Holdem probability question

[BlueBear]

Hi,

Assuming that I flopped a middle set, what is the probability there is a higher set assuming there is 9 other random hands? (For example, i hold 66, table flops, 7 6 2, what is the probability that someone among there other 9 other random hands hold 77).

Secondly, assuming that I flopped the king-high flush, what is the probability that someone else has flopped the ace-high flush assuming that there are 9 other opponents (eg. I hold Kxs, flop 2s 4s 6s, what is the prob that someone has Axs assuming 9 other opponents).

It would be much appreciated if anybody could enlighten me on how to do these calculations. Thanks.

BlueBear

[AJo Go All In]

ok i'll try.

well in the first example there are 3 combinations of top set here. 47 unknown cards, so 47C2 = 1081 combinations.

so the prob. of someone having it is 1 - (1078/1081)^9 = .0247

similar calculations for the flush example, except now there are 7 combinations, so 1 - (1074/1081)^9 = .0568

hmm, not really sure if this is right, don't really want to think about it/

[BlueBear]

Thanks. Look's absolutely right to me.

[SaintAces]

[pzhon]

[ QUOTE ]

Secondly, assuming that I flopped the king-high flush, what is the probability that someone else has flopped the ace-high flush assuming that there are 9 other opponents (eg. I hold Kxs, flop 2s 4s 6s, what is the prob that someone has Axs assuming 9 other opponents).


[/ QUOTE ]

The exact calculation here is relatively simple.

There are 47 cards you don't see, 18 of which are held by your opponents. There is an 18/47 chance that the ace of your suit is in someone's hand. If so, then 7 of 46 possible kickers hurt. The probability is (18/47)(7/46) or about 5.83% that Axs is out there.