#1
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low hand
what are the odds against there being a low hand possible im omaha8
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#2
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Re: low hand
In my first calculation, I came up with 50.99% which I'm almost positive is wrong. Interesting question. If no one answers, I'll give it a run on my next break.
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#3
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Re: low hand
we need at least three cards 9-K, right?
assuming no known hole cards the number of boards containing at least three cards 9-K is: (20*19*18*49*48/5!) and the total number of boards: C(52,5) probability of the board precluding a low is (20*19*18*49*48/5!) / (52*51*50*49*48/5!) 0.0515837104 or about 1/20 hands. |
#4
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Re: low hand
no three cards A-8
i no 1/20 isnt right as there is usually a low hand |
#5
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Re: low hand
[ QUOTE ]
no three cards A-8 i no 1/20 isnt right as there is usually a low hand [/ QUOTE ] uh ok 19/20 then edit: what I mean is, I was calculating the odds that no low hand is possible (this is what preclude means). in order for no low to be possible, there must be at least three cards 9-K, right? |
#6
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Re: low hand
You're forgetting about situations where the board pairs low cards. For example no low is possible on a board of 2233K or 775JQ
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#7
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Re: low hand
ok i got it now
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#8
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Re: low hand
Not taking into account the possible player holdings.... the board will be low hand friendly 60.0904977% of the time. (meaning that there will be atleast 3 different low cards showing)
So there will be no low hand 39.9095023% of the time. Here's my calculations for those who may want to check/correct... Possible boards = 52c5 = 2598960 let a,b,c,d,e be different low ranks the board must contain 1 of the following combinations a,b,c,high,high = 8c3 * 4^3 * 20c2 = 680960 a,b,c,d,high = 8c4 * 4^4 * 20 = 358400 a,b,c,d,e = 8c5 * 4^5 = 57344 a,a,b,c,high = 8*6 * 7c2 * 4^2 * 20 = 322560 a,a,b,c,d = 8*6 * 7c3 * 4^3 = 107520 a,a,b,b,c = 8c2 * 6^2 * 6*4 = 24192 a,a,a,b,c = 8*4 * 7c2 * 4^2 = 10752 adding these together we get 1561728 boards that are favorable to a low hand. 1561728 / 2598960 = .600904977 |
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