Probability question

[MathBabe]

I almost posted the other day and said exactly what you said, but I realized later he's actually right. It's a question of conditional probability.

"What's the probability of the fourth Ace in play GIVEN there are three Aces on the board".

A = three aces on the board
B = exactly one hole card ace

P(B|A) = P(A and B)/P(A)
=1/1353 / 1/553
=553/1353
=1/2.45
which is about 40%.

My calculations assume 10 players, therefore 20 hole cards, and the three Aces being anywhere on the board - not just on the flop.

I guess we'll have to agree to disagree...

[Talking Poker]

Earlier in this thread, you said it was 74%. So, which is it?

I'm not certain I follow your exact math above (I don't know where you came up with those numbers nor do I understand why you changed from the flop to the full board), so let me ask you this: What's the probability of the fourth Ace in play GIVEN there are four Aces on the board? Please use the same "math" you used above to show me how this is also 37%, as I believe you claimed earlier in this thread (you said it's always 37%, regardless of what comes on the flop).

As for agreeing to disagree, I don't see how we could agree to do that. There are right and wrong answers here.

I'm also surprised more people haven't weighed in on this thread. Is it really over everyone else's head, or do they just not care?

[GTDawg]

That's the wrong way to look at probability. You don't put probabilities on events that have already happened. You put probabilities on events that are about to happen given past events.

If you want to ask what the probability of someone having the fourth ace, given AAA flop...sure we can calculate that.

What are the chances of getting any one single hand in poker? Do those probabilities change by what card comes on the flop...turn...river?

The probabilities don't change based on what cards come out afterwards. Why?

[Talking Poker]

No, the PAST probabilities don't change. But I promise you that it is FAR less likely that someone was dealt AA when the flop comes AAA than when the flop comes 234. Yes, when the cards were dealt, the probability for any given player to be dealt AA was 220:1. We all agree with that. But that is completely useless information to us now that we've seen the flop. When putting our opponent on a hand (why else would we care about these probabilities in the first place?), we need to use all of the information available to us, including the flop. To ignore it and think that there is still approximately a 5% chance that someone at the table is holding AA would be asinine.

I really don't get what is so difficult about this. Maybe I'm WAY OFF in my thinking here (that certainly could be the case), but this just seems like common sense to me.

I use the AA hole cards with an AAA flop because I think it is so obvious and simple to understand. A more practical application would be what I posted (and no one responded to) in this post: