Quick for you guys

[ThinkQuick]

I know this comes up every once in a while but can someone confirm this?

Chance of at least one of 3 given cards coming on the flop:

= 1 - P(not coming)

= 1 - [ 10/13 * 39/51 * 38/50 ]

= 1 - 0.4471

= 0.5529 = 55.29%

[BruceZ]

[ QUOTE ]
I know this comes up every once in a while but can someone confirm this?

Chance of at least one of 3 given cards coming on the flop:

= 1 - P(not coming)

= 1 - [ 10/13 * 39/51 * 38/50 ]

= 1 - 0.4471

= 0.5529 = 55.29%

[/ QUOTE ]

That's correct for at least one of 3 denominations.

[AaronBrown]

This is the correct formula for one of three ranks, as BruceZ points out, but only for a spectator. If you see your hand in hold'em, you know two cards. That decreases your denominators to 50, 49 and 48 instead of 52, 51 and 50. If one or two of your cards are of the three ranks, it will decrease your numerators by one or two as well.

[BruceZ]

[ QUOTE ]
This is the correct formula for one of three ranks, as BruceZ points out, but only for a spectator.

[/ QUOTE ]

For anyone before the cards are dealt.

[AaronBrown]

And for a guy who can't remember his cards, a dealer who forgot to deal the pocket cards and a game where you deal the pocket cards from one deck and the board from another.

I didn't mean to criticize your answer, it was completely correct. I just wanted to expand on it because you don't have to make any decisions in hold'em (except whether or not to play) before you see your hand. So the combinations out of 50 or fewer cards are usually more important than the combinations out of 52.

[BruceZ]

[ QUOTE ]
I didn't mean to criticize your answer, it was completely correct. I just wanted to expand on it because you don't have to make any decisions in Hold'em (except whether or not to play) before you see your hand.

[/ QUOTE ]

Proposition bets are usually made before the cards are dealt. Unless I'm given other information, I generally interpret questions like this to be asking for the overall percentage of flops with certain properties (assuming all flops are equally probable).

[CitricAcid13]

I think it would be best to keep the denominator as 52,51,50, and change accordingly with what you had, so you can just see your chance before you know any advanced information (specifically what your cards are).

[AaronBrown]

You're right, of course, I didn't recognize this for what it is. This is the old Ace/Jack/Ten game of Mississippi riverboats. The dealer bets even money that he will get at least one of those three cards out of three cards dealt ("only three ways to win, ten ways to lose, and I'm giving even money; I'll even let you pick the three cards that give me a win").

[ThinkQuick]

Thanks all for the quick response.
you were right, I meant at least one of 3 ranks hitting the flop.

And of course I assume hole cards are yet unknown, as the prop bet would go. It's actually becoming more common here to hear people asking newcomers if they want to play 3/6/9 for a dollar a flop.