so, i'm not the greatest math wizard, what are the odds of being dealt the same hand back to back? and what are the odds of being dealt the same hand back to back to back? if you could show your work, that'd be great, i'd like to learn from it.

depends on the hand, but if the probability of being dealt the hand once is p, then the probability of being dealt it twice in a row is p*p and the probability of being dealt it three times in a row is p*p*p

If you mean the exact same hand, including suits, the chance in 1 in 1,326. There are 52*51/2 = 1,326 different hands, and they are equally likely. Three times in a row is 1 in 1,326^2 or 1 in 1,758,276. This assumes that you only deal two (or three for the second answer) hands. Over the course of 1,000 poker hands, you have 999 chances to get the same hand twice is a row, so there's a 53%, 1-(1-1/1,326)^999 = 0.53, chance it will happen.

If you mean the same hand like "a pair of nines" or KJo, it does depend on the hand. You can get a pair six ways, so it's 6/1,326. You can get unmatched suited cards 4 ways, so it's 4/1,326. You can get unmatched unsuited cards 12 ways, so it's 12/1,326. You can get unmatched cards without specifying the suits 16 ways, so it's 16/1,326. In all cases you square the answer to get the probability of three times in a row.

It's means the rigged dealing software has crashed and started over again.

yes, i meant the same exact hand 3 times in a row, suits and all. thanks for the help.

I'll take a shot but I believe this what Aaron has already said.

Out of 52 cards, there are 52*51 hands=2652 that can be dealt. However, AcAh is the same as AhAc so we take out duplicates and get 1326 unique hands (taking suits into account).

We start with a random hand. The chances of getting the same hand again is 1/1326. The chance of getting the same hand a third time is again 1/1326.

Therefore, my guess is that the chances of getting the exact same hand three times is a row is 1/(1326*1326)=1/1758276=.00000057 or .000057%.

That's almost a one in two million chance so not very likely at all. Off the top of my head, it would be unlikely in one's lifetime.

1500 hands a day for 7 years makes you a favorite to see it happen by my math

(1758245 / 1758246) ^ (500 * 365 * 7) ~ 48%

So it's unlikely, but not unheard of.

I just asked about this over here before I found this thread.

Today I got dealt [7h Tc] then [Tc 7h] and then [Th 7c]. I've played 130k lifetime.

OK, what about the same hand to the river, like quad Ks for example?
And how can this be calculated, say instead of back to back hands, rather within (ie) 50 hands, or even within the same tourney (within X hands)?

Cant edit post for some reason...
Even limit this to just the flop, not all the way to the river.

As Aaron pointed out, problems like this can only be answered in context, and not in isolation as if somebody only plays 3 hands in their life. The answer in that context is nonsense, but what that answer actually gives you is the chance for the event to happen on the very NEXT 3 hands. Not the ones that already happened. You only notice it when it occurs, and that is always within a series of X hands. The calculation for that is in Aaron's post. And on a message board the context is in reality even larger than your hand history, because out of everyone who sees the event, somebody in that set is bound to post it. That's why events that seem amazingly unlikely are posted all the time. Because they are expected to happen all the time in a large enough population.

But those aren't all the same! Allowing for reversal of suits makes it much much more common.

And the last one shown has totally different cards.
The chance to be dealt T7 then T7 is exactly the same as the chance to be dealt T7 then 24. They are just different cards.

A bit of a necro but I got the exact same hand back to back to back.


Edit: not sure why I get a 404 so here is the link.
https://www.dropbox.com/s/uo76t10p0c...20row.png?dl=0

Still, with the number of hands dealt (particularly if you're playing online) it's not all that unlikely to occur.
From what I gather you can see up to 250 hands an hour in Zoom. Let's say someon is 4-tabling and playing 6 hours a day then that's 6000 hands per day.
At that rate - if he plays 6 days a week -he's can expect to see this happen roughly once every year.