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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
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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.

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