Omaha high odds calculation - for Buzz

Hey Buzz, a friend of mine recently played a hand against me which i won, and he accused me of sucking out against him. I told him that even though he had flopped the nuts i was a strong favourite to win the hand but he doesn't believe me, and won't trust my calcualtions. Can you work out the odds of each hand winning here.


My hand (1) AcKcQdQh vs his hand (2) Th9h8s6d


Flop was QcJc8d.


As you can see i have top set, the nut flush draw and a wraparound draw to a higher straight than his hand, which apart from two running 8s cannot improve (except of course for making a smaller full).


All the money went in on the flop, and turn was 7c, river Kd giving me both the better straight and the nut flush.

Pete - Never a guarantee my math is correct.

Don't have time to check it for errors today.

I'll check it tomorrow and post a correction if I'm wrong.


IMHO the probability of your winning is 543/820 = 0.662


making the odds 543 to 277 in your favor,

or almost two to one in your favor.


Hope this helps.


Buzz

Thanks Buzz. Same figure i came up with and he now accepts my play was correct.

P(straight wins)= P(he gets 2 of the 25 goods cards w/o the board repairing)+P(quad 8's)


(the 25 good cards are all the cards wchich don't pair the flop, and aren't clubs or T's)


P(straight wins)= 25C2 - 23 +1 /(41 C2)


= 278/820= 0.339.

Suspicious - Thank you. You are correct. I missed the quad eights.


Pete - Please amend my original reply to read:


IMHO the probability of your winning is 542/820 = 0.661

making the odds 542 to 278 in your favor,

or almost two to one in your favor.


Buzz