Flush draw HELP

[dgekson879]

2/5 nlhe

You have two spades and there are 2 spades on the flop. I'm only concerned with flush draw and not total outs.


Playing 10 handed. How many outs do you have to hit your flush? Also what
percentage is this?

From books I have read it states 9 outs with an approximate chance of winning of 36%, rule of 4.

But why are we counting 9 spades? That means that the other 9 players did not get dealt a spade. I wouldn't even know how to calculate 9 players not getting dealt at least 1 spade, but the odds must be huge.

So my question is mathematically and realistically how many spades out should be calculated in a 10 handed game. 9,8,7,6,5?

[HalfSugar]

Interesting question. Since it is impossible to know what cards your opponents have/had, you cannot factor this in with any certainty.

Poker hand odds ONLY work correctly in a 1 vs 1 situation. Whilst they are still entirely relevant at a 3-10 handed table also, they are not as accurate because of the mucked cards.

If you want be prudent, maybe you could subtract one out for every X number of players depending on what you are drawing to. For example, with a flush draw, you could say that since there are four suits, assuming they are dealt evenly to each player, every fourth card off the deck is potentially one of your outs. With a 10-handed table when looking at a flush draw you might deduct three outs because of the 20 cards dealt, five (20/4) could have been your suit. You are holding two of them (presumably) so the other three could be dead.

Extending that further to an up and down straight draw with (up to) 8 outs, this time you would assume that with 13 ranks of card, 2 of which you need, 1 in every 6.5 cards are your outs. Since you are obviously holding neither, 3 of the 20 (20/6.5) that have been dealt could be your cards so again you could be facing three dead outs.

The above approach probably leads to more accurate odds in the long run but would lead to such prudent play that it still might end up as a negative overall result because of all the missed draws. I don't know that for sure but my gut says............maybe

[golddog]

There's a difference between calculating the odds of unknonwn cards (what is commonly shown on TV and used in poker), and calculcating the odds of more specific events.

You're right in that, to calculate the true odds, you'd have to calculate the odds down the stream of events. Something like:

9/47 * (odds against nobody having a spade) + 8/47 * (odds against exactly 1 spade being dealt) +...

where "odds against nobody having a spade" is something on the order of:

38/47 * 37/46 * 36/45 ...

(In other words, player one has to have one of the 38 remaining non-spades AND one of the 37 remaining non spades once the first card is selected. Then we move on to player two, etc...)

Not worth the trouble. Just go with the unknown cards method. I don't believe that the correct calculation can be carried out in one's head accurately, and the delta is not going to be enough to change your action anyway.