Does a formula exist?

[benedetti]

Hi,

I would like to have a formula that allows to calculate (approximately) as I go along the probability of another player having a particular card, taking into account the number of players in the hand.

For instance, say that I am playing A3s. The flop comes A-A-9. How can I calculate in that very moment what are the chances of another player having the other A if there are 4 players in the hand?

Say that I have Jh-Th and the board shows 3h-7h-Qh-8h. How can I figure out the probability that one of the other 3 players have either Kh or Ah?

I would like a short cut that gives me a good approximation. Thanks very much for your help.

[Paul2432]

there isn't a formula for this.

Paul

[Nottom]

You can come up with an approximate chance just by doing some quick math.

In case 1, there is 1 A remaining and your opponents hold 8 unseen cards. Just simple math tells you that in a group of 8 random cards there is approx an 8/47 ~ 1/6 chance that the remaining A is out there. You can do a similar calculation in the second case.

The problem with this is that it assumes a random distribution, which is usually not the case. In the AA9 problem, there is a better than average chance that the A is out there because people are more likely to play an A than any other card. If the flop were 229 on the other hand, it would be less likely someone had the case 2.

[benedetti]

But the second case is not that straightforward. 2 cards, 8 cards and 46 cards. How do you get the approximation in this case? Is simply 48/16?