I was thinking after making some "close" calls in a session. If I am at a six max table, and I have a flush draw HU with another player.say board is A 9 2. I have K Q......I cannot calculate for nine outs. Here it is. maybe everyone know this and I am just new, but nine outs is the number of outs you use in any book I've read so far. With Ten dead cards( folded hands and burns) before I see the turn, don't I HAVE to assume that 25% of the dead cards are diamonds? This leaves my " break even call" # of outs seven...or accually 7.5 making my % 30 to win? rule of 4=36% with nine outs. 30% with 7.5... I have never seen anyone mention the cards that are dead to the hand...Old school method comes up with, what? 36 cards left in deck and nine win? thats 25%...seems like mine is most precise. Or am I a nit, LOL ?

The cards folded by other players, the burn cards and the cards that remain undealt should all be treated the same, i.e. they are all unseen and hence unknown.

The way you should look at it is that you have seen 5 cards, and not seen 47 cards. Of those 47, 9 are diamonds, making the likelyhood of a flush by the river:

1 - ((38/47)(37/46)) = 35%

I disagree! you HAVE to assume that some are your suit.to get it "just right" If I don't the formula isn't right and therefore the result is wrong.I would love to see someone with like 1M hands tracked in poker Tracker to see how it reads on this point.

sure they should be treated as unknown, but you know one quarter of the deck are your suite...so any cards that CAN'T yet come on the turn and river have to be concidered 25% your suite.

If other players have 10 cards and on the flop you have a flush draw then on average they have about 1.9 cards of your suit and 8.1 cards not of your suit.

So this leaves us with 7.1 outs and 37 cards in the deck.


7.1/37 = 9/47 (perhaps slightly off due to my rounding but that's the idea)

Bolded is wrong.
It's wrong because of the 5 cards you have seen, 4 are diamonds.

You have essentially shortened the remaining deck to 47 cards of which 9 are diamonds (19.1%)

In case this isn't completely obvious, consider a variant game in which you get 12 cards in your hand instead of 2. If you hold 12 diamonds in your hand, are 25% of possible turn and river cards diamonds?

Lets say we've dealt out the cards 6 handed, then dealt the flop and you have a flush draw in diamonds.

There are only 2 cards in the deck that are going to get dealt - we burn 1, deal 1, burn 1, deal 1. So just the 2nd and 4th card in the stub matters. No other card of any rank or suit can get dealt.

So, it doesn't matter if there are cards in your opponent's hands, or at the bottom of the deck. Only those 2 particular cards can be dealt.

Lego's explanation is correct and is another way to visualize why what you bring up doesn't change the numbers.

Also, simulation obviously bears out this result. I've written a deal simulator, and I can deal cards to 2 players, 6 players, 10 players, 20 players whatever, until you run out of cards, and it doesn't change the chance that you'll make a flush, given that you've flopped a flush draw.

Further, you can try it yourself, either by writing software, or by sitting there with a deck of cards. First to make things simple take the AhKh out the of deck and put the Qh, Jh and 2d on the flop, for example. Then deal out 5 other hands, deal the flop/turn, record whether flush got there or not. Shuffle everything except the cards you've kept for your hand and the flop, then deal 5 hands, deal flop and turn, record, rinse and repeat. It shouldn't take long to converge to the true number.

You're calculating wrong on several levels.

First, assuming "25% of the dealt cards are your suit" is wrong for more than one reason. First off, there are already at least four of the 13 diamonds dead, so it would technically only be 19% of the remaining cards that are diamonds, not 25%.

Second, unknown cards are unknown. It might be easier for you to think of the "35% to hit" as an average of all of the possibilities. You could have only one out if four people who folded had two diamonds in their hand. You could also be in a hand where everyone had clubs spades and hearts, but no one had a diamond at all. In this instance you'd have a better than 50% chance of hitting your draw.

The point is, unless you're playing in a game where everyone turns up every card that they were dealt then folded, you can't make an assumption about what suit they had, any more than you can make an assumption that some of your ace and king outs are dead when you have AK, just because "on average", 15% of the total deck is aces and kings.

TY everone I see how I got to the conclusion and I do see where I got the second estimating example wrong, thanks for your posts...and I see how I just shortened the deck... I understand....TY ...Does anyone have a buttload of tracked hands and the way to calc the outcomes of these draws exactly? LOL

You are all totally right. Its clear to me now. weird how a goofy idea can set so deeply into a tired mind...havin a bad morning. O.R.

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