Tell me I'm wrong

[Danger]

I was talking to a guy who didn't seem to know a lot about poker but like to think he does. (You know the type) Well, we started talking about odds and he said you have to consider the other peoples cards(unseen to you) when figuring out your odds. Well this goes against everything I've ever read. I kind of wrote him off but later I was thinking about it and something wasn't setting right with me. So I tried to work out the math and this is the example I worked out.

Say you have a flush draw on the flop with two cards to the flush in your hand. Normally, your looking at 9 outs and 47 unseen cards which works out to about a 19% chance of hitting your flush on the turn. But here is what I tried.

You have 2 cards out of the 13 suited cards in your hand. (13-2=11)
And 2 cards out of the deck. (52-2=50)
If on average the rest of the suited card are distributed evenly through out the deck and there are 9 other players at the table then on average 4 of your suit will have been dealt out. (11/50*9*2 = 3.96 ~ 4)
11 of your suit, 50 cards in the deck, 9 players, 2 cards each.
So now 3.96 gets subtracted from the 11 and now there is only 7.04 of your suit, but there is also 18 more cards off the deck. So to update: 7.04 of your suit and 32 (50-18 = 32) left in the deck. Now the flop comes and there's your flush draw. 2 more cards get subtracted from your suit and 3 from the deck. Update: 5.04 of your suit and 29 left in the deck. Now your chance of making the flush on the turn is 5.04/29 = 17%

Now, I know what your thinking. All that work for a 2% difference. And I agree, you still should be looking for about 4 to 1 on your money for ok pot odds, but there still seems to be a discrepancy in the numbers. What do you think?

[Vincent Lepore]

All of the work you've done does not change the fact that on the flop there are 47 UNSEEN cards and 9 of them are your suit. That is that.

Vince

[Snarf]

You're wrong. (but I only said it 'cuz your title told me to)

Reverse implied odds - dude. You have to factor in the % of times that you will hit your draw - and still lose.

a couple examples:

a) Board: 4 h 5 h 6s
You have: Ac 7c
You have 8 outs to win the hand w/your straight...but only 6 outs if your opponent has a hand like Ah 6h.
b) Board: 4 s 5s Jc
You have: 8 s 9 s
Opponent: As Jd
You have 8 (not 9) outs for your flush = BUT you need to hit exactly ONE spade to win.

c) Board: 2c 8c 2d
You have: K c Q c
Opponent: A s 2 s
You can win with any club - but you need to avoid the last 2, any 8, ace or the pairing of the turn card on the river.

d) You have A s Q d
Board reads: K d Qs 5 h
w/all the betting goin on you think you figure you're behind and need to catch up...but how do you know how many outs you have?
If your opponent has A K you have TWO outs.
KJ gives you 5 outs
55 means you need runner runner for full house
KK means drawing dead.


Coolio?

not sure if this is helpful. but not just reverse implied odds. but often you have to discount outs as you aren't really sure if they'll win for you.

you may have had nut flush or nut straight example where it's straight-forward.

but most times you have to give some consideration to your opponents cards... and in the nut flush example, what if your opponent has 2 of the suit too, so there are less in the deck for you to hit

[Xhad]

Yes, you are wrong. I'm too lazy to comb over your math too thoroughly but I did notice one elementary mistake: you can't assume your opponents have a normal distribution of "your" suit in their hands if two of your suit hit the flop. The fact that you caught your flush draw at all makes it slightly less likely others were dealt that suit, though I don't know quite how much it matters.

Intuitive explanation: It does not matter where the cards are that you have not seen, only that they exist. Look at it this way; would the calculation be any different if the dealer burned 19 cards and then dealt the 20th as opposed to just dealing the card off the top of the deck? Obviously not. So why does it matter if the first 18 cards went to other people instead?

Mathematical explanation: I started to do this but it got hairy and I don't like posting things if there might be errors if I'm tired. I'll post it tomorrow if you want.

[MikeBandy]

Xhad, thank you for your thoughtful intuitive explanation. Whether the dealer burns x cards, or puts x cards into the opponents’ hands, the chances of making the flush on the turn are the same.

Unless I’m in error, the OP demonstrated a somewhat surprising conclusion. If the flush cards are normally distributed, the odds against making the flush on the turn are affected. As the OP said, "Tell me I’m wrong."

[soko]

You're wrong because if your outs are evenly distributed throughout the deck and your opponents hands, so are junk cards that will not improve your hand. therefore, if you do the math you will come up with the same odds of hitting your draw if all your opponents cards are in the muck or shuffled back in to the deck, just as long as you don't know what the cards are.

[MikeBandy]

[ QUOTE ]
You're wrong because if your outs are evenly distributed throughout the deck and your opponents hands, so are junk cards that will not improve your hand. therefore, if you do the math you will come up with the same odds of hitting your draw if all your opponents cards are in the muck or shuffled back in to the deck, just as long as you don't know what the cards are.

[/ QUOTE ]
Soko, that’s what I thought: It’s intuitive. However, can you find an error in the OP’s math? I couldn’t.

[Xhad]

[ QUOTE ]
[ QUOTE ]
You're wrong because if your outs are evenly distributed throughout the deck and your opponents hands, so are junk cards that will not improve your hand. therefore, if you do the math you will come up with the same odds of hitting your draw if all your opponents cards are in the muck or shuffled back in to the deck, just as long as you don't know what the cards are.

[/ QUOTE ]
Soko, that’s what I thought: It’s intuitive. However, can you find an error in the OP’s math? I couldn’t.

[/ QUOTE ]

Here is the error: OP assumes that your opponents are dealt an average number of cards in "your" suit. However, you will be more likely to flop a flush draw those times your opponents are dealt fewer cards in your suit than average.

If OP wants to fix his math he's going to either need to apply Bayes' Theorem, or deal the flop first then determine the average amount of cards that appear in his opponents' hands.

[Xhad]

[ QUOTE ]
Unless I’m in error, the OP demonstrated a somewhat surprising conclusion. If the flush cards are normally distributed, the odds against making the flush on the turn are affected. As the OP said, "Tell me I’m wrong."

[/ QUOTE ]

Part in bold is the faulty assumption. You are more likely to flop a flush draw those times that your opponents are dealt fewer of your suit than normal.