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. For example, in seven-card stud, if a player’s four of the first five cards are all spades, but the hand is otherwise weak, he is drawing for a flush. If an opponent has a made hand that will beat the player’s potential flush, then he is drawing dead, that is, even if he make his flush, he will lose. In contrast, a made hand already has value and does not need additional cards to improve.
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 of catching an out with one card to come is:
- Probability = NumberOfOuts / NumberOfUnseenCards
The probability of catching at least one out with two cards to come is:
- Probability = 1 − (NumberOfNonOuts / NumberOfUnseenCards) * ((NumberOfNonOuts − 1) / (NumberOfUnseenCards − 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.
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