Two cards

Early in a poker hand you often require a lot of help even after a promising start. Here the distinction between possibilities and probabilities looms large, and distinguishing between them is often what separates the good player from the pigeon.

Suppose you have three clubs, headed by the ace, and think that an ace high club flush would be a winner in this seven-card stud game. If you have received five cards and seen sixteen cards in total, of which five (including your three) are clubs what are your chances? Well, you need to get a club on the sixth card (8 chances in 36) and a club on the seventh (7 in 35). That’s roughly 1 in 5 each time. But you must do both; 1 / 5 x 1 / 5 = 1 / 25.

Of course this is possible, but it’s not very likely. Only someone with luck on their side, can expect to pull it off.

But suppose you have your three clubs in the first four cards. You still need two more clubs, but now you have three chances to get two cards. You still have roughly 1 chance in 25 of getting them in any two cards, but now there are three different ways you might succeed; on the fifth and sixth cards, on the fifth and seventh cards, or on the sixth and the seventh cards

A player should always remember that knowing the number of different routes to achieve a given result is often the key to quick, short cut estimation of the relevant probabilities of getting particular Poker hands.