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Odds

For a given number of outs, i.e. cards that would complete a drawing hand, there is a unique probability that such a card will be dealt next. This probability is usually expressed as odds, or odds against; a probability that the draw does not hit.

Odds against = failures : successes

For the next card, this means

Odds against = unhelpful cards : helpful cards

or

Odds against = unknown cards - Outs : Outs

Example (Texas Hold'em):

Player	Flop

The players has a draw to a flush in hearts. There are still nine other hearts in the deck, so he has nine outs. There are five cards showing so the player knows that these cannot be dealt again. Since the deck has 52 cards in all, 52-5=47 cards could show up on the turn. Of those, 47-9=38 are worthless to the player. The odds against the player hitting another heart are therefore

Odds against = 38:9 = 4.2:1

In other words, the flush will be hit about 19% of the time. 35% of the time, he will have completed by the river, giving him odds of 1.9:1.



Related Topics:

Outs, Pot Odds