Odds Question

[mojorisin24]

So last night I'm playing in a tournament and am dealt pocket Queens as the short-stack. I raise, and only the big blind (who is chip leader) calls. The flop is 7-8-J rainbow, he checks, I move all-in. He quickly calls and turns over 9-10, for the nuts off the flop. Needless to say, I nearly threw up in my mouth and walked away shaking my head. My question is: what are the odds of flopping a straight like that?

[Mike Haven]

you'd probably have thrown up if he'd turned over 77, 88 or JJ, as well

i'm not sure that this is correct but the way i would look at it is you know five cards, and therefore there are 47 x 46 = 2162 ways of dealing him his two

there are 3 x 2 = 6 ways each to deal him 77, 88, or JJ, = 18, and 8 x 4 = 32 ways of dealing him T9 or 9T, = 50 total

which means it is 2112 to 50 = 42 to 1 to get your second dinner free

[mojorisin24]

Thanks a lot

[skipc]

actually, the true odds are 75.6 to 1. not that i am a math guru, i looked it up in mike caro's odds tables.

good luck
skipc

[Mike Haven]

the way MC has done it is by saying there were 50 x 49 = 2450 ways of dealing him his two before the flop

there are 8 x 4 = 32 ways of dealing him T9 or 9T

which means it would be (2450 - 32) to 32 = 2418 to 32 = 75.6 to 1

but this is wrong in this case because we know the three flop cards (which obviously could not have been dealt to the other guy, or, vice versa, could not have flopped to create the problem we are being asked to solve)

so it should be ((47 x 46) - 32) to 32 = (2162 - 32) to 32 = 2130 to 32 = 66.6 to 1, if we leave out the pairs i mentioned earlier

[Lost Wages]

If you hold QQ and he holds T9o, what are the odds that he will flop a straight? I think that is your question.

He can flop a straight with 678, 78J, 8JQ or JQK. He can flop 678 or 78J 4*4*4=64 ways each and 8JQ or JQK 4*4*2=32 ways each (you hold 2 queens). Total ways to flop a straight = 192. With 48 unseen cards there are a total of (48*47*46)/(3*2) = 17,296 possible flops. Probability = 192/17,296 = 1.11%. Odds = (1-.0111)/.0111 = 89.1:1.

Caro's number aren't right because they answer the question, "If I have a max stretch connector, what are the odds I will flop a straight?" In this instance, you have more information.

Lost Wages