Quote Originally Posted by RML604
Quote Originally Posted by Evansgambit
Now would the probability that villian has AA be dependent on what comes on the flop, turn and river? The answer I believe is yes, since the probability of the flop is dependent on the hole cards. This in turn, whilst not changing the actual outcome, changes the random preflop odds. If the flop comes with two aces, the chance of him having AA is slimmer, and if the flop is AAA, the chance of him having AA is zero. So a relationship exists. (I could be wrong of course)
I'm not positive about this, but I think your thinking is backwards. If the flop comes AAA, you're right that there's no chance of him having AA. But since the hole cards are dealt before the flop, isn't it correct to think of it in terms of him having AA means there is a 0% chance of the flop coming AAA?

You can use the flop to better deduce what cards he may (or more likely may not) be holding, but I don't think the flop necessarily changes the odds of what he's holding. After all, how can action A change the odds of action B when A comes after B?

So what does this mean? I don't know. But I think what it means is that if an A is on board, that doesn't necessarily mean that a player has slimmer odds of holding AA. You can say he only has 3 ways to make AA now instead of 6, so he's 50% less likely to hold AA, but he did have 6 ways to have AA when the cards were dealt.

Just because an A is showing doesn't mean he couldn't have had that card in his hand. It just means that he doesn't now.

I'm not sure if I'm right about this, especially when you consider the case of the board coming AAA, because this does mean that the probability of villain holding AA is 0%.

Anyone agree with anything I'm saying, or am I way off on this?

Now that we've seen the ace we have more information. When we decided preflop that he had 6 ways to make AA that was because we didn't know that at least 1 A was still in the deck. He only had 3 ways to make AA, we just didn't know it.

Now that we know it, we go back and revise to say that he only could have had 3 combos of AA.