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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