Hello,Mathematicians! Probability question on...
 

7-card stud.
Let's assume that U have (4,3) 4 4 on 4th and there are 3 other players in.
Player1 has (5 10) 10 10
Player2 has a flush draw
Player3 has a flush draw.

Can u give me an approximate ball park idea of the probability of winning at the showdown with your final hand if ALL players remain thru 6th Str.??
I know that I'm giving u very little information to go on--but use your imagination(LOL)! Fill in the gaps! [img]/forums/images/icons/laugh.gif[/img]

Happy pokering , Analysts!

Sitting Bull

Re: Hello,Mathematicians! Probability question on...
 

My estimate:

Your chance of making boat or quads by river, assuming your cards are completely live the whole way:
1 - (38/42 * 31/38 * 24/34) = 48%

The guy with trip 10's has the same odds of filling or making quads. Your odds of winning is the odds of you filling and the other guy not filling = .48(1-.48) = 25%.

I don't see why the flush draws matter. You need to fill to win anyway, because of the trip 10's, so it doesn't matter if the flush draws get there or not. It doesn't impact the percentage of the time you win.

Simulation:

With credit to www.twodimes.net/poker pokenum simulator (well, it's not exactly a simulator, as it figures out all possible combinations, to get an exact answer):

7-card Stud Hi: 500000 sampled outcomes:

cards win %win lose %lose tie %tie EV
4s 4c 8d 4h 134746 26.95 365254 73.05 0 0.00 0.269
Ts Tc Td 5h 239771 47.95 260229 52.05 0 0.00 0.480
Ah Jh 7h 3h 77762 15.55 422238 84.45 0 0.00 0.156
Kd 9d 6d 2d 47721 9.54 452279 90.46 0 0.00 0.095

The sim result and my result are fairly close...

-- Homer

Goodafternoon,Homer! Thanks!