Omaha 8/b board question

[Stork]

What % of the time will the board allow for a qualifying low hand, without knowing anyones hole cards? How about if you and a lone opponent each have 2 low cards?

[gaming_mouse]

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What % of the time will the board allow for a qualifying low hand, without knowing anyones hole cards? How about if you and a lone opponent each have 2 low cards?

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Stork,

I don't play O/8, so correct me if I'm misunderstanding, but I think you are asking what percent of the time will a 5-card board contain at least 3 distinct low cards (ie, cards whose value is <= 8).

Number of boards with:

Exactly 3 distinct low cards and two highcards:

(8 choose 3)*4^3*(20 choose 2) = 680960

Exactly 3 distinct low cards, one of which is paired, and 1 highcard:

3*6*4^2*(8 choose 3)*20 = 322560

Exactly 3 distinct low cards, two of which are paired:

3*6*6*4*(8 choose 3) = 24192

Exactly 3 distinct low cards, one of which are tripped:

3*3*4^2*(8 choose 3) = 8064

Exactly 4 distinct low cards and 1 highcard:

(8 choose 4)*4^4*20 = 358400

Exactly 4 distinct low cards, one of which is paired:

4*6*4^3*(8 choose 4) = 107520

Exactly 5 distinct low cards:

(8 choose 5)*4^5 = 57344

Put it all together:


(680960 + 322560 + 24192 + 8064 + 358400 + 107520 + 57344)/(52 choose 5) = 0.599870718

Almost exactly 60%

I did it fast, so there may be a mistake....

gm

[Stork]

Thanks for the info, mouse. How would you solve for all boards with at least 3 distinct low cards, as opposed to exactly 3?

[gaming_mouse]

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Thanks for the info, mouse. How would you solve for all boards with at least 3 distinct low cards, as opposed to exactly 3?

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hey stork,

that is actually what i did. i just broke it down into exactly 3, exactly 4 and exactly 5, and added them up. read it over again and it should be clear.

cheers,
gm

[Stork]

My fault. I don't read too good. Thanks.