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
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♦.
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.
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.
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.
When evaluating a hand before the flop, it’s useful to have some idea of how likely the hand is dominated. A dominated hand is a hand that is beaten by another hand (the dominant hand) and is extremely unlikely to win against it. Often the dominated hand has only a single card rank that can improve the dominated hand to beat the dominant hand (not counting straights and flushes.) For example, KJ is dominated by KQ—both hands share the king and the queen kicker is beating the jack kicker. Barring a straight or flush, the KJ will need a jack on the board to improve against the KQ (and will still be losing if a queen comes on the board also.) A pocket pair is dominated by a pocket pair of higher rank.
Pocket pairs
Barring a miracle straight or flush, a pocket pair needs to make three of a kind to beat a higher pocket pair.
To calculate the probability that another player has a higher pocket pair, first consider the case against a single opponent. The probability that a single opponent has a higher pair can be stated as the probability that the first card dealt to the opponent is a higher rank than the pocket pair and the second card is the same rank as the first. Where r is the rank of the pocket pair (assigning values from 2–10 and J–A = 11–14), there are (14 − r) × 4 cards of higher rank. Subtracting the two cards for the pocket pair leaves 50 cards in the deck. After the first card is dealt to the player there are 49 cards left, 3 of which are the same rank as the first. So the probability of a single opponent being dealt a higher pocket pair is
P = (((14-r)x4)/50) x (3/49)
The following approach extends this equation to calculate the probability that one or more other players has a higher pocket pair.
Multiply the base probability for a single player for a given rank of pocket pairs by the number of opponents in the hand;
Subtract the adjusted probability that more than one opponent has a higher pocket pair. (This is necessary because this probability effectively gets added to the calculation multiple times when multiplying the single player result.)
Where n is the number of other players still in the hand and Pma is the adjusted probability that multiple opponents have higher pocket pairs, then the probability that at least one of them has a higher pocket pair is
P = ((84-6r)/1225) x n – Pma.
The calculation for Pma depends on the rank of the player’s pocket pair, but can be generalized as
Pma = P
+ 2P
+ … + (n-1)Pn,
where P
is the probability that exactly two players have a higher pair, P
is the probability that exactly three players have a higher pair, etc. As a practical matter, even with pocket 2s against 9 opponents, P
< 0.0015 and P
< 0.00009, so just calculating P
and P
gives an adequately precise result.
The following table shows the probability that before the flop another player has a larger pocket pair when there are one to nine other players in the hand.
Probability of facing a
larger pair when holding
Against 1
Against 2
Against 3
Against 4
Against 5
Against 6
Against 7
Against 8
Against 9
KK
0.0049
0.0098
0.0147
0.0196
0.0244
0.0293
0.0342
0.0391
0.0439
QQ
0.0098
0.0195
0.0292
0.0388
0.0484
0.0579
0.0673
0.0766
0.0859
JJ
0.0147
0.0292
0.0436
0.0577
0.0717
0.0856
0.0992
0.1127
0.1259
TT
0.0196
0.0389
0.0578
0.0764
0.0946
0.1124
0.1299
0.1470
0.1637
99
0.0245
0.0484
0.0718
0.0946
0.1168
0.1384
0.1593
0.1795
0.1990
88
0.0294
0.0580
0.0857
0.1125
0.1384
0.1634
0.1873
0.2101
0.2318
77
0.0343
0.0674
0.0994
0.1301
0.1595
0.1874
0.2138
0.2387
0.2619
66
0.0392
0.0769
0.1130
0.1473
0.1799
0.2104
0.2389
0.2651
0.2890
55
0.0441
0.0862
0.1263
0.1642
0.1996
0.2324
0.2623
0.2892
0.3129
44
0.0490
0.0956
0.1395
0.1806
0.2186
0.2532
0.2841
0.3109
0.3334
33
0.0539
0.1048
0.1526
0.1967
0.2370
0.2729
0.3040
0.3300
0.3503
22
0.0588
0.1141
0.1654
0.2124
0.2546
0.2914
0.3222
0.3464
0.3633
The following table gives the probability that a hand is facing two or more larger pairs before the flop. From the previous equations, the probability Pm is computed as
Pm = P
+ P
+ … + Pn.
Probability of facing multiple
larger pairs when holding
Against 2
Against 3
Against 4
Against 5
Against 6
Against 7
Against 8
Against 9
KK
< 0.00001
0.00001
0.00003
0.00004
0.00007
0.00009
0.00012
0.00016
QQ
0.00006
0.00018
0.00037
0.00061
0.00091
0.00128
0.00171
0.00220
JJ
0.00017
0.00051
0.00102
0.00171
0.00257
0.00360
0.00482
0.00621
TT
0.00033
0.00099
0.00200
0.00335
0.00504
0.00709
0.00950
0.01226
99
0.00054
0.00164
0.00330
0.00553
0.00836
0.01177
0.01580
0.02045
88
0.00081
0.00244
0.00493
0.00828
0.01253
0.01769
0.02378
0.03084
77
0.00112
0.00341
0.00689
0.01160
0.01758
0.02487
0.03351
0.04353
66
0.00149
0.00454
0.00918
0.01550
0.02353
0.03335
0.04503
0.05861
55
0.00191
0.00583
0.01182
0.01998
0.03040
0.04318
0.05840
0.07619
44
0.00239
0.00728
0.01480
0.02506
0.03821
0.05438
0.07371
0.09635
33
0.00291
0.00890
0.01812
0.03075
0.04698
0.06699
0.09099
0.11919
22
0.00349
0.01068
0.02180
0.03706
0.05673
0.08107
0.11034
0.14484
From a practical perspective, however, the odds of out drawing a single pocket pair or multiple pocket pairs are not much different. In both cases the large majority of winning hands require one of the remaining two cards needed to make three of a kind.
Hands with one ace
When holding a single ace (referred to as Ax), it is useful to know how likely it is that another player has a better ace—an ace with a higher second card. The weaker ace is dominated by the better ace. The probability that a single opponent has a better ace is the probability that they have either AA or Ax where x is a rank other than ace that is higher than the player’s second card. When holding Ax, the probability that the other player has AA is (3/50) x (2/49) ~ 0.00245. Where x is the rank 2–K of the second card (assigning values from 2–10 and J–K = 11–13) the probability that a single opponent has a better ace is calculated by the formula
P = ((3/50) x (2/49)) + ((3/50) x (((13-x) x 4)/49) x 2) = (3/1225) + (12 x (13 – x))/1225 = (159 – 12x)/1225.
The probability (3/50) x (((13-x) x 4)/49) of a player having Ay, where y is a rank such that x < y <= K, is multiplied by the two ways to order the cards A and y in the hand.
When facing two opponents, for any given starting hand the number of possible combinations of hands the opponents can have is
(50/2)(48/2) = 1,381800
hands. For calculating probabilities we can ignore the distinction between the two opponents holding A♠J♥ and
♥
♣ and the opponents holding ♥
♣ and A♠J♥. The number of ways that hands can be distributed between n opponents is n! (pronounced n factorial). So the number of unique hand combinations H against two opponents is
H = (50/2)(48/2) -: 2! = 690,900
and against three opponents is
H = (50/2)(48/2)(46/2) -: 3! = 238,360,500
and against n opponents is
H = nk=1Π((50-2k)/2) -: kor alternately H = (50/2n) x (2n-1)!!
where (2n − 1)!! (!! is the double factorial operator) is the number of ways to distribute 2n cards between n hands of two cards each. The following table shows the number of hand combinations for up to nine opponents.
Opponents
Number of possible hand combinations
1
1,225
2
690,900
3
238,360,500
4
56,372,258,250
5
≈9.7073 × 1012 (more than 9.7 trillion)
6
≈1.2620 × 1015 (more than 1.2 quadrillion)
7
≈1.2674 × 1017 (more than 126 quadrillion)
8
≈9.9804 × 1018 (almost 10 quintillion)
9
≈6.2211 × 1020 (more than 622 quintillion)
An exhaustive analysis of all of the match ups in Texas Hold ‘em of a player against nine opponents requires evaluating each possible board for each distinct starting hand against each possible combination of hands held by nine opponents, which is
69 x (50/18) x 17!! x (32/5) ~ 2.117 x 1028 (more than 21 octillion.)
If you were able to evaluate one trillion (1012) combinations every second, it would take over 670 million years to evaluate all of the hand/board combinations. While it is possible to significantly reduce the total number of combinations by pruning combinations with identical properties, the total number of situations is still well beyond the number that can be evaluated by brute force. For this reason, most software programs compute probabilities and expected values for Hold ‘em poker hands against multiple opponents by simulating the play of thousands or even millions of hands to determine statistical probabilities.
For any given starting hand, there are 50 × 49 ÷ 2 = 1,225 hands that an opponent can have before the flop. (After the flop, the number of possible hands an opponent can have is reduced by the three community cards revealed on the flop to 47 × 46 ÷ 2 = 1,081 hands.) Therefore, there are
(52/2)(50/2) -: 2 = 812.175
possible head-to-head match ups in Hold ‘em. (The number of total number of match ups is divided by the two ways that two hands can be distributed between two players to give the number of unique match ups.) However, since there are only 169 distinct starting hands, there are 169 × 1,225 = 207,025 distinct head-to-head match ups.[2]
It is useful and interesting to know how two starting hands compete against each other heads up before the flop. In other words, we assume that neither hand will fold, and we will see a showdown. This situation occurs quite often in no limit and tournament play. Also, studying these odds helps to demonstrate the concept of hand domination, which is important in all community card games.
This problem is considerably more complicated than determining the frequency of dealt hands. To see why, note that given both hands, there are 48 remaining unseen cards. Out of these 48 cards, we can choose any 5 to make a board. Thus, there are
(48/5) = 1.712.304
possible boards that may fall. In addition to determining the precise number of boards that give a win to each player, we also must take into account boards which split the pot, and split the number of these boards between the players.
The problem is trivial for computers to solve by brute force search; there are many software programs available that will compute the odds in seconds. A somewhat less trivial exercise is an exhaustive analysis of all of the head-to-head match ups in Texas Hold ‘em, which requires evaluating each possible board for each distinct head-to-head match up, or 1,712,304 × 207,025 = 354,489,735,600 (≈354 billion) results.[2]
Head-to-head starting hand matchups
When comparing two starting hands, the head-to-head probability describes the likelihood of one hand beating the other after all of the cards have come out. Head-to-head probabilities vary slightly for each particular distinct starting hand matchup, but the approximate average probabilities, as given by Dan Harrington in Harrington on Hold’em [p.125], are summarized in the following table.
Favorite-to-underdog matchup
Probability
Odds for
Pair vs. 2 undercards
0.83
4.9 : 1
Pair vs. lower pair
0.82
4.5 : 1
Pair vs. 1 overcard, 1 undercard
0.71
2.5 : 1
2 overcards vs. 2 undercards
0.63
1.7 : 1
Pair vs. 2 overcards
0.55
1.2 : 1
These odds are general approximations only derived from averaging all of the hand matchups in each category. The actual head-to-head probabilities for any two starting hands vary depending on a number of factors, including:
Suited or unsuited starting hands;
Shared suits between starting hands;
Connectedness of non-pair starting hands;
Proximity of card ranks between the starting hands (lowering straight potential);
Proximity of card ranks toward A or 2 (lowering straight potential);
Possibility of split pot.
For example, A♠A♣ vs. K♠Q♣ is 87.65% to win (0.49% to split), but A♠A♣ vs. ♦ ♦ is 76.81% to win (0.32% to split).
The mathematics for computing all of the possible matchups is quite complex. However, a computer program can perform a brute force evaluation of the 1,712,304 possible boards for any given pair of starting hands in seconds.
Notes
^ ab By removing reflection and applying aggressive search tree pruning, it is possible to reduce the number of unique head-to-head hand combinations from 207,205 to less than 50,000. Reflection eliminates redundant calculations by observing that given hands h1 and h2, if w1 is the probability of h1 beating h2 in a showdown and s is the probability of h1 splitting the pot with h2, then the probability w2 of h2 beating h1 is w2 = 1 − (s + w1), thus eliminating the need to evaluate h2 against h1. Pruning is possible, for example, by observing that Q♥ J♥ has the same chance of winning against both 8♦ 7♣ and 8♦ 7♠ (but not the same probability as against 8♥ 7♣ because sharing the heart affects the flush possibilities for each hand.)
The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold ‘em, a player is dealt two down (or hole) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 combinations are divided by the 2 ways of ordering two cards.) Alternately, the number of possible starting hands is represented as the binomial coefficient
(52/2) = 1,326
which is the number of possible combinations of choosing 2 cards from a deck of 52 playing cards.
The 1,326 starting hands can be reduced for purposes of determining the probability of starting hands for Hold ‘em—since suits have no relative value in poker, many of these hands are identical in value before the flop. The only factors determining the strength of a starting hand are the ranks of the cards and whether the cards share the same suit. Of the 1,326 combinations, there are 169 distinct starting hands grouped into three shapes: 13 pocket pairs (paired hole cards), 13 × 12 ÷ 2 = 78 suited hands and 78 unsuited hands; 13 + 78 + 78 = 169. The relative probability of being dealt a hand of each given shape is different. The following shows the probabilities and odds of being dealt each type of starting hand.
Hand shape
Number
of hands
Permutations
for each hand
Combinations
Pocket pair
13
(4/2) = 6
13 × 6 = 78
Suited cards
78
(4/1) = 4
78 × 4 = 312
Unsuited cards
78
(4/1)(3/1) = 12
78 × 12 = 936
Hand shape
Dealt specific hand
Dealt any hand
Probability
Odds
Probability
Odds
Pocket pair
/1326 ~ 0.00453
220 : 1
8/1326 ~ 0.0588
16 : 1
Suited cards
/1326 ~ 0.00302
331 : 1
12/1326 ~ 0.2353
3.25 : 1
Unsuited cards
2/1326 ~ 0.00905
110 : 1
36/1326 ~ 0.7059
0.417 : 1
Here are the probabilities and odds of being dealt various other types of starting hands.
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Joe Hachem, winner of 2005 World Series of Poker main event
In 1998, the movie Rounders starring Matt Damon and Edward Norton gave moviegoers a romantic view of poker as a way of life. Texas hold ‘em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the “Cadillac of Poker”. There was also a clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker incorporated into the film.
CommanderBond.net reports that the centerpiece card game in the next James Bond film, Casino Royale, will be no-limit Texas hold ‘em instead of Baccarat as in the original Ian Fleming novel.
Spectator sport
Hold ‘em first caught the public eye as a spectator sport in the United Kingdom with the Late Night Poker TV show in 1999. The popularity of the show led to lipstick cameras also being used for American poker programs.
In 2003, hold ‘em exploded in popularity as a spectator sport in the United States. This was due to several factors, including the introduction of lipstick cameras that allowed the television audience to see the players’ hidden cards. ESPN’s coverage of the 2003 World Series of Poker featured the unexpected victory of Internet player Chris Moneymaker, an amateur player who gained admission to the tournament by winning a series of online tournaments. Moneymaker’s victory initiated a sudden surge of interest in the WSOP, based on the egalitarian idea that anyone – even a rank novice – can become a world champion.
In 2003, there were 839 entrants in the WSOP Main Event. In 2004, that number tripled. The crowning of the 2004 WSOP champion, Greg “Fossilman” Raymer, a patent attorney from Connecticut whose trademark holographic sunglasses have become legendary, further fueled the popularity of the event among amateur (and particularly internet) players. In the 2005 Main Event, an unprecedented 5,619 entrants vied for a first prize of $7,500,000. The winner, Joseph Hachem of Australia, was a semi-professional player. The runner-up, Steve Dannenmann, an amateur from Maryland, opined that he was only “the fourth or fifth best player” in his regular home game.
Two additional hold ‘em series debuted in 2003, the World Poker Tour and Celebrity Poker Showdown. All three of these shows are still currently in production and garner a large and loyal viewership.
With the ability to edit a tournament that lasts days into just a few hours, ESPN’s World Series of Poker focuses on showing how various star players fared in each event. Key hands from throughout the many days of each event are shown, and similar, highly edited coverage of final tables is also provided.
The World Poker Tour does not offer general coverage of the multi-day poker tournaments. Instead, WPT covers only the action at the final table of each event. With aggressive play and increasing blinds and antes, the important action from a single table can easily be edited into a two hour episode. Although the tournament fate of fewer stars are chronicled this way, it allows the drama to build more naturally toward the final heads up showdown.
Celebrity Poker Showdown coverage is a single table like World Poker Tour, however, the players are much less skilled and are invited to participate instead of winning their way on.
There are (52 × 51)/2 = 1,326 distinct possible combinations of two hole cards from a standard 52-card deck. However, since suits are only relevant for flushes, many of these hands are indistinguishable from the point of view of pre-flop strategy. In fact, considering suits to be equivalent unless both cards are the same suit, there are precisely 169 distinct possible starting hands in hold ‘em.
As an example, although J♥ J♣ and J♦ J♠ are distinct combinations of hole cards, they are indistinguishable as starting hands. Any starting hand comprising two Jacks is called pocket jacks and is denoted JJ. Similarly, any starting hand comprised of two Aces is called pocket Aces and is denoted AA, and any starting hand comprised of two 7′s is called pocket sevens and is denoted 77. Each of these starting hands is called a pocket pair or a wired pair.
The starting hands which are not pocket pairs fall into two classes – the suited hands and the unsuited hands. An example of a suited hand is 8♠ 7♠. Any starting hand comprised of an 8 and a 7 of the same suit is called 8-7 suited and is denoted 87s, where “s” is an abbreviation for “suited”. An example of an unsuited hands is Q♣ 9♦. Any starting hand comprised of a Queen and a 9 of different suits is called queen-nine offsuit and is denoted Q9 (or sometimes Q9o, where “o” is an abbreviation for “offsuit”). Remember, an “s” always denotes a suited starting hand, while the absence of an “s” always denotes an offsuit starting hand.
In almost all poker writing, the rank of 10 is abbreviated with the letter “T”, so that all the ranks can be written with a single character, unless cards are featured pictorially when “10″ is often used.
Consecutive cards of the same suit are called suited connectors. Many starting hands have colloquial names.
Strategy
Most poker authors recommend a tight-aggressive approach to playing Texas hold ‘em. This strategy involves playing relatively few hands (tight), but betting and raising often with those that one does play (aggressive). Although this strategy is often recommended, some professional players successfully employ other strategies as well. While most poker authors focus on playing primarily premium starting hands, some authors claim that the importance of starting hands is overstated.
Almost all authors agree that position is an important element of Texas hold ‘em strategy. Players who act later have more information than players who act earlier. As a result, players typically play fewer hands from early positions than later positions.
The no-limit and fixed limit versions of hold ‘em are strategically very different. Doyle Brunson states, “In fact, the games are so different that there are not many players who rank with the best in both types of hold ‘em. Many no-limit players have difficulty gearing down for limit, while limit players often lack the courage and ‘feel’ necessary to excel at no-limit.” Because the size of bets are restricted in limit games, the ability to bluff is somewhat curtailed. Since one is not (usually) risking all of one’s chips in limit poker, players are sometimes advised to take more chances.
Lower stakes limit games also exhibit different properties than higher stakes games. Small stakes games often involve more players in each hand and can vary from extremely passive (little raising and betting) to extremely aggressive (many raises). The difference of small stakes games have resulted in several books dedicated to only those games.
The descriptions below assume a familiarity with the general game play of poker, and with poker hands.
Objective
Like most variants of poker, the objective of Texas hold ‘em is to win pots, where a pot is the sum of the money bet by oneself and other players in a hand. A pot is won either at the showdown by forming the best five card poker hand out of the seven cards available, or by betting to cause other players to fold and abandon their claim to the pot.
Betting structures
Hold ‘em is normally played using small and big blind bets. Antes may be used in addition to blinds, particularly in later stages of tournament play. A dealer button is used to represent the player in the dealer position; the dealer button rotates clockwise after each hand, changing the position of the dealer and blinds. The small blind is posted by the player to the left of the dealer and is usually equal to half of the big blind. The big blind, posted by the player to the left of the small blind, is equal to the minimum bet. In tournament poker, the blind/ante structure periodically increases as the tournament progresses. (In some cases, the small blind is some other fraction of a small bet, e.g. $10 is a common small blind when the big blind is $15. The double-blind structure described above is relatively recent; until the 1980s, a single-blind structure was most common.)
The three most common variations of hold ‘em are limit hold ‘em, no-limit hold ‘em and pot-limit hold ‘em. Limit hold ‘em has historically been the most popular form of hold ‘em found in casino live action games in the United States. In limit hold ‘em, bets and raises during the first two rounds of betting (pre-flop and flop) must be equal to the big blind; this amount is called the small bet. In the next two rounds of betting (turn and river), bets and raises must be equal to twice the big blind; this amount is called the big bet. No-limit hold ‘em is the form most commonly found in televised tournament poker and is the game played in the main event of the World Series of Poker. In no-limit hold ‘em, players may bet or raise any amount over the minimum raise up to all of chips the player has at the table (called an all-in bet). In pot-limit hold ‘em, the maximum raise is the current size of the pot.
Play of the hand
Play begins with each player being dealt two cards face down. These cards are the player’s hole or pocket cards. These are the only cards each player will receive individually, and they will only (possibly) be revealed at the showdown, making Texas hold ‘em a closed poker game. The hand begins with a “pre-flop” betting round, beginning with the player to the left of the big blind (or the player to the left of the dealer, if no blinds are used) and continuing clockwise.
After the pre-flop betting round, assuming there remains at least two players taking part in the hand, the dealer deals a flop, three face-up community cards. The flop is followed by a second betting round. This and all subsequent betting rounds begin with the player to the dealer’s left and continue clockwise.
After the flop betting round ends a single community card (called the turn or fourth street) is dealt, followed by a third betting round. A single community card (called the river or fifth street) is dealt, followed by a fourth betting round and the showdown, if necessary.
The showdown
If a player bets and all other players fold, then the remaining player is awarded the pot and is not required to show his hole cards. If two or more players remain after the final betting round, a showdown occurs. On the showdown, each player plays the best five-card hand he can make from the seven cards comprising his two hole cards and the board (the five community cards). A player may use both of his own two hole cards, only one, or none at all, to form his final five-card hand. If the five community cards form the player’s best hand, then the player is said to be playing the board and can only hope to split the pot, since the other player can also use the same five cards to construct the same hand.
If the best hand is shared by more than one player (e.g. if no player is able to beat the board), then the pot is split equally amongst all remaining players, with any extra chips going to the person closest to the button in clockwise order. However, it is common for players to have closely-valued, but not identically ranked hands. In particular, kickers are often needed to break ties. Nevertheless, one must be careful in determining the best hand. The goal is to make the best five-card hand; if the hand involves fewer than five cards, such as two pair or three of a kind, then kickers are used to settle ties (see the second example below.) Straights sometimes split the pot.
The best possible hand given the five community cards is referred to as the nuts. The lowest possible nuts is three Queens (this occurs with 2 3 7 8 Q on the board with no more than two cards of any one suit).
Examples
Sample showdown
Here’s a sample showdown:
Board 4♣ K♠4♥8♠ 7♠
Bob A♣ 4♦
Carol A♠ 9♠
Ted K♥ K♦
Alice 5♦ 6♦
Each player plays the best 5 card hand they can make with the 7 cards available. They have:
Bob
4♣ 4♥ 4♦ A♣ K♠
Three 4s, A and K kickers
Carol
A♠ K♠ 9♠ 8♠ 7♠
A-high flush
Ted
K♠ K♥ K♦ 4♣ 4♥
Full house
Alice
8♠ 7♠ 6♦ 5♦ 4♥
8-high straight
In this case, Ted’s full house is the best hand.
Sample hand
The blinds for this example hand
Here’s a sample deal involving our four players. The players’ individual hands will not be revealed until the showdown, to give a better sense of what happens during play:
Compulsory bets: Alice is the dealer. Bob, to Alice’s left, posts a small blind of $1, and Carol posts a big blind of $2.
Pre-flop: Alice deals two hole cards face down to each player, beginning with Bob and ending with herself. Ted must act first because he is the first player after the big blind. He cannot check, since the $2 big blind plays as a bet, so he folds. Alice calls the $2. Bob adds an additional $1 to his $1 small blind to call the $2 total. Carol’s blind is “live”, so she has the option to raise here, but she checks instead, ending the first betting round. The pot now contains $6, $2 from each of three players.
Flop: Alice now deals the flop of three face-up community cards, 9♣ K♣ 3♥. On this round, as on all subsequent rounds, the player on the dealer’s left begins the betting. In this case it is Bob who checks. Carol opens for $2, Ted has already folded and Alice raises another $2, making the total bet now facing Bob $4. He calls (puts in $4, $2 to match Carol’s initial bet and $2 to match Alice’s raise). Carol calls as well, putting in her $2. The pot now contains $18, $6 from the last round and $4 from three players this round.
Turn: Alice now deals the turn card face up. It is the 5♠. Bob checks, Carol checks, and Alice checks; the turn has been checked around. The pot still contains $18.
River: Alice deals the final river card, the 9♦, making the final board 9♣ K♣ 3♥ 5♠ 9♦. Bob bets $4, Carol calls, and Alice folds (Alice’s holding was A♣ 7♣; she was hoping the river card would be a club to make her a flush).
Showdown: Bob shows his hand of Q♠ 9♥, so the best five-card hand he can make is 9♣ 9♦ 9♥ K♣ Q♠, for three 9′s, with a King and a Queen as kickers. Carol shows her cards of K♠ J♥, making her final hand K♣ K♠ 9♣ 9♦ J♥ for two pair, Kings and 9′s, with a Jack kicker. Bob wins the showdown and the $26 pot.
Kickers and ranks
The following is another situation which illustrates the importance of breaking ties with kickers and card ranks, as well as the use of the five-card rule. After the turn, the board and players’ hole cards are as follows (though none of the players know each other’s hole cards):
Board (after the turn) 8♠ Q♣ 8♥ 4♣
Bob K♥ Q♠
Carol Q♥ 10♦
Ted J♣ 2♣
Alice 10♣ 9♣
At the moment, Bob is in the lead with a hand of Q♠ Q♣ 8♠ 8♥ K♥, making two pair, Queens and 8′s, with King kicker. This beats Carol’s hand of Q♥ Q♣ 8♠ 8♥ 10♦ by virtue of his King kicker. Both Alice and Ted are hoping the final card is a club, which will make them both a flush, but in that case, Ted would have the higher flush and win the showdown. For example, if the final card was the 7♣, Ted’s flush would be Q-J-7-4-2, while Alice’s would be Q-10-9-7-4. Alice could still win, though, if the final card were the J♦, as that would give her a Queen-high straight. On this deal, however, the final card was the A♠, which didn’t help either of them. Bob and Carol still each have two pair, but notice what happened: both of them are now entitled to play the final Ace as their fifth card, making their hands both two pair, Queens and 8′s, with an Ace kicker. Bob’s King no longer plays, because the Ace on the board plays as the fifth card in both hands, and a hand is only composed of five cards. They therefore split the pot.
Texas hold ‘em (also hold’em, holdem) is the most popular of the community card poker games. It is also the most popular poker variant played in most casinos in the United States. Its no-limit betting form is used in the main event of the World Series of Poker (WSOP), as seen on ESPN, and the World Poker Tour, seen on The Travel Channel, and is widely regarded as the premier poker game.
Although it can theoretically be played by up to 22 players (or 23 if burn cards are not used), it is generally played with between 2 and 10 people. It is one of the most positional of all poker variants, since the order of betting is fixed throughout all betting rounds. Hold ‘em is commonly played outside of the United States, but seven-card stud, Omaha hold ‘em and other games may be more popular in some places.
Origins
There is no precise information on where or when Texas hold ‘em Poker was first played. According to legend, the earliest game played was in Robstown, Texas, in the early 1900s and it first came to Dallas, Texas in 1925. Texas hold ‘em was introduced to Las Vegas by a group of Texan gamblers and card players, including Crandell Addington, Doyle Brunson, and Amarillo Slim. The game was later introduced to Europe by bookmakers Terry Rogers and Liam “The Gentleman” Flood.
In popular culture
In 1998, the movie Rounders starring Matt Damon and Edward Norton gave moviegoers a romantic view of poker as a way of life. Texas hold ‘em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the “Cadillac of Poker”. There was also a clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker incorporated into the film.
CommanderBond.net reports that the centerpiece card game in the next James Bond film, Casino Royale, will be no-limit Texas hold ‘em instead of Baccarat as in the original Ian Fleming novel.
Spectator sport
Joe Hachem, winner of 2005 World Series of Poker main event
Hold ‘em first caught the public eye as a spectator sport in the United Kingdom with the Late Night Poker TV show in 1999. The popularity of the show led to lipstick cameras also being used for American poker programs.
In 2003, hold ‘em exploded in popularity as a spectator sport in the United States. This was due to several factors, including the introduction of lipstick cameras that allowed the television audience to see the players’ hidden cards. ESPN’s coverage of the 2003 World Series of Poker featured the unexpected victory of Internet player Chris Moneymaker, an amateur player who gained admission to the tournament by winning a series of online tournaments. Moneymaker’s victory initiated a sudden surge of interest in the WSOP, based on the egalitarian idea that anyone – even a rank novice – can become a world champion.
In 2003, there were 839 entrants in the WSOP Main Event. In 2004, that number tripled. The crowning of the 2004 WSOP champion, Greg “Fossilman” Raymer, a patent attorney from Connecticut whose trademark holographic sunglasses have become legendary, further fueled the popularity of the event among amateur (and particularly internet) players. In the 2005 Main Event, an unprecedented 5,619 entrants vied for a first prize of $7,500,000. The winner, Joseph Hachem of Australia, was a semi-professional player. The runner-up, Steve Dannenmann, an amateur from Maryland, opined that he was only “the fourth or fifth best player” in his regular home game.
Two additional hold ‘em series debuted in 2003, the World Poker Tour and Celebrity Poker Showdown. All three of these shows are still currently in production and garner a large and loyal viewership.
With the ability to edit a tournament that lasts days into just a few hours, ESPN’s World Series of Poker focuses on showing how various star players fared in each event. Key hands from throughout the many days of each event are shown, and similar, highly edited coverage of final tables is also provided.
The World Poker Tour does not offer general coverage of the multi-day poker tournaments. Instead, WPT covers only the action at the final table of each event. With aggressive play and increasing blinds and antes, the important action from a single table can easily be edited into a two hour episode. Although the tournament fate of fewer stars are chronicled this way, it allows the drama to build more naturally toward the final heads up showdown.
Celebrity Poker Showdown coverage is a single table like World Poker Tour, however, the players are much less skilled and are invited to participate instead of winning their way on.
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The blinds for this example hand
Joe Hachem, winner of 2005 World Series of Poker main event
