. For example, A and B could play for $10/unit, while all other pairs play for $1/unit. Many variations of scoring are in common use. Refer to the external links for more information.
The poker game called Chicago is one of the most popular card games in Sweden today. Relying on the keeping of score instead of the placing of bets, it is suitable even for environments such as schools, where gambling is often prohibited. The game exists in countless versions, so here a (somewhat arbitrarily chosen) basic game will be followed by a number of possible variations.
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.
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
Texas Hold’em Bonus Poker is a gambling card game is owned and licensed by Mikohn Gaming/Progressive Gaming International Corporation. The game is based on traditional multi-player Texas Hold’em poker.
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.
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.
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:
Take the high card and score it. A=10,K=8,Q=7,J=6,T-2 = 1/2 value shown.
If the 2nd card pairs the first the value is either twice the high card point or 5 which ever is greater.
If they are not paired then calculate the gap for the lower card and subtract off a gap penalty:.
For a 0 gapper subtract 0,
For a 1 gapper subtract 1
For a 2 gapper subtract 2
For a 3 gapper subtract 4
For a 4 gapper or more subtract 5 (includes A2,A3,A4).
If the cards are of the same suit apply a flush bonus of +2 pts.
If the cards are a 0 or 1 gap and the top card is a J or lower apply a +1 straight bonus
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
^ Lou Krieger, Hold’em Excellence, ch Power Rating ISBN 1886070148
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.
Pre-Flop Basic Strategy
A
K
Q
J
T
A
3
3
7
7
8
8
8
8
8
8
K
3
7
7
7
Q
3
4
3
8
J
3
4
4
3
T
4
7
8
7
6
9
8
7
3
6
8
8
4
6
7
4
6
6
5
8
5
5
4
5
3
5
2
5
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:
Take the high card and score it. A=10,K=8,Q=7,J=6,T-2 = 1/2 value shown.
If the 2nd card pairs the first the value is either twice the high card point or 5 which ever is greater.
If they are not paired then calculate the gap for the lower card and subtract off a gap penalty:.
For a 0 gapper subtract 0,
For a 1 gapper subtract 1
For a 2 gapper subtract 2
For a 3 gapper subtract 4
For a 4 gapper or more subtract 5 (includes A2,A3,A4).
If the cards are of the same suit apply a flush bonus of +2 pts.
If the cards are a 0 or 1 gap and the top card is a J or lower apply a +1 straight bonus
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
^ David Sklansky and Mason Malmuth (1999). Hold ‘em Poker for Advanced Players. Two Plus Two Publications. ISBN 1880685221
^ Lou Krieger, Hold’em Excellence, ch Power Rating ISBN 1886070148
Twist is poker jargon for a round with specific rules which is sometimes used in the poker variant stud poker.
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.
There are (52 × 51)/2 = 1,326 distinct possible combinations of two hole cards from a standard 52-card deck in hold ‘em, but since suits have no relative value in poker, many of these hands are identical in value before the flop. For example, A♣J♣ and A♥J♥ are identical, because each is a hand consisting of an ace and a jack of the same suit. There are 169 nonequivalent starting hands in hold ‘em (13 pocket pairs, 13 × 12 / 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 13 × 13 = 169). These 169 hands are not equally likely. Hold ‘em hands are sometimes classified as having one of three “shapes”:
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
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.
Some outs for a hand require drawing an out on both the turn and the river—making two consecutive outs is called a runner-runner. Examples would be needing two cards to make a straight, flush, or three or four of a kind. Runner-runner outs can either draw from a common set of outs or from disjoint sets of outs. Two disjoint outs can either be conditional or independent events.
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
.00093
080 : 1
.02
Three of a kind (with no pair)
.00278
59 : 1
.07
.00556
79 : 1
.13
.00925
07 : 1
.22
Two pair or three of a kind (with no pair)
.01388
1.1 : 1
.33
.01943
0.5 : 1
.46
.02590
7.6 : 1
.61
.03330
9.0 : 1
.78
Flush
0
.04163
3.0 : 1
.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 0 and either a K or 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}, {
, J} or {
,
}. The number of outs for the second card is conditional on the first card—a Q or
(8 cards) on the first card leaves only 4 outs (J or
, respectively) for the second card, while a J or
(8 cards) for the first card leaves 8 outs ({Q,
} or {J,
}, 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
.04440
1.5 : 1
.04
Inside+outside straight
.02960
2.8 : 1
.70
Inside-only straight
.01480
6.6 : 1
.35
Outside straight flush
.00278
59 : 1
.07
Inside+outside straight flush
.00185
40 : 1
.04
The preceding table assumes the following definitions.
Outside straight and straight flush
Drawing to a sequence of three cards of consecutive rank from
-4-5 to 0-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 -7-8 which requires a plus either a or as well as the sequences J-Q-K, which requires a 0 plus either a or A, and -3-4 which requires a plus either an A or .
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 -7-9 which requires a and an as well as A-2-3 which requires a and a .
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 Ps is the probability of a runner-runner straight, Pf is the probability of a runner-runner flush, and Psf is the probability of a runner-runner straight flush, then the compound probability P of getting one of these hands is
P = Ps + Pf − Psf.
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
.08326
1.0 : 1
.98
Flush, inside+outside straight or straight flush
.06938
3.4 : 1
.65
Flush, inside-only straight or straight flush
.05550
7.0 : 1
.30
Some hands have even more runner-runner chances to improve. For example, holding the hand J♠ Q♠ after a flop of 0♠ 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
or 0 (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 {
,
} or {0, 0} (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 , [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 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
^ 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♦.
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 ♠, Carol the K♦, David the ♦, and Alice the ♣. Because they are playing with a $1 bring-in, David is required to start the betting with a $1 bring-in (his ♦ is lower than Bob’s ♠ 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 ♠. 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.
During play—that is, from the flop and onwards—drawing probabilities come down to a question of outs. All situations which have the same number of outs have the same probability of winning. For example, an inside straight draw (e.g. 34 67 missing the 5 for a straight), and a full house draw (e.g. 66KK drawing for one of the pairs to become three-of-a-kind) are equivalent. Each can be satisfied by four cards—four 5s in the first case, and the other two 6s and other two kings in the second.
The probabilities of drawing these outs are easily calculated. At the flop there remain 47 unseen cards, so the probability is (outs ÷ 47). At the turn there are 46 unseen cards so the probability is (outs ÷ 46). The cumulative probability of making a hand on either the turn or river can be determined as the complement of the odds of not making the hand on the turn and not on the river. The probability of not drawing an out is (47 − outs) ÷ 47 on the turn and (46 − outs) ÷ 46 on the river; taking the complement of these conditional probabilities gives the probability of drawing the out by the river which is calculated by the formula
P = 1 – (((47 – outs)/47) x ((46-outs)/46))
For reference, the probability and odds for some of the more common numbers of outs are given here.
Likely drawing to
Outs
Make on turn
Make on river
Make on turn or river
Prob.
Odds
Prob.
Odds
Prob.
Odds
Inside straight flush; Four of a kind
1
0.0213
46.0 : 1
0.0217
45.0 : 1
0.0426
22.5 : 1
Open-ended straight flush; Three of a kind
2
0.0426
22.5 : 1
0.0435
22.0 : 1
0.0842
10.9 : 1
High pair
3
0.0638
14.7 : 1
0.0652
14.3 : 1
0.1249
7.01 : 1
Inside straight; Full house
4
0.0851
10.8 : 1
0.0870
10.5 : 1
0.1647
5.07 : 1
Three of a kind or two pair
5
0.1064
8.40 : 1
0.1087
8.20 : 1
0.2035
3.91 : 1
Either pair
6
0.1277
6.83 : 1
0.1304
6.67 : 1
0.2414
3.14 : 1
Full house or four of a kind; (see note)
Inside straight or high pair
7
0.1489
5.71 : 1
0.1522
5.57 : 1
0.2784
2.59 : 1
Open-ended straight
8
0.1702
4.88 : 1
0.1739
4.75 : 1
0.3145
2.18 : 1
Flush
9
0.1915
4.22 : 1
0.1957
4.11 : 1
0.3497
1.86 : 1
Inside straight or pair
10
0.2128
3.70 : 1
0.2174
3.60 : 1
0.3839
1.60 : 1
Open-ended straight or high pair
11
0.2340
3.27 : 1
0.2391
3.18 : 1
0.4172
1.40 : 1
Inside straight or flush; Flush or high pair
12
0.2553
2.92 : 1
0.2609
2.83 : 1
0.4496
1.22 : 1
13
0.2766
2.62 : 1
0.2826
2.54 : 1
0.4810
1.08 : 1
Open-ended straight or pair
14
0.2979
2.36 : 1
0.3043
2.29 : 1
0.5116
0.955 : 1
Open-ended straight or flush; Flush or pair;
Inside straight, flush or top pair
15
0.3191
2.13 : 1
0.3261
2.07 : 1
0.5412
0.848 : 1
16
0.3404
1.94 : 1
0.3478
1.88 : 1
0.5698
0.755 : 1
17
0.3617
1.76 : 1
0.3696
1.71 : 1
0.5976
0.673 : 1
Inside straight or flush or pair;
Open-ended straight, flush or high pair
18
0.3830
1.61 : 1
0.3913
1.56 : 1
0.6244
0.601 : 1
19
0.4043
1.47 : 1
0.4130
1.42 : 1
0.6503
0.538 : 1
20
0.4255
1.35 : 1
0.4348
1.30 : 1
0.6753
0.481 : 1
Open-ended straight, flush or pair
21
0.4468
1.24 : 1
0.4565
1.19 : 1
0.6994
0.430 : 1
Note: When drawing to a full house or four of a kind with a pocket pair that has hit trips (three of a kind) on the flop, there are 6 outs to get a full house by pairing the board and one out to make four of a kind. This means that if the turn does not pair the board or make four of a kind, there will be 3 additional outs on the river, for a total of 10, to pair the turn card and make a full house. This makes the probability of drawing to a full house or four of a kind on the turn or river 0.334 and the odds are 1.99 : 1. This makes drawing to a full house or four of a kind by the river about 8½ outs.
It is worth noting in the preceding table that if a player doesn’t fold before the river, a hand with at least 14 outs after the flop has a better than 50% chance to catch one of its outs by the river. With 20 or more outs, a hand is a better than 2 : 1 favorite to catch at least one out by the river.
The game begins with each player being dealt two cards face down and one card face up. If played with a bring-in, the player with the lowest-ranking upcard pays the bring-in, and betting proceeds after that in normal clockwise order. The bring-in is considered an open, so the next player in turn may not check. If two players have equally ranked low cards, suit may be used to break the tie and assign the bring-in. If there is no bring-in, then the first betting round begins with the player showing the highest-ranking upcard, who may check. In this case, suit should not be used to break ties. If two players have the same high upcard, the one first in clockwise rotation from the dealer acts first.
After the first betting round, another upcard is dealt to each player (after a burn card, and starting at the dealer’s left as will all subsequent rounds), followed by a second betting round beginning with the player whose upcards make the best poker hand. Since fewer than five cards are face up, this means no straights, flushes, or full houses will count for this purpose. On this and all subsequent betting rounds, the player whose face-up cards make the best poker hand will act first, and may check or bet up to the game’s limit.
The second round is followed by a third upcard and betting round, a fourth upcard and betting round, and finally a downcard, a fifth betting round, and showdown if necessary. Seven-card stud can be summarized therefore as “two down, four up, one down”. Upon showdown, each player makes the best five-card poker hand he can out of the seven cards he was dealt.
You may note that seven cards to eight players plus four burn cards makes 60 cards, and there are only 52 in the deck. In most games this is not a problem because several players will have folded in early betting rounds. But there are certainly low-stakes home games where few if any players fold. If this is the case in your game, you may want to limit the game to seven players. If the deck does become exhausted during play, previously-dealt burn cards can be used when only a few cards are needed to complete the deal. If even those are not sufficient, then on the final round instead of dealing a downcard to each player, a single community card is dealt to the center of the table, and is shared by everyone (that is, each player treats it as his seventh card). Under no circumstances can any discarded card from a folded hand be “recycled” for later use. Unlike draw poker, where no cards are ever seen before showdown, stud poker players use the information they get from face-up cards to make strategic decisions, and so a player who sees a certain card folded is entitled to make decisions knowing that the card will never appear in another opponent’s hand.
It is useful to look at the chances different starting hands have of either improving on the flop, or of weakening on the flop. One interesting circumstance concerns pocket pairs. When holding a pocket pair, overcards (cards of higher rank than the pair) weaken the hand because of the potential that an overcard has paired a card in an opponent’s hand. The hand gets worse the more overcards there are on the board and the more opponents that are in the hand because the probability that one of the overcards has paired a hole card increases. To calculate the probability of no overcard, take the total number of outcomes without an overcard divided by the total number of outcomes.
Where x is the rank 3–K of the pocket pair (assigning values from 3–10 and J–K = 11–13), then the number of overcards is (14 – x) x 4 and the number of cards of rank x of less is 0 – (14-x) x 4 = 4x – 6. The number of outcomes without an overcard is the number of combinations that can be formed with the remaining cards, so the probability P of an overcard on the flop is
P = ((4x-6)/3)/(50/3),
and on the turn and river are
P = ((4x-6)/4)/(50/4) and P = ((4x-6)/5)/(50/5), respectively.
The following table gives the probability that no overcards will come on the flop, turn and river, for each of the pocket pairs from to K.
Holding pocket pair
Overcard on flop
Overcard by turn
Overcard by river
Prob.
Odds
Prob.
Odds
Prob.
Odds
KK
0.7745
0.29 : 1
0.7086
0.41 : 1
0.6470
0.55 : 1
QQ
0.5857
0.71 : 1
0.4860
1.06 : 1
0.4015
1.49 : 1
JJ
0.4304
1.32 : 1
0.3205
2.12 : 1
0.2369
3.22 : 1
TT
0.3053
2.28 : 1
0.2014
3.97 : 1
0.1313
6.61 : 1
99
0.2071
3.83 : 1
0.1190
7.40 : 1
0.0673
13.87 : 1
88
0.1327
6.54 : 1
0.0649
14.40 : 1
0.0310
31.21 : 1
77
0.0786
11.73 : 1
0.0318
30.48 : 1
0.0124
79.46 : 1
66
0.0416
23.02 : 1
0.0133
74.26 : 1
0.0040
246.29 : 1
55
0.0186
52.85 : 1
0.0043
229.07 : 1
0.0009
1057.32 : 1
44
0.0061
162.33 : 1
0.0009
1095.67 : 1
0.0001
8406.78 : 1
33
0.0010
979.00 : 1
0.0001
15352.33 : 1
0.0000
353125.67 : 1
Notice that there is a better than 35% probability that an ace will come by the river if holding pocket kings, and with pocket queens, the odds are slightly in favor of an ace or a king coming by the turn, and a full 60% in favor of an overcard to the queen by the river. With pocket jacks, there’s only a 43% chance that an overcard won’t come on the flop and it’s better than 3:1 that an overcard will come by the river.
Seven-card stud is a variant of stud poker. Until the recent increase in popularity of Texas hold ‘em, seven-card stud was the most popular poker variant in home games across the United States, and in casinos in the eastern part of the country. Seven-card stud is also played in western American casinos, but Texas hold ‘em is far more popular there. Two to eight players can play.
The descriptions below assume that you are familiar with the general game play of poker, and with hand values. They also make no assumptions about what poker betting structure is used. In casino play, it is common to use a small ante and bring-in. In home games, it is typical to use an ante only.
Quick play overview
Play proceeds as follows (“player” refers only to those who have not folded and are still in the game), with betting rounds in-between.
Betting is clockwise, the player with the highest poker hand showing starts (ie 2-2 beats K-Q).
2 cards dealt face down to each player, 1 card dealt face up
The value of a starting hand can change dramatically after the flop. Regardless of initial strength, any hand can flop the nuts—for example, if the flop comes with three 2s, any hand holding the fourth 2 has the nuts. Conversely, the flop can undermine the perceived strength of any hand—A♣A♥ would not be happy to see
♠ 9♠ 10♠ on the flop because of the straight and flush possibilities.
There are
(50/3) = 19,600
possible flops for any given starting hand. By the turn the total number of combinations has increased to
(50/4) = 230,300
and on the river there are
(50/5) = 2,118,760
possible boards to go with the hand.
The following are some general probabilities about what can occur on the board. These assume a “random” starting hand for the player.
Board consisting of
Making on flop
Making by turn
Making by river
Prob.
Odds
Prob.
Odds
Prob.
Odds
Three or more of same suit
0.05177
18.3 : 1
0.13522
6.40 : 1
0.23589
3.24 : 1
Four or more of same suit
0.01056
93.7 : 1
0.03394
28.5 : 1
Rainbow flop (all different suits)
0.39765
1.51 : 1
0.10550
8.48 : 1
Three cards of consecutive rank (but not four consecutive)
0.03475
27.8 : 1
0.11820
7.46 : 1
0.25068
2.99 : 1
Four cards to a straight (but not five)
0.03877
24.8 : 1
0.18991
4.27 : 1
Three or more cards of consecutive rank and same suit
0.00217
459 : 1
0.00869
114 : 1
0.02172
45.0 : 1
Three of a kind (but not a full house or four of a kind)
0.00235
424 : 1
0.00935
106 : 1
0.02128
46 : 1
A pair (but not two pair or three or four of a kind)
0.16941
4.90 : 1
0.30417
2.29 : 1
0.42450
1.36 : 1
Two pair (but not a full house)
0.01037
95.4 : 1
0.04716
20.2 : 1
An interesting fact to note from the table above is that more than 60% of the flops will have at least two of the same suit—you’re likely to either be drawing to a flush or worried about one.
Roll your own is poker jargon used for a particular ruleset in certain poker variants, particularly in stud poker.In traditional stud poker games, cards are simply dealt to each player, either face up or face down according to the rules of the game being played, followed by betting. In roll your own games this is different in one of three possible ways. These are called:
simultaneous choose-after
in turn choose-after
choose-before
In simultaneous choose-after in every round where an upcard is normally dealt, each player is instead dealt a downcard. All players then look at all of their downcards and choose one to turn face up, then all players turn their chosen card at once.
In in turn choose-after the game begins the same way with each player being dealt a downcard, but then the first player to act (determined by the rules of the particular game) turns over his choice of upcard, then the next player can use that information to decide which of his cards to turn up, and then all players follow in turn.
Choose-before is always played in turn. On upcard rounds, before a card is dealt to each player, that player must choose whether he wants to receive it up or down. If he wants to receive it up, he says so. If he wants to receive it down, he must first turn one of his already-dealt downcards face up, so that all players will still have the same number of up and down cards. When using this method cards are not dealt to players starting at the dealer’s left as usual, but start with the high hand showing.
Roll your own should not be confused with rollouts, which, while similar, is fundamentally different.
Some forms of poker, often called lowball, sometimes called “low poker,” reward poor poker hands (in the traditional sense). There are three common variations on this idea, differing in whether aces are treated as high cards or low cards, and whether or not straights and flushes are used. The methods are:
Ace-to-five low: The lowest possible hand is -4-3-2-A, called a wheel. Aces are low and straights and flushes are ignored. This is the most common method.
Ace-to-six low: Also called 6-4 low, since the lowest possible hand is
-4-3-2-A. Aces are low and straights and flushes count as high hands.
Deuce-to-six low: The other, mostly unused, possibility would be 6-5 low. Aces are high, straights and flushes are ignored.
Some games are played high-low split, where the player with the best traditional poker hand (called the “high hand”) splits the pot with the best low hand. The low hand is decided by one of the methods above. According to Official Rules of Card Games by Albert Morehead[1], the low hand in high-low is generally the deuce-to-seven low, although many on-line casinos use ace-to-five low, with a qualifier, e.g., no card higher than an 8. Low hands tie more frequently than high hands, especially in community card games, so it is not uncommon for such a hand to win a small fraction of a poker pot. For example, if one player has the high hand on showdown, and two other players tie for the best low hand, the high hand wins half of the pot and each low hand wins only a quarter of the pot. Playing ace-to-five high-low greatly increases the chances of the “scoop”–winning both hands–because a low flush or straight may count for both high and low.
References
^ Albert H. Morehead (1996). Official Rules of Card Games. Ballantine Books. ISBN 0449911586.
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