[Copernicus]

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I don't know if this is a stupid question or not, but my question is regarding the probability of hitting a flush when you are at a 10-handed table, you have two hole cards of the same suit and two of that same suit hit the flop.

With 20 cards being dealt preflop, isn't there the probability that 5 cards of each suit were dealt out? If so, wouldn't you assume you most likely only have 6 outs to make your flush, not 9, and adjust your required pot odds higher in order to make a call? Surely the odds that you were the only one of 10 people to get any cards of that suit in your hand are very low. Could you actually assume that all of the 9 other cards of your suit remain in the deck? What are the odds of that happening?

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To look at in a slightly different way, when the deck was shuffled the cards were randomly placed in the deck and the deck cut. Where the deck was cut results in the nth and n+2 cards being the turn and river cards after the burn. Since each card was randomly placed, there was originally a 1-(39/52*38/51) chance of a given suit showing NOT showing up on the turn or river. However you know four cards of your suit and one card of another suit werent available to go to the turn or river because you have them. Therefore the probability that neither the turn nor river is your suit changes to 1-(38/47*37/46)=.3496. [9 out of the 47 unknown were your suit so 38 werent]. Note that the fact that a bunch of cards were dealt to other players first doesnt mean anything..we are just looking at the cards available to be placed at the turn or river spot when the cards were shuffled.

Now what does it mean to say you have 9 outs? It means you the turn and river go Suit suit (9/47*8/46) suit non suit (9/47*38/46) non-suit suit (38/47*9/46) and non-suit non suit (38/47*37/46). The first 3 are good for you and if you add the up, = .3496. (or note that the only bad one is the last one, which is what we subtracted from 1 in the first calculation. and we never considered the positions of any other cards that might have been dealt pre-flop, since they were set based on the random shuffle.