Basic Prob Question - Flush Draw

[Peleus]

Hi all,

I was wondering if someone could tell me when I'm heads up, and two suited cards come on the flop, that not only will a 3rd suited card come on the turn, but my opponent is holding that particular suited flush draw.

My calc says - 1/4.2 (Odds of two suited cards) * 1/9 (Odds of flopping a further two suited cards) * 1/4 (Odds of flush draw coming).

(0.24)*(0.11)*(0.25) = 0.0066, less then 1%.

Seems way two low, hence I'm asking. Am i doubling up on the odds with the two suited cards preflop and the odds of flopping two further ones?

Cheers.

[AaronBrown]

You are dealt suited cards 12 times in 51 (your first card can be anything, there are 12 out of the remaining 51 that match). That's 4/17 or 1/4.25.

Once you have two cards of a suit in your hand, there are only 11 left unseen. Flopping exactly 2 of those 11 can happen C(11,2)*39 = 2,145 ways out of 19,600 flops. That's 1/9.1.

Now that there are four suited cards in your hand and on the board, there are 9 left among the 47 unseen cards. So the chance of getting one on the turn is 9/47.

Multiply them all together, (4/17)*(2,145/19,600)*(9/47) = 77,220 / 15,660,400 = 3,861 / 783,020 = 0.5%.

[Peleus]

Hmm very interesting. I think in a heads up match from now I'm really going to have to bet according to what I think will give me the most value, rather then trying to protect against a flush draw.

[nlwolf]

[ QUOTE ]

Multiply them all together, (4/17)*(2,145/19,600)*(9/47) = 77,220 / 15,660,400 = 3,861 / 783,020 = 0.5%.

[/ QUOTE ]

I think this is incorrect.
Its an answer to the question: "what is the probability that two-flush flop will come, my opponents has matching suited hole card and third suit comes on the turn".

But we're already on the flop and its two-suited, so the probability is: P(opponent has suited hand)*P(another suit comes on the turn)

(Note: this assumes hero doesn't have suit matching 2-suited board)
Opponent has a matching suited hand: 11/47 * 10/46 = 0.051
Another suit comes on the turn: 9/45 = 0.2

Final probability = 0.2 * 0.051 = 0.01 = 1%

In reality its a bit higher, because villain is more likely to see the flop with suited hand than offsuit (eg 53s vs 53o), but I dont think its bigger than hmm 1.5%