WOHEP: Backdoor flush outs estimates

[binions]

I don't think DIPO works that way when you are trying to figure runner runner. DIPO is usually applied trying to figure outs for the next card.

Put another way, you need 23.5:1 under DIPO to see both cards, not just the turn.

So really, you should divide 1.91 by 2 to get 0.96 outs for a backdoor flush draw. This is accurate. I have rounded to 1.

[ninjia3x]

OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[binions]

[ QUOTE ]
OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[/ QUOTE ]

You are figuring implied odds, and the savings you make when you miss your draw on the turn.

That is not an answer to the math problem. This gets into why Ed says to value the backdoor flush draw as 1.5 outs instead of its true math "out value."

The fact remains that you have a 4.16% chance to hit your hand with 2 to come. This equals one out.

[ninjia3x]

[ QUOTE ]
[ QUOTE ]
OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[/ QUOTE ]

You are figuring implied odds, and the savings you make when you miss your draw on the turn.

That is not an answer to the math problem. This gets into why Ed says to value the backdoor flush draw as 1.5 outs instead of its true math "out value."

The fact remains that you have a 4.16% chance to hit your hand with 2 to come. This equals one out.

[/ QUOTE ]

The only implied odd that may be the last 2 dollars u make off of him. which he is getting 15:1.

other wise, there is no implied odd included in that, I think it is pretty clear, please go read again.

[King Yao]

[ QUOTE ]
I don't think DIPO works that way when you are trying to figure runner runner. DIPO is usually applied trying to figure outs for the next card.

[/ QUOTE ]

DIPO is used to figure out if you have pot odds to call a bet. You need to know your expected outs in order to use DIPO correctly. Figuring out the expected outs on a runner-runner draw fits in with this idea. I think it works good (or is that 'works well'?)

[binions]

[ QUOTE ]
[ QUOTE ]
I don't think DIPO works that way when you are trying to figure runner runner. DIPO is usually applied trying to figure outs for the next card.

[/ QUOTE ]

DIPO is used to figure out if you have pot odds to call a bet. You need to know your expected outs in order to use DIPO correctly. Figuring out the expected outs on a runner-runner draw fits in with this idea. I think it works good (or is that 'works well'?)

[/ QUOTE ]

I agree you can call with a backdoor flush draw if you get 23:1 to see BOTH cards, ie you are all in on the flop and will not be faced with another bet.

But if you are only getting 23:1 to see the turn card, you are overpaying if you will also be faced with calling a bet to see the river.

[King Yao]

very nice.

[SlantNGo]

Alright, here's my take on it. Binion is arguing that a backdoor flush draw is 2 outs for 2 streets, which should be reduced to 1 out for 1 street, since most of what we do in limit hold'em is using street to street odds.

By definition, a 1 outer hits:
1 / 47 + 46 / 47 * 1 / 46 = 4.26% of the time by the river.
Similarly, a 2 outer hits:
2 / 47 + 45 / 47 * 2 / 46 = 8.42% of the time by the river.
A backdoor flush draw, mathematically, hits 4.16% of the time by the river; hence, it is equivalent to about 1 out, mathematically.

The second argument is about how much we should add to the mathematical out due to other factors, such as the savings on the turn when we do not pick up our flush draw. SSH says approximate it as 1.5 outs. Well, ninjia and I had this discussion many months ago, and he feels that 1.5 is a bit low of an approximation, and that it's closer to 2. That's what he's trying to show by his calculation here.

King, your calculation showing that the backdoor flush draw is 1.91 outs was as follows:
10 / 47 * 9 / 46 = 4.16%
4.16% * 46 = 1.91 outs

However, that is a 2-street out calculation. Using that logic, a regular flush draw is:
9 / 47 + 38 / 47 * 9 / 46 = 34.9%
34.9% * 46 = 16.1 outs which is clearly incorrect because we know a flush draw is 9 outs. The 16.1 outs is a 2-street figure, similar to the 1.91 outs you arrived at for the backdoor flush draw. Hence, Binion says to divide by 2 to get the actual mathematical outs, which is approx. 1.

[binions]

[ QUOTE ]
OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[/ QUOTE ]

47*46=2162 possible combinations.

Assuming one opponent:

37*46=1702 of those combinations, you lose 1 small bet.

10*37=370 of those combinations, you lose 1 small bet and 1 big bet, or 3 small bets.

So, when we miss, we lose 2812 small bets.

We hit 90 times. 2812/90= 31.2.

So to break even, we need to win 31.2 small bets if we hit.

We win 1 big bet (ie 2 small bets) on the turn and river from our opponent when we hit.

31.2 - 5 = 26.2 is the number of small bets we need in the pot on the flop in order to call 1 small bet.

[binions]

[ QUOTE ]
[ QUOTE ]
OMG, this is so simple to find, I don't get what you ppl are writting about. Just run all possible combinationas and find the EV, here is my crude and straightfoward method.

odds of hitting the cards we need on the turn is 10/47, river is 9/46

so to get through all the possible cases, i'm going to run it 2162 times

so first, u'll lose -2162 on the flop to see the turn card,

next, on the turn, 460 times u'll get your four flush draw. so u'll have to pay to see it, so -2*460

now, for u'r pay off, it will be final pot times 90. cause u'll hit 90/460 times.


so u hae FinalPot*90 = 2162 + 2*460 for 0EV


Final Pot = 34.24

so working backward, -2(him) for his call on the river, -2(you) -2(him) for the turn, -1(you) -1(him) for the flop bet, u'r left with 26.24

so pot needs to be 26.24 on the flop. with the pot odd on the flop, u can easily figure out the number of outs it equals.. add 1 for his bet, and u get the pot odd you need.

which is 27.24

so u need to get 27.24:1, so that is 1/27.24 * 47 = 1.73 outs. (out/47* pot = 1 ...out = 1/pot *47 )

Q.E.D.

[/ QUOTE ]

47*46 = 2162 possible combinations.

Assuming one opponent:

37*46 = 1702 of those combinations, you lose 1 small bet.

10*37 = 370 of those combinations, you lose 1 small bet and 1 big bet, or 3 small bets.

So, when we miss, we lose 2812 small bets.

We hit 90 times. 2812/90 = 31.2.

So to break even, we need to win 31.2 small bets if we hit.

We win 1 big bet (ie 2 small bets) on the turn and river from our opponent when we hit.

31.2 - 5 = 26.2 is the number of small bets we need in the pot on the flop in order to call 1 small bet.

[/ QUOTE ]

Correction: 31.2 small bets is the final pot we need to win to break even, so that means 31.2 - 2 big bets on the turn (ours and his) - 2 big bets on the river (ours and his) - 1 small bet on the flop (ours) is 22.2 small bets on the flop that we need to call 1 small bet on the backdoor flush draw against one opponent.