I'm not great at maths but I was curious about this. what is the probability of getting quads twice in a row? this happened the other night to the SAME guys in one of my home games.

thanks,

sam

Your question is poorly defined and therefore, depending on how someone interprets it, there are 0 right answers or many right answers.

If you want a single right answer, provide more detail. It was a single person who got back to back quads? Would you have been impressed if it were someone other than that specific person this happened to? If so, how many people were playing in the game? What if they got quads followed by a royal flush? Would you still find that interesting? If so we should include the probability also. What game were you playing? Quads is easier to get omaha than hold'em. And it is even easier to get in a game I play where everyone gets dealt 52 cards.

You should also realize that to get quads twice in a row someone first has to get quads. So if you don't start counting (i.e. predicting that someone will get it twice in a row) until after they already have the first one, the odds are the same as the getting quads once. The cards don't remember that a player was just dealt quads.

FWIW, if you have two independent events and you want to know their combined probability, it is simply p(event 1) * p(event 2). But again, that is assuming you don't know the outcome of event 1 in advance.

The most useful interpretation of the question is, "What is the chance that after I have gotten quads in hold'em, I get it again on the very next hand assuming I play the next hand all the way to the river?" (or until quads aren't possible). And as Sherman said, that is simply the chance to get it once. In hold'em that's 1 in 595.

It was likely the first occurrence that made it interesting, not that out of the blue someone wants to know "what is the chance I get quads on my next two hands". As pointed out, that's a different question but not a very useful one. If you want to know it, it's just the above squared or about 1 in 354K, and that assumes playing to the river on both of your next hands. And if we are considering it happening to anyone at a 9-player table, then about 9x more likely than that.