Odds to make a low in 7 Card Stud Hi/Lo

[Manimal]

How do you calculate this? For simplicity's sake, let's assume that you must make an 8 low or better after starting with 3 cards 8 or lower.

[gaming_mouse]

[ QUOTE ]
How do you calculate this? For simplicity's sake, let's assume that you must make an 8 low or better after starting with 3 cards 8 or lower.

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Ignoring the other players' face-up cards...

We may complete our low hand by:

1. Having exactly 2 new low cards in the four remaining cards.
2. Having exactly 3
3. Having exaclty 4

Number of ways for each case:

1. (5 choose 2)*4*4*(35 choose 2) = 95200
2. (5 choose 3)*4*4*4*(39 choose 1) = 24960
3. (5 choose 4)*4^4 = 1280

Final answer:

EDITED to fix denominator:

(95200 + 24960 + 1280)/(49 choose 4) = 57.31%