Probability question

[GTDawg]

But when you originally calculate the probability of the events when dealing cards...the flop doesn't matter.

And, when you see an ace on the board, it doesn't change the probability of someone being dealt those cards...it changes the probability of someone having those cards.

Two different things.

[Talking Poker]

Yes, of course. I was never suggesting otherwise. You'll notice I said "the probability of someone holding" those cards, and not "the probabability of someone having been dealt" those cards before we saw the flop. Obviously the preflop probabilities will never change (other than when you are talking about more than one player, where the number of players makes a difference).

When I'm playing poker, I don't care about past proababilites. Once that flop hits, I don't care what the odds WERE of someone being dealt AA. I care what the odds ARE of them holding AA right now. So I need to use all the information available to me when making decisions, and after the flop, the information from the flop is available!

The most practical example I can think of is this: If you are holding KK, which of these two flops would you rather see?
A92
AA9

I would much rather see the second, because with two Aces on the board, it is less likely that one of my opponents is holding one of the remaining two Aces. Take it one step farther:
A92
AA9
AAA

Now I'd rather see flop #3, because now it's even LESS LIKELY that someone is holding a hand better than mine. You can talk about all the preflop probabilities that you want, but I promise you that your KK will be the best hand much more often against a random hand (or random hands) when the flop is AAA then when it is AA9 or when it is A92. And believing otherwise will certainly affect your game.

[Talking Poker]

I've decided to settle this once and for all, so I'm spending some time here creating a simulation. What I'm going to test is (approximately) this:

I'm going to force the above three flops and run run 100,000 hands with 10 opponents each for a total of 1 million hands dealt for each scenario. I will then see how many times AA was dealt to each player, and compare the totals.

I believe that AA will be dealt more times when the flop is A92 than when it is AA9 or AAA. Please correct me if I am wrong, but I believe MathBabe thinks that AA will be dealt the same number of times regardless of the flop (well, between the AA9 and A92 flops). Is that correct, MB?

I haven't run this yet, so I don't KNOW the answer. But I'm going to find out and we are going to settle this today.