Probabilities that Opponents will flop a given hand

[richrf]

Hi,

I have been experimenting with Texas Calculatum, and I have noticed that the odds that an opponent, in say a 10 player game, of catching a hand (flush, full house, straight, etc.) are much higher than I had originally thought. Is there a book, article, or software that can help me better understand the probabilities that an opponent will have a given hand after a flop. Thanks.

Rich

[suitedaces84]

Preflop this is pretty easy.

Let's say you have pocket kings and you're worried about someone having pocket aces...

Odds of a specific person getting pocket an A for their first card; 4/50 = .08
Odds the same person getting another A; 3/49 = .0612
Odds of specific person getting pocket aces; .0612*.08 = .00489
Odds of specific person not getting pocket aces; .9951
Odds of player 1, player 2...player n all not getting pocket aces = .9951^n

So if you're under the gun ten handed with pocket kings...

the odds of someone else not having aces= .995^9 = .952
the odds of someone having pocket aces = .048 or 4.8%

If four players have already folded playing ten handed...
the odds of someone else not having aces; .9951^5 = .976
the odds of someone else having pocket aces; .0245 or 2.4%

Let's say you have AdKd the flop comes AcKc3s (he checks, you bet, he calls), the turn is 8h (he checks, you bet, he calls), and the river is 9c (he bets). You perform a quick calculation and determine there is a very low percentage chance he has two clubs. So you raise, he re-raises, you cap it and discover he has a flush. That's strange. Was this just a fluke? No, once your oppoent makes a move of any kind (fold, check, call, bet, or raise) he no longer has two random cards and these numbers are worthless.

[gol4pro]

If you're good at math... I posted "probability for dummies" in the online holdem forum a while back.

But nobody understood it so I guess I'm not much of a teacher.