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As mentioned in a previous thread it can be a bit of a piggy if two players in a pot both flop a set. Now it doesn't really serve any useful purpose but I thought I would go through the process of working out how often this occurs. There's really no getting away from putting all your chips in when this happens but at least you'll know just how many times this is likely to happen.

I'm going to skip the probability of both people being dealt a pocket pair as we're primarily only interested in the chances of them both flopping a set when they both have one. For this we shall say one player has pocket kings and the other has pocket aces, a definite stack buster methinks !

OK first of all we have to work out how many different possible flops there are. OK well we know what four of the 52 cards available are, AA and KK so that leaves us 48 unknown cards. How many possible three card flops are there with 48 cards.

The formula to work out how many possible combinations of anything being selected from anything is: N!/ ( (N-S)! * S! ) Where N is the number of things, S is the number of things being selected. The ! is factorial. 5! = 5*4*3*2*1 , 7! = 7*6*5*4*3*2*1 etc. Scientific calculators have a factorial button usually denoted x! or n! So from a 3 card flop of 48 cards we get: 48! / ( (48 - 3)! * 3! ) = 17 296 so 17 296 possible flops there.

Right we now need to work out how many of those flops will have both an ace and a king. So our flop must be of the form A-K-X where A is any ace, K is any king and X is any of the other remaining cards. We have a choice of 2 of the remaining aces or 2 of the remaining kings of course and then that leaves 44 remaining cards. Note that I have left out flops where one person flops quads and the other a full house.

So we have 2 * 2 * 44 = 176

176 of those flops will contain both a king and an ace with another card (whch isn't the other king or ace): 176 of 17 296 flops will see both players flopping a set.

176 / 17 296 = 0.01017576

I will round up and that makes for a probability of 0.0102 To get this as a percentage we multiply by 100% ie 0.0102 * 100% = 1.02% chance of this happening.

There's the answer, it's a 1.02% chance of both players flopping a set. If you don't like things expressed in percentages we can take the figure in traditional odds style: 100 / 1.02 = 98.039 So approximately a 1 in 98 chance of it happening; or 97/1 shot if you prefer traditional fractional odds.

Ultimately, both players flopping a set doesn't happen very often so you can't be worrying about it too much. The one time you do go bust is more than made up for by the numerous times the raiser cannot throw his AA or KK as an overpair to the board and you bust him.