Number of players dealt in affecting flush draws?

[PantsOnFire]

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So in a 6 handed game, you are dealt 2 hearts. On average 3 hearts are dealt pre-flop in a 6 handed game. When the flop comes with 2 hearts we should therefor on average have 8 outs out of 37 cards that are left in the deck yes?

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In statistics, you must use all knowledge you have at the time to make calculations.

So if you have a 52 card deck, then 3 hearts on average will be dealt to six players. However, once you know that you have two hearts, it is incorrect to say that there will only be one more heart in the remaining 5 hands.

Fundamentally, the remaining hearts will be equally distributed among all the remaining unseen cards so the number of players is irrelevent.

Let me try an analogy. There are 2 white cards and 2 black cards, all face down. You get one card and your opponent gets one card and the deck has two cards.

You look at your card at it is black. What are the chances of flipping the first card in the deck and matching a black card. I would say it is one in three since there are 2 white cards and 1 black card unseen.

Before the deal the preflop odds are as follows. Since the deck is 50% black and 50% white then out of the two cards dealt, one will be black. This is the same as saying preflop that out of 6 players there will be 3 hearts. So now, when you see your black card, using your example that 2 of the 3 hearts are in your hand, you are saying that you have used up the black card for you and your opponents hand and therefore the other black card must be in the deck. Then, the chance of that first card being black becomes one in two. It should be clear that this isn't correct.

I have probably proved nothing but I had fun.

[T50_Omaha8]

I made a post a while ago atempting to refute the notion that you should consider other players and their actions in order to calculate the probability of filling your draw. It's not the exact same problem, but I think it illustrates how small the effect, at best, could possibly be.

Link

[Usagi_yo]

I think, and somebody tell me if I'm grossly wrong. that with XX unkown cards dealt and YY remaining cards that yea, you can calculate the most probably distribution.

But is it useable information? Not really. Because the sum total of all the other unfavorable and favorable distributions will erode its usefullness.

Does how other players act give you information on potential flushes? Most definetly.

Case in point. NL game, seemingly abandoned pot, I'm in BB with A9s and I back door the stone cold nuts. I jokingly over bet the pot by about 10X and actually get raised by the 2nd flush.

His comment after the hand was: "Wow, the likely hood of both of us having a flush are astronomical". My thought was: "No, as far as you were concerned, the likelyhood of both of us having a flush after I bet 25X the pot on the river was about 99.9999... Given the .0111111111% some freak accident like in the process of checking I accidently said all-in.

[T50_Omaha8]

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But is it useable information? Not really.

[/ QUOTE ] So it's not useful knowing whether you'll make a draw 90% of the time as opposed to 5% of the time?

[Usagi_yo]

Thats not what I said.

What I said is that assuming standard distribution, on the remainder of the cards dealt out is not usefull information.

It's different in bridge when you are trying to finess one more of a suite because you know there is one and only 1 card of that type out and one of two players has it. But if there are 3 cards out, you have one. Whats the distribution of the remaining two?

1-1-0-1, 1-2-0-0, 1-0-0-2

See the point now? Whatever usefull information you think you are obtaining from assuming standard distribution is eroded, if not entirely wiped out by variances in the actual distribution you are likely to encounter.

6 players left and your on a flush draw, using standard distribution you assume that 2 of your suites are out between the 6 players -- sounds usefull, but sometimes there is going to be 7 of your suite out, and sometimes there is going to be 0 of your suite out

[T50_Omaha8]

[ QUOTE ]
6 players left and your on a flush draw, using standard distribution you assume that 2 of your suites are out between the 6 players -- sounds usefull, but sometimes there is going to be 7 of your suite out, and sometimes there is going to be 0 of your suite out



[/ QUOTE ] Your use of the term 'standard distribution' is really throwing me off, but whatever.

Right: it's not useful thinking about the number of spades among other opponents. This is because there is some mean portion of spades among cards not dealt to your opponents and this is the same mean number of spades available without any opponents. You've chosen the most bewildering way possible to say this, however:

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What I said is that assuming standard distribution, on the remainder of the cards dealt out is not usefull information.

[/ QUOTE ] [img]/images/graemlins/confused.gif[/img]