low hand

[spaminator101]

what are the odds against there being a low hand possible im omaha8

[LetYouDown]

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.

[jba]

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.

[spaminator101]

no three cards A-8
i no 1/20 isnt right as there is usually a low hand

[jba]

[ 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?

[Tom1975]

You're forgetting about situations where the board pairs low cards. For example no low is possible on a board of 2233K or 775JQ

[spaminator101]

ok i got it now

[MickeyHoldem]

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