Would it be around 600-1 or much more as its 3 times in row?

Thanks

Do you mean on the next three deals or sometime in your life?

3 consecutive deals/hands

A friend just had it.

Right, but the chance that happened is 100%. There are at least two ways to answer the question as Didace alluded to. We can easily calculate the chance this happens to a player on the very next 3 hands dealt starting now. Or we can calculate the chance it happens within the span of some amount of hands played.

First, heads-up or not is irrelevant, the chance for it to happen to your friend specifically, or to you, is exactly the same no matter how many players are in the game.

So, in the example you gave, if your friend has played a million hands then this event may be very likely to occur in that span. You having witnessed it is just coincidental to that.

To be dealt AA on the very next 3 hands dealt to you starting now, the chance is 1/221^3. Or about 1 in 11 million. But it would probably be equally interesting to you if it happened with KK KK KK, or JJ JJ JJ. So for any identical paired rank to be dealt on all 3 of your very next 3 hands dealt, that chance is only about 1 in 49,000.

But the more relevant statistic is within some context. So the chance you get 3 AA in a row sometime in the next hundred thousand hands you are dealt, is about 1 in 108. And if we count any identical paired rank happening 3 times in a row, it's 87% to happen at least once.

So it matters how you ask the question.

I think you mean 1/17 * 1/49,000. 1/17 is the probability you get a pair the next hand and 1/49,000 is the probability you get the same pair the next two hands.


Another way is to divide the 11 million by 13.

Good catch, thanks.

Thanks for the very detailed and informative answer. Fascinating for a non maths guy even though I can work out pot odds etc quite easily I cant do any of this stuff. There must be players who have played a million hands + who have had AA or some other pair 3,4,5,6 etc + times in a row then . Wonder what the record is.

This may be a dumb question and its 03.06 and I am tired but what are the odds then for 1 pair of Aces worked out for 100,000 hands. Must be much lower than 1/221? ....Its weird to me though that the chance of one pair of Aces is 1/221 but AA 3 times in a row is 1/108 sometime in 100K hands.




Does this change the 1/108 calculation?

No that was correct. As for AA, you expect one for every 221 deals, on average. So in 100,000 hands you should get about 100000/221 or about 450 AA hands. Was that your question?

Did you expect it to be more probable or less?
If you mean the chance of getting AA at least once in 100k hands, that's 1 - (220/221)^100000, which WolframAlpha says is

99.99999999999999999999999999999999999999999999999 999999999999999999999999999999
99999999999999999999999999999999999999999999999999 99999999999999999999999999999
99999999999999999999999999999999999999890171839539 680249960190759616770103312683173 %

I think you're missing a 9.

OK got it thanks.

Well I can see now that its not so special within 100000 hands. I was thinking of asking the rigged threads as I was thinking it was the RnGs way of sucking me in or even tilting me as all my 3 consecutive AAs didn't produce very much as it was in a $1 spin and go. But now I realize or I hope I do that massive volume is need in this game. Time for a bigger monitor.

Thanks everyone

Three AA in a row to one player is reason to doubt the quality of the shuffle. Lots of people are sloppy shufflers, even professional dealers.

Suppose that the two Aces are gathered together and exactly one card is inserted between them in a riffle shuffle. The chance of getting AA on the next hand jumps from 1/211 to 1/48. The chance of getting three in a row is now 100 times as great.

Of course, a sloppy shuffler doesn't always insert exactly one card in between two cards that started out together. But sloppy shuffling does result in statistical similarities between hands, two cards that were close together last hand are more likely than not to be close together this hand.

True in live poker, but not online obviously. Unless someone believes a deal rigged like this would somehow benefit the poker site.

You're right of course. Electronic shuffles don't have the same issues. If you were to get suspicious, your first guesses would be the site is cheating (as you suggest) or that some glitch was causing the same hands to be repeated.

I've been away from forum. Thanks for your advice plus the other recent advice too. I am wondering about the glitch thing you suggested. I have seen tons of weird coincidences in life outside poker so I don't doubt that these things happen to people.

I know this is an old thread, but I want to practice my math. Here is the odds of being dealt aces each of the next 3 hands. Someone please correct me if incorrect


(1/221) * (1/221) * (1/221) = 9.264525455719691e-8
= 1: (1/9.264525455719691e-8) * (1-9.264525455719691e-8)

= 1:10793860

almost 11 million to 1

That's right.

1 in 221^3 chance, which is odds of (221^3 - 1) to 1 against.

Hey,

This just happened to me. Felt obligated to post. It happens, guys. It happens.

Global Poker PLO50
Lost all three; was put in by opponents twice. Rough game sometimes.

GL out there Gents!