What are the odds of this happening?

Texas Hold 'em. 7 Players.

Someone got 4 of a kind (8's) on a hand. Pocket 8's and 2 on the board.

On the next hand, someone else got 4 of a kind, and it was 8's again. 1 8 in hand, 3 on board.

The next hand, someone got 4-of-a-kind - Kings. Pocket Kings, 2 on board.

So, what are the odds of getting the same four-of-a-kind two hands in a row?

And then, getting another four-of-a-kind hand after that?

  • If this is a live game, hand shuffled deck, people eating hand held food strange bias can develop. – Jon Nov 8 '16 at 2:29
  • To answer this question requires some more information - for example whether we are to assume that anyone dealt a hand which could develop into the relevant quads will be played to showdown and a host of other variables which your question does not specify. Suffice to say, the chances of what you've described are very very very small and I would suggest you consider investigating the shuffling and dealing technique in this game. – 3N1GM4 Dec 7 '16 at 13:27
  • I just had the same dude hit quads 2 hands in a row both times with a pocket pair. What are the odds of that happening? – Coby Mar 7 at 13:59

Assuming that everyone goes to showdown every hand (which is obviously a massive and unrealistic assumption, but makes the calculation much easier), the chances of at least one player in your 7-handed game makes quads on any given hand is:

0.168% * 7 = 1.176%

For someone to get the same quads on another hand is:

(0.168% / 13) * 7 = 0.0905%

So for these two events to both occur would be:

1.176% * 0.0905% = 0.00106428%

For someone to additionally then get any other 4OAK on the 3rd hand:

0.00106428% * (0.168% * 7) = 0.000000125159328%

or roughly 1 in 8 million.

To be any more accurate, we need to model player behaviour and figure out chances that particular hands get to showdown etc, which makes the calculation non-trivial.

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.