GuardiansWorlds.com - Gambling Guide

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.

Outs

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.

Types of draws

Flush draw

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).

Outside straight draw

An outside straight draw, or open-ended 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

An inside straight draw, or gutshot draw or belly buster draw, is a hand with four of the five cards need 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 roughly half that of catching an out for an outside straight draw.

Double inside straight draw

A double inside straight draw, or double gutshot draw or double belly buster draw, is a hand with three of the five cards need for a straight in sequence, plus two additional cards one gap from each end. For example, 9-x-7-6-5-x-3. An double inside straight draw has eight outs (four cards to fill either missing internal rank). Double inside straights only occur in games with seven or more cards. The probability of catching an out for double inside straight draw is the same as for an outside straight draw.

Other draws

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. 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

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 of catching two outs with two cards to come is:

Probability = NumberOfOuts / NumberOfUnseenCards * [(NumberOfOuts - 1) / (NumberOfUnseenCards - 1)]

For example, if after the flop in Texas hold 'em, a player a backdoor flush draw (e.g., three spades), the probability of catching two outs on the turn and river is (9 / 47) * (8 / 46) = 3%.

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