A poker player is drawing if they have a hand that is incomplete and needs further cards to become valuable. The hand itself is called a draw or drawing hand. For example, in seven-card stud, if four of a player's first five cards are all spades, but the hand is otherwise weak, they are drawing to a flush. In contrast, a made hand already has value and does not necessarily need to draw to win. A made starting hand with no help can lose to an inferior starting hand with a favorable draw. If an opponent has a made hand that will beat the player's draw, then the player is drawing dead; even if they make their desired hand, they will lose. Not only draws benefit from additional cards; many made hands can be improved by catching an out — and may have to in order to win.

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Calculating Poker Odds for Dummies - A FREE, #1 guide to mastering odds. How to quickly count outs to judge the value & chance of winning a hand in 2020. In the poker game of Texas hold 'em. There are 25 starting hands with a probability of winning at a 10-handed table of greater than 1/7. Limit hand rankings. Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold'em. These rankings do not apply to. Probabilities in Two-Player Texas Hold 'Em Introduction. This page examines the probabilities of each final hand of an arbitrary player, referred to as player two, given the poker value of the hand of the other player, referred to as player one. The following is a passage from Wikipedia on starting hands probability. 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.

Six-plus hold 'em (also known as short-deck hold 'em) is a community card poker game variant of Texas hold 'em, where the 2 through 5 cards are removed from the deck.Each player is dealt two cards face down and seeks to make the best five card poker hand from any combination of the seven cards (five community cards and their own two hole cards). In the poker game of Texas hold 'em. There are 25 starting hands with a probability of winning at a 10-handed table of greater than 1/7. Limit hand rankings. Some notable theorists and players have created systems to rank the value of starting hands in limit Texas hold'em. These rankings do not apply to no limit play.

• 2Types of draws

Outs[edit]

An unseen card that would improve a drawing hand to a likely winner is an out. Playing a drawing hand has a positive expectation if the probability of catching an out is greater than the pot odds offered by the pot.

The probability ${\displaystyle P_1}$ of catching an out with one card to come is:

${\displaystyle P_1=\frac{\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}}{\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}}}$

The probability ${\displaystyle P_2}$ of catching at least one out with two cards to come is:

${\displaystyle P_2=1-\frac{\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}}{\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}}\times \frac{\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}-1}{\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}-1}}$

${\displaystyle \mathrm{n}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}=\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}-\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}}$

A dead out is a card that would normally be considered an out for a particular drawing hand, but should be excluded when calculating the probability of catching an out. Outs can be dead for two reasons:

• A dead out may work to improve an opponent's hand to a superior hand. For example, if Ted has a spade flush draw and Alice has an outside straight draw, any spades that complete Alice's straight are dead outs because they would also give Ted a flush.
• A dead out may have already been seen. In some game variations such as stud poker, some of the cards held by each player are seen by all players.

Types of draws[edit]

Flush draw[edit]

A flush draw, or four flush, is a hand with four cards of the same suit that may improve to a flush. For example, K♣ 9♣ 8♣ 5♣ x. A flush draw has nine outs (thirteen cards of the suit less the four already in the hand). If you have a flush draw in Hold'em, the probability to flush the hand in the end is 34.97 percent if there are two more cards to come, and 19.56 percent (9 live cards divided by 46 unseen cards) if there is only one more card to come.

Outside straight draw[edit]

An outside straight draw, also called up and down, double-ended straight draw or open-end(ed) straight draw, is a hand with four of the five needed cards in sequence (and could be completed on either end) that may improve to a straight. For example, x-9-8-7-6-x. An outside straight draw has eight outs (four cards to complete the top of the straight and four cards to complete the bottom of the straight). Straight draws including an ace are not outside straight draws, because the straight can only be completed on one end (has four outs).

Inside straight draw[edit]

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An inside straight draw, or gutshot draw or belly buster draw, is a hand with four of the five cards needed for a straight, but missing one in the middle. For example, 9-x-7-6-5. An inside straight draw has four outs (four cards to fill the missing internal rank). Because straight draws including an ace only have four outs, they are also considered inside straight draws. For example, A-K-Q-J-x or A-2-3-4-x. The probability of catching an out for an inside straight draw is half that of catching an out for an outside straight draw.

Double inside straight draw[edit]

A double inside straight draw, or double gutshot draw or double belly buster draw can occur when either of two ranks will make a straight, but both are 'inside' draws. For example in 11-card games, 9-x-7-6-5-x-3, or 9-8-x-6-5-x-3-2, or in Texas Hold'em when holding 9-J hole cards on a 7-10-K flop. The probability of catching an out for a double inside straight draw is the same as for an outside straight draw.

Other draws[edit]

Sometimes a made hand needs to draw to a better hand. For example, if a player has two pair or three of a kind, but an opponent has a straight or flush, to win the player must draw an out to improve to a full house (or four of a kind). There are a multitude of potential situations where one hand needs to improve to beat another, but the expected value of most drawing plays can be calculated by counting outs, computing the probability of winning, and comparing the probability of winning to the pot odds.

Backdoor draw[edit]

A backdoor draw, or runner-runner draw, is a drawing hand that needs to catch two outs to win. For example, a hand with three cards of the same suit has a backdoor flush draw because it needs two more cards of the suit. The probability ${\displaystyle P_{rr}}$ of catching two outs with two cards to come is:

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${\displaystyle P_{rr}=\frac{\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}}{\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}}\times \frac{\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}-1}{\mathrm{u}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{s}-1}}$

For example, if after the flop in Texas hold 'em, a player has a backdoor flush draw (e.g., three spades), the probability of catching two outs on the turn and river is (10 ÷ 47) × (9 ÷ 46) = 4.16 percent. Backdoor draws are generally unlikely; with 43 unseen cards, it is equally likely to catch two out of seven outs as to catch one out of one. A backdoor outside straight draw (such as J-10-9) is equally likely as a backdoor flush, but any other 3-card straight combination isn't worth even one out.

Drawing dead[edit]

A player is said to be drawing dead when the hand he hopes to complete will nonetheless lose to a player who already has a better one. For example, drawing to a straight or flush when the opponent already has a full house. In games with community cards, the term can also refer to a situation where no possible additional community card draws results in a win for a player. (This may be because another player has folded the cards that would complete his hand, his opponent's hand is already stronger than any hand he can possibly draw to or that the card that completes his hand also augments his opponent's.)

See also[edit]

• Poker strategy

References[edit]

1. ^Odds Chart. 'How to play texas holdem poker'. Howtoplaytexasholdempoker.org. Archived from the original on 13 January 2010. Retrieved 22 February 2010.

External links[edit]

In poker, pot odds are the ratio of the current size of the pot to the cost of a contemplated call.^[1] Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value.

• 3Implied pot odds
• 4Reverse implied pot odds
• 5Manipulating pot odds

Converting odds ratios to and from percentages[edit]

Odds are most commonly expressed as ratios, but converting them to percentages often make them easier to work with. The ratio has two numbers: the size of the pot and the cost of the call. To convert this ratio to the equivalent percentage, these two numbers are added together and the cost of the call is divided by this sum. For example, the pot is $30, and the cost of the call is $10. The pot odds in this situation are 30:10, or 3:1 when simplified. To get the percentage, 30 and 10 are added to get a sum of 40 and then 10 is divided by 40, giving 0.25, or 25%.

To convert any percentage or fraction to the equivalent odds, the numerator is subtracted from the denominator and then this difference is divided by the numerator. For example, to convert 25%, or 1/4, 1 is subtracted from 4 to get 3 (or 25 from 100 to get 75) and then 3 is divided by 1 (or 75 by 25), giving 3, or 3:1.

Using pot odds to determine expected value[edit]

When a player holds a drawing hand (a hand that is behind now but is likely to win if a certain card is drawn) pot odds are used to determine the expected value of that hand when the player is faced with a bet.

The expected value of a call is determined by comparing the pot odds to the odds of drawing a card that wins the pot. When the odds of drawing a card that wins the pot are numerically higher than the pot odds, the call has a positive expectation; on average, a portion of the pot that is greater than the cost of the call is won. Conversely, if the odds of drawing a winning card are numerically lower than the pot odds, the call has a negative expectation, and the expectation is to win less money on average than it costs to call the bet.

Implied pot odds[edit]

Implied pot odds, or simply implied odds, are calculated the same way as pot odds, but take into consideration estimated future betting. Implied odds are calculated in situations where the player expects to fold in the following round if the draw is missed, thereby losing no additional bets, but expects to gain additional bets when the draw is made. Since the player expects to always gain additional bets in later rounds when the draw is made, and never lose any additional bets when the draw is missed, the extra bets that the player expects to gain, excluding his own, can fairly be added to the current size of the pot. This adjusted pot value is known as the implied pot.

Example (Texas hold'em)[edit]

On the turn, Alice's hand is certainly behind, and she faces a $1 call to win a $10 pot against a single opponent. There are four cards remaining in the deck that make her hand a certain winner. Her probability of drawing one of those cards is therefore 4/47 (8.5%), which when converted to odds is 10.75:1. Since the pot lays 10:1 (9.1%), Alice will on average lose money by calling if there is no future betting. However, Alice expects her opponent to call her additional $1 bet on the final betting round if she makes her draw. Alice will fold if she misses her draw and thus lose no additional bets. Alice's implied pot is therefore $11 ($10 plus the expected $1 call to her additional $1 bet), so her implied pot odds are 11:1 (8.3%). Her call now has a positive expectation.

Reverse implied pot odds[edit]

Reverse implied pot odds, or simply reverse implied odds, apply to situations where a player will win the minimum if holding the best hand but lose the maximum if not having the best hand. Aggressive actions (bets and raises) are subject to reverse implied odds, because they win the minimum if they win immediately (the current pot), but may lose the maximum if called (the current pot plus the called bet or raise). These situations may also occur when a player has a made hand with little chance of improving what is believed to be currently the best hand, but an opponent continues to bet. An opponent with a weak hand will be likely to give up after the player calls and not call any bets the player makes. An opponent with a superior hand, will, on the other hand, continue, (extracting additional bets or calls from the player).

Limit Texas hold'em example[edit]

With one card to come, Alice holds a made hand with little chance of improving and faces a $10 call to win a $30 pot. If her opponent has a weak hand or is bluffing, Alice expects no further bets or calls from her opponent. If her opponent has a superior hand, Alice expects the opponent to bet another $10 on the end. Therefore, if Alice wins, she only expects to win the $30 currently in the pot, but if she loses, she expects to lose $20 ($10 call on the turn plus $10 call on the river). Because she is risking $20 to win $30, Alice's reverse implied pot odds are 1.5-to-1 ($30/$20) or 40 percent (1/(1.5+1)). For calling to have a positive expectation, Alice must believe the probability of her opponent having a weak hand is over 40 percent.

For example this table shows that if you play 10,000 hands of blackjack the probability is 90% of finishing within 192 units where you started after subtracting the expected loss due to the house edge. 6 deck shoe blackjack strategy. I recently replaced my with some information about the standard deviation which may help. It is more a matter of degree, the more you play the more your results will approach the house edge.

Manipulating pot odds[edit]

Often a player will bet to manipulate the pot odds offered to other players. A common example of manipulating pot odds is make a bet to protect a made hand that discourages opponents from chasing a drawing hand.

No-limit Texas hold 'em example[edit]

With one card to come, Bob has a made hand, but the board shows a potential flush draw. Bob wants to bet enough to make it wrong for an opponent with a flush draw to call, but Bob does not want to bet more than he has to in the event the opponent already has him beat.

Assuming a $20 pot and one opponent, if Bob bets $10 (half the pot), when his opponent acts, the pot will be $30 and it will cost $10 to call. The opponent's pot odds will be 3-to-1, or 25 percent. If the opponent is on a flush draw (9/46, approximately 19.565 percent or 4.11-to-1 odds against with one card to come), the pot is not offering adequate pot odds for the opponent to call unless the opponent thinks they can induce additional final round betting from Bob if the opponent completes their flush draw (see implied pot odds).

A bet of $6.43, resulting in pot odds of 4.11-to-1, would make his opponent mathematically indifferent to calling if implied odds are disregarded.

Bluffing frequency[edit]

According to David Sklansky, game theory shows that a player should bluff a percentage of the time equal to his opponent's pot odds to call the bluff. For example, in the final betting round, if the pot is $30 and a player is contemplating a $30 bet (which will give his opponent 2-to-1 pot odds for the call), the player should bluff half as often as he would bet for value (one out of three times).

However, this conclusion does not take into account some of the context of specific situations. A player's bluffing frequency often accounts for many different factors, particularly the tightness or looseness of their opponents. Bluffing against a tight player is more likely to induce a fold than bluffing against a loose player, who is more likely to call the bluff. Sklansky's strategy is an equilibrium strategy in the sense that it is optimal against someone playing an optimal strategy against it.

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See also[edit]

Notes[edit]

References[edit]

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• David Sklansky (1987). The Theory of Poker. Two Plus Two Publications. ISBN1-880685-00-0.
• David Sklansky (2001). Tournament Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-28-0.
• David Sklansky and Mason Malmuth (1988). Hold 'em Poker for Advanced Players. Two Plus Two Publications. ISBN1-880685-22-1.
• Dan Harrington and Bill Robertie (2004). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume I: Strategic Play. Two Plus Two Publications. ISBN1-880685-33-7.
• Dan Harrington and Bill Robertie (2005). Harrington on Hold'em: Expert Strategy For No-Limit Tournaments; Volume II: The Endgame. Two Plus Two Publications. ISBN1-880685-35-3.
• David Sklansky and Ed Miller (2006). No Limit Hold 'Em Theory and Practice. Two Plus Two Publications. ISBN1-880685-37-X.

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