stud8 making a low?

[nearlyalex]

in stud 8 i was trying to find the probability of making a low with 3 cards to come if you have 4 cards to a low. i came up with this but wasn't sure whether it was right?

L = no. of low cards left in the deck on 4th street
N = total no. of unknown cards left in the deck on 4th street

P(making low) = (L/N) + [((N-L)(L))/(N(N-1))] + [{(N-L)(N-L-1)(L)}/{N(N-1)(N-2)}]

the 1st term on the equation is making it on 5th, 2nd for missing 5th making it on 6th and the 3rd is missing 5th + 6th and making it on 7th.

[Phil153]

You need at least one unique low card to come. This is equivalent to 1-(the probability of no unique low cards coming out)

So, the probability of making a low is

1 - C(N-L,3)/C(N,3).

Where C(N-L,3) is a combination, giving the number of ways of choosing 3 items out of (N-L) items.

To play around with various values, you can type this into the google search box as

1 - ((N-L) choose 3)/(N choose 3)

Substituting N and L for their numeric values, obviously. For example, 10 low cards remaining out of a deck of 30 gives 71.9% chance of hitting a low

[Phil153]

Just to be clear...L refers to the number of low cards left of a different rank to the ones in your hand.

[nearlyalex]

thanks, i thought it was a off as it was giving me like 90%+ chance of making a low

[Grasshopp3r]

I always bet that, though. Especially if there is a coordinated str8 or flush on your low. The worst you could have is A835, which is somewhat coordinated.