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.
In poker, a bad beat occurs when a hand, which was at one time a big favourite to win, loses. Typically the term is only applied in this way when the player holding the eventual winning hand misplayed it spectacularly.
Alternatively, the term is also applied when a particularly strong hand loses to an even stronger one. In some casinos there is a “bad beat jackpot” awarded whenever a player suffers a particular beat.
A typical example of the first type of bad beat, in No Limit Texas hold ‘em:
Alice (the hero) holds A♦ A♣ – pocket aces, the strongest possible starting hand.
Bob (the villain) holds Q♣ 8♥ – a weak hand.
The players have the same amount of chips. Before the flop, Alice raises to 15 times the big blind, placing a fifth of her stack in the pot, and only Bob calls. The flop comes A♥ 8♠ 7♠. Although Alice has the nuts at this point, making 3 aces, she is concerned about possible draws to a straight or flush, and goes all-in with a bet that is twice the size of the pot. Bizarrely, Bob, who has only middle-pair, calls.
At this point, Bob’s chances of winning are precisely 1 in 990. [1] He can only win if both the turn card and the river card are eights. Since this is a bad beat story, the turn and river naturally bring precisely that, and Bob scoops the pot, leaving Alice cursing Bob’s appalling play – he should not have called such a big bet before the flop, nor on the flop.
Reacting to bad beats
Bad beats can be infuriating, but mathematically “Alice” actually wants “Bob” to play in this manner. Bob took a gamble that should not have worked; his odds were 989-to-1 against. It worked this time, but if he continues to play in such a careless manner, he will almost certainly lose more than he wins. He is essentially giving away his money—and if Alice is careful, it will all go to her. Thus, the more stoic poker players accept bad beats as an unpleasant but necessary drawback to a tactic that works the vast majority of the time (989 of 990 instances, in this case). Nevertheless, a bad beat is often a profound psychological blow, and can easily lead to a player going on tilt. Professional player Phil Hellmuth, among others, is notorious for his pronounced reactions to bad beats.
In online poker rooms, bad beats often lead to accusations that the random number generator is “rigged”, even though such beats occur in offline games.
Bad beat jackpot
A bad beat jackpot is a prize that is paid when a sufficiently strong hand is shown down and loses to an even stronger hand held by another player. Not all poker games offer bad beat jackpots, and those that do have specific requirements for how strong a losing hand must be to qualify for the jackpot. For example, the losing hand may be required to be four-of-a-kind or better. There may be additional requirements as well. For example, in Texas hold ‘em there is usually a requirement that both hole cards play in both the losing and winning hands. These rules vary from one cardroom to the next.
Bad beat jackpots are usually progressive, often with a small rake being taken out of each pot to fund the jackpot (in addition to the regular rake). When the jackpot is won, it is usually split among all players sitting at the table at the time of the bad beat, including players that folded their hands (usually a 25% share), with the largest shares of the jackpot going to the players holding the winning (usually 25%) and losing hand (usually 50%). Because such bad beats are rare, jackpots can grow to be quite large, sometimes reaching hundreds of thousands of dollars.
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.
To mix the deck by spreading the cards face down on the table and mixing them up. A dealer may wash the deck before shuffling.
weak ace
An ace with a low kicker (e.g. four). Also “small ace,” “soft ace,” “ace-rag.”
whipsaw
When a player is caught in the middle between two raisers and must call each bet because of the pot odds. Compare to “crossfire”.
window card
An upcard in stud poker. The first window card in stud is called the “door card”.
wired pair
A “pocket pair”.
wrap
In Omaha, the term for an open ended straight that consists of two board cards and three or four cards from a player’s hand. An example would be a player holding 345A with the board 67K is said to have a “wrap” as any 3, 4, or 5, or 8 will make a straight. A hand of 4589 would also be a wrap draw, but would often be refered to as a “big wrap” due to twenty cards making the straight as opposed to thirteen in the first example.
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
In the game of poker, opens and raises are considered aggressive plays, while calls and checks are considered passive (though a check-raise would be considered a very aggressive play). It is said that “aggression has its own value”, meaning that often aggressive plays can make money with weak hands because of bluff value. Aggressive plays also tend to give the opponents more opportunities to make mistakes.
While it is true that aggressive play is generally superior to passive play, using any play exclusively can lead to predictability, and being too predictable is far worse than being too passive. A player who is constantly aggressive and plays many inferior hands is called a “maniac”, and skilled players will take advantage of him by calling him more often, using isolation plays, and by other means.
If a player is not aggressive with his weaker hands, the opponents can safely fold whenever the player does bet or raise. The appropriate amount of aggression can be computed using game theory, and depends on the game being played and the tendencies of the opponents.
The playing position to the direct left of the blinds in Texas hold ‘em or Omaha . The player who is under the gun must act first on the first round of betting.
underfull
In a community card game, a full house that is one of the lowest full houses possible. For example: in Texas hold ‘em, a player holding a pair of deuces with a final board of 2A33Q holds an underfull (Deuces full of Treys). The highest possible full house is Aces full of Treys. Also “underboat”.
up
When used with a card rank to describe a poker hand, refers to two pair with the named card being the higher pair. For example, a hand of QQ885 might be called “queens up”.
upcard
See upcard.
up the ante
Increase the stake. Also commonly used outside the context of poker.
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.
A player who gets up from his seat in a cash game, after two other players are already away from the table, is referred to as the “third man walking”. In a casino with a “third man walking rule”, this player may be required to return to his seat within 10 minutes, or one rotation of the deal around the table, or else his seat in the game will be forfeited if there is a waiting list for the game.
throwing a party
A player who is playing like a fool and gambling all of their money away is said to be throwing a party.
trey
A 3-spot card. Casino personnel refer to the 3♣ as the “trey of clubs”.
2-way straight draw
A hand in draw poker such as 6♥ 7♥(Joker) 9♣, in which any of twelve cards (4 fives, 4 eights, 4 tens) can fill a straight.
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
A tournament in which the prize is a free entrance to another (larger) tournament.
scare card
A card that comes that may have improved an opponent’s hand. The Jack of spades on the turn was a scare card because it put both flush and straight possibilities on the board.
scoop
In high-low split games, to win both the high and the low half of the pot.
set
Three of a kind, esp. the situation where two of the cards are concealed in the player’s hole cards.
set-up
A deck that has been ordered, usually King to Ace by suit (spades, hearts, clubs and diamonds). In casinos, it is customary to use a set-up deck when introducing a new deck to the table. The set-up is spread face up for the players to demonstrate that all of the cards are present before the first shuffle. Also called to “spade the deck”.
shootout
A poker tournament format where the last remaining player of a table goes on to play the remaining players of other tables. Each table plays independently of the others; that is, there is no balancing as players are eliminated. This format is particularly common in European televised poker programs, including Late Night Poker.
side pot
A separate pot created to deal with the situation of one player going “all in”.
-way straight draw
A hand in draw poker such as 6♥ 7♥8♠ (Joker), in which any of sixteen cards (4 fours, 4 fives, 4 nines, 4 tens) can fill a straight.
slow roll
To delay or avoid showing one’s hand at showdown, forcing other players to expose their hands first. When done while holding a good hand likely to be the winner, it is considered poor etiquette, because it often gives other players “false hope” that their hands might win before the slow-roller’s is exposed.
small blind special
A situation in which (assuming no raising) a player is dealt weak hole cards in the small blind, but ends up making the best hand because they got to see a relatively inexpensive flop.
smooth call
A “flat call”.
speeding
To play very loose with no identifiable pattern, or to bluff frequently. Also known as speeding around.
spike
When a flop is spread out, if the first card revealed is the card an underdog needs, they spike that card. More loosely, if any of the flop cards help you, then you spike it. I had Q9 to my opponent’s pocket jacks, but I spiked a queen on the flop to take the lead.
splash the pot
To throw one’s chips in the pot in a disorderly fashion. Not typically allowed, because the dealer can’t tell how much has been bet.
spread
The range between a table’s minimum and maximum bets.
stack
A collection of 20 poker chips of the same denomination, usually arranged in an orderly column.
stakes
The definition of the amount one buys in for and can bet. For example, a “low stakes” game might be a $10 buy-in with a $1 maximum raise.
stand pat
In draw poker, playing the original hand using no draws, either as a bluff or in the belief it is the best hand.
steam
Act of playing recklessly when one is frustrated.
stop ‘n go
When a player bets into another player who has previously raised or otherwise shown aggression. Example: On the flop, Bill bets into Tom, Tom raises, and Bill just calls. On the turn, Bill bets into Tom again. Bill has just pulled a stop ‘n go.
straight
Poker hand
When used with an amount, indicates that the speaker is referring to the total bet, versus the amount being raised. Alice bets twenty. Bob raises to fifty straight.
strategy card
A wallet sized card that is commonly used to help with poker strategies in online and casino games.
string bet
To call with one motion and raise with another, or to reach for more chips in the middle of laying a bet/raise without stating the intended amount. String bets are prohibited in public cardroom rules.
stuck
Having lost money. I’m stuck $300 right now.
stud
A variant of poker.
A card dealt face up in Stud poker.
suck out
To draw a winning hand despite poor odds.
sucker straight
In community card poker variants, a straight completed on the low end of the possible straight on the board.
suited
Having the same suit. See card suits.
super satellite
A multi-table poker tournament in which the prize is a free entrance to a satellite tournament or a tournament in which all the top finishers gain entrance to a larger tournament.
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.
After a hand is over, a rabbit hunt means to reveal the last card that would have come up in a community card game with a fixed number of cards. Such activity is usually prohibited in casinos.
rack
. A collection of 100 chips of the same denomination, usually arranged in 5 stacks in a plastic tray.
. A plastic tray used for storing a rack of chips.
rags
Worthless (or apparently worthless) cards. Most often refers to small cards in high-hand games, while high cards in low games are more often called “bricks” or “bombs”. Also “blank”.
rail
The rail is the sideline at a poker table – the (often imaginary) rail separating spectators from the field of play. Watching from the rail means watching a poker game as a spectator. People on the rail are sometimes called railbirds.
rainbow
Three or four cards of different suits, especially said of a flop.
rakeback
Rebate/repayment to a player of a portion the rake paid by the player, normally from a non-cardroom, third-party source such as an affiliate. Applies only to online poker.
ram and jam
To aggressively bet, raise, and reraise.
ratholing
To “go south”.
rebuy
An amount of chips purchased after the buy-in.
redeal
To deal a hand again, possibly after a misdeal.
redraw
To make one hand and have a draw for a better hand. Ted made a straight on the turn with a redraw for a flush on the river..
Second or later draws in a draw game with multiple draws.
reraise
Raise after one has been raised. Also coming “over the top”.
river rat
A player whose hand was dominated from the start, but improves his hand on the river to win the pot.
rock
A very tight player (plays very few hands and only continues with strong hands).
A bundle of chips held together with a rubber band, or other token signifying an obligatory live straddle. If the player under the gun has the rock, he must use it to post a live straddle. The winner of the pot collects the rock and is obligated to use it in turn.
rolled-up trips
In seven-card stud, three of a kind dealt in the first three cards.
runner
A tournament entrant, a contestant.
runner-runner
A hand made by hitting two consecutive cards on the turn and river. Also “backdoor”.
rush
Winning streak. A player who has won several big pots recently is said to be on a rush.
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.
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