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- This article refers to poker terminology relating to drawing cards or drawing hands. Go here for an article dealing with various draw poker games.

A poker player is drawing if he has 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, he is 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 he makes his desired hand, he 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.

The probability $P\_1$ of catching an out with one card to come is:

- $P\_1\; =\; frac\{mathrm\{outs\}\}\{mathrm\{unseen\},,mathrm\{cards\}\}$

The probability $P\_2$ of catching at least one out with two cards to come is:

- $P\_2\; =\; 1\; -\; frac\{mathrm\{non\},mathrm\{outs\}\}\{mathrm\{unseen\},,mathrm\{cards\}\}\; times\; frac\{mathrm\{non\},mathrm\{outs\}\; -\; 1\}\{mathrm\{unseen\},,mathrm\{cards\}\; -\; 1\}$

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.

- $P\_\{rr\}\; =\; frac\{mathrm\{outs\}\}\{mathrm\{unseen\},,mathrm\{cards\}\}\; times\; frac\{mathrm\{outs\}\; -\; 1\}\{mathrm\{unseen\},,mathrm\{cards\}\; -\; 1\}$

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.

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.

- Poker jargon
- Poker probability
- Poker probability (Texas hold 'em)
- Poker probability (Omaha)
- Poker strategy

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Last updated on Monday August 11, 2008 at 10:43:43 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday August 11, 2008 at 10:43:43 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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