Hand probabilities.

[Jim Morgan]

Suppose I have Ad2d3hKh in a 10-handed game.
Somewhere I have seen a stat that says that there is a 36% chance that someone was dealt the nut heart draw.
However, I am not so sure this number is accurate (though in real play, I am sure it is close enough)
If the flush never shows, then I really don't care about that opposing AhXh. The only time I care is when I see the board. But now the deck composition is very different. The pool of unseen cards is no longer 48 cards with 11 hearts.
Assuming we are at the river, the pool of unseen cards is down to 43 and only 8 of them are hearts.

It seems this makes the K-high flush quite a bit more likely to be the winner. On the other hand, I don't know how the 36% figure was calculated or if it accounted for the board cards in this way.

I believe a similar situation exists with nut low (A2 for simplicity). But in this case I think it weakens our holding. Once the 5 cards on the board have no A or 2, it is MORE likely that we are facing another A2 than it was before we see those cards. What I don't know is how this impacts the probability or if that is already accounted for when people speak of the odds of having the only nut low.

Anybody know the gory details here?

Jim Morgan