HE:Probability:Flop

No matter how good or how poor a player's pocket cards, all hands must be quickly reassessed on the flop. A monster pocket can quickly turn into a second rate hand, and similarly a limper can turn into the nuts.

Essentially, your hand on the flop will fall into one of three types:

Made Hands - A pair or better. These hands are usually playable.

Drawing Hands - Four flushes, four straights and overcards. These hands are playable at the right odds, and have a very good chance of being made on the turn or river.

Garbage - Cards that won't improve to the level of an average hand even after the draw. These hands should be folded immediately.

First question - how strong is my hand likely to be?
Good players calculate if there is any one card that is likely to beat the hand they hold, and the likelihood of that card being in an opponent's hand. This calculation is fairly complex. However, it can be expressed more simply. If, for example, if you hold KK and there is an Ace on the flop with 9 other opponents, you're essentially betting that none of the 18 cards they hold is an Ace - possible but not very likely as about one of every 16 outstanding cards is an Ace.

Expert players consider the odds that a player may hold a 2 card combination that could also hurt. Although there are only 169 "basic" pockets pre-flop, suits become important on the flop, meaning all 1,326 combinations of 2 card pockets must be considered, each with a 1/1326 chance of being in an opponent's hand. For example:

You are lucky enough to have pocket AA, and K 9 3 rainbow comes up on the flop. What are the odds someone holds a hand that can beat you? The only hands that can are:

KK, 99, 33 - each with 6 possible combinations

K9, K3, 93 - each with 9 possible combinations

Total combinations - 45 out of 1,326 possible hands - about 3% per opponent.

As such, head to head, you are a heavy favourite. However, against nine opponents, you have about a 27% chance of facing an opponent who can beat you.