Newbie - Odds Calculation Question

[Pyle]

I understand (or am told) that to calculate the odds of hitting a flush after the flop when holding 2 of the same suit and having 2 hit the board is 1-[(38/47)*(37/46)] =.35 or 35%. This is because you need to calculate the odds of NOT hitting your flush.

I don't understand. Why cant you calculate it as the odds of hitting your flush, like so:
9/47 + 9/46 = .387 or almost 39%.

I am obviosuly not a math wiz, but I dont understand why the # is different, or why this isnt the same thing...

Sorry for the simple question.

Thanks - been lurking for a while and am getting up the nerve to ask some questions.

[Lost Wages]

Why cant you calculate it as the odds of hitting your flush, like so: 9/47 + 9/46 = .387

Hi again /images/graemlins/smile.gif, because sometimes you will make your flush on the turn so you are double counting the times that you draw a flush card on both the turn and river.

Lost Wages

[Kluddeludde]

It is possible, but you are doing it a bit wrong...

P = 9/47*38/46 + 38/47*9/46 + 9/47*8/46 = 0.35 = 35%

where the last term is the probability that two more of your suit appears.

Kludde

[BruceZ]

[ QUOTE ]

I don't understand. Why cant you calculate it as the odds of hitting your flush, like so:
9/47 + 9/46 = .387 or almost 39%.

[/ QUOTE ]

This is often asked. The probability of hitting on the river is 9/46 only after you miss on the turn, so you must multiply 9/46 by the probability of missing on the turn which is 38/47.

9/47 + 9/46 * 38/47 = 35%

You can also do this:

9/47 + 9/47 - (9/47 * 8/46) = 35%.

That is, before the turn, the probability for hitting on either card is 9/47, but since this double counts the times we hit it on both cards, we subtract off the probability of hitting twice.

[Pyle]

Great replies - people like you make these forums so helpful.

Thanks again!