Which is correct regarding a flush draw?

[semipro]

Pardon my ignorance,
What is ncr? And please explain the math.

Thank you.

[gaming_mouse]

nCr(n,r) is the number of ways you can choose r things from a total of n things.

Thus, for example:

nCr(2,2) = 1
nCr(3,1) = 3
nCr(4,2) = 6

The formula is given by:

nCr = n!/( (n-r)! * r!)

where n! = n*(n-1)*(n-2)*...*3*2*1

Search google for "n choose r" or combinatorics for more info.

If you are not familiar with these concepts, I won't be able to explain the math to you.

gm

[mannika]

The 60% probability probably refers to the probability of the flop being two-suited, not the entire board.

Probability of flop being two suited = 1 - prob(rainbow) - prob(single suit)

prob(rainbow) = (52/52)*(39/51)*(26/50) = 0.3976
prob(single suit) = (52/52)*(12/51)*(11/50) = 0.0518

prob(two-suited) = 1 - 0.3976 - 0.0518 = 0.5506

Which is fairly close to your 60% figure. Not sure if this is what was intended when you heard that remark.

[Dave H.]

That may very well be what I read...thanx much!

[Dave H.]

[ QUOTE ]
ncr(4,2)* (ncr(13,1)*ncr(13,4)*2 + ncr(13,2)*ncr(13,3)*2)/ncr(52,5)

This works out to 14.5%. So yes, the 60% is way off.

[/ QUOTE ]

gm,

I'm struggling with this...can you help?

1. ncr(4,2) would be the number of ways to combine 4 suits two ways...CORRECT?

2. ncr(13,1)*ncr(13,4) refers to the number of ways to get 1 card of one suit and 4 cards of another suit...CORRECT?

3. ncr(13,2)*ncr(13,3) refers to the number of ways to get 2 cards of one suit and 3 cards of another suit...CORRECT?

4. the ncr(52,5) term is obvious and the '+' sign is obvious

5. What is the *2 factor that's used with both terms in the parentheses?

Thank you.

[gaming_mouse]

ncr(4,2) would be the number of ways to combine 4 suits two ways...CORRECT?

Correct.

ncr(13,1)*ncr(13,4) refers to the number of ways to get 1 card of one suit and 4 cards of another suit...CORRECT?

Correct.

ncr(13,2)*ncr(13,3) refers to the number of ways to get 2 cards of one suit and 3 cards of another suit...CORRECT?

Correct.


What is the *2 factor that's used with both terms in the parentheses?

Take two particular suits, hearts and clubs. We can have:

1 heart, 4 clubs
2 heart, 3 clubs
3 heart, 2 clubs
4 heart, 1 clubs

But the # of combos for "1 heart, 4 clubs" = # of combos for "4 clubs, 1 heart". Similarly for 2,3. So we just multiply each by 2.

gm