The Notorious Ed Miller 'Backdoor Two Pair'

[JacksonTens]

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That doesn't mean we should could a four-out gutshot as 4.5 outs.

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That was the part about SSHE that I didn't understand, maybe Miller et al added it in for some other obscure reason.

JT [img]/images/graemlins/spade.gif[/img]

[Jake (The Snake)]

Yeah, I didn't understand either.

But I don't completely grasp the whole thing yet and it's Ed so I just figured I was wrong.

Maybe he's thinking the river bets alone make it about 1.5, and that we don't have to discount more than that since we don't have to pay the turn when we miss?

[FlyingSumo]

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Firstly, thankyou for your statistical input.

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(6/47)(5/46). Do I need to go on you're a 76:1 dog

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You are failing to take into account the remaining bets we will win if we make 2pair. Also if we make a pair on the turn, we will be more than happy to call the river.

If you still don't want to call, some guy walking buy just threw two $100 bills into the pot, they don't call it the "Banana" for no reason!

JT [img]/images/graemlins/spade.gif[/img]

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I remembered. The pot is 25BB on the flop. I added four on the turn which makes it 29, you've paid 1.5 BB so far. Lets add another 5 on the river. You get 34 BB for you're 1.5 BB investment. You're getting 22.66:1 effective odds and you were a 76:1 dog to make your two pair or trips. It's not even close. Even if you assume that everyone will call on the turn and everyone will call on the river and call your raise on the river, then it's 24.5+9+19=52.5BB final pot. You paid 1.5 BB to see your draw. Thus you were getting 35:1 effective/implied odds on your 76:1 draw. I really hope you folded this hand.

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I think you misunderstand... Let's oversimplify:

You call flop
For a total of 41 times, you will miss and fold turn
For a total of 6 times you will see the river, lets say approx. 1.5 BB put in on turn
For a total of 41 times, you will miss and fold river
For a total of 5 times, you will hit the river, paying lets say 1.5 BB on avg, and winning 60 % of the time
Lets say avg profit when winning is 50BB's. Lets add up the numbers:

41 X 0.5 BB = 20.5 BB's (lost)
6 X 41 X 2.0 BB = 492.0 BB's (lost)
(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

This looks like a pretty easy call to me given those assumptions. Am I doing everything wrong here?

[JacksonTens]

[ QUOTE ]
You call flop
For a total of 41 times, you will miss and fold turn
For a total of 6 times you will see the river, lets say approx. 1.5 BB put in on turn
For a total of 41 times, you will miss and fold river
For a total of 5 times, you will hit the river, paying lets say 1.5 BB on avg, and winning 60 % of the time
Lets say avg profit when winning is 50BB's. Lets add up the numbers:

41 X 0.5 BB = 20.5 BB's (lost)
6 X 41 X 2.0 BB = 492.0 BB's (lost)
(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

This looks like a pretty easy call to me given those assumptions.

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...can't believe what a number crunch my post turned into. But good work guys. I'm interested to hear Hammers reply.

JT [img]/images/graemlins/spade.gif[/img]

[Catt]

Your math is off, but I don't want to run through it in detail. Basically, 41 times you lose 0.5 SBs, so you lose 20.5 BBs these 41 times. Of those 6 times you see a river, you hit on the river 12.5% (hitting 5/40 for two pair or trips). So you miss 6 * 87.5% of the time, or 5.25 times. This costs you 2 BBs * 5.25 or -10.5 BBs. Hitting happens 0.75 times when you win your assumed 50 BBs 60% of the time, meaning you win 0.75 * 50 BBs * 60% or 22.5 BBs. Overall you lose -8.5 BBs using your assumptions.

[FlyingSumo]

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You call flop
For a total of 41 times, you will miss and fold turn
For a total of 6 times you will see the river, lets say approx. 1.5 BB put in on turn
For a total of 41 times, you will miss and fold river
For a total of 5 times, you will hit the river, paying lets say 1.5 BB on avg, and winning 60 % of the time
Lets say avg profit when winning is 50BB's. Lets add up the numbers:

41 X 0.5 BB = 20.5 BB's (lost)
6 X 41 X 2.0 BB = 492.0 BB's (lost)
(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

This looks like a pretty easy call to me given those assumptions.

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...can't believe what a number crunch my post turned into. But good work guys. I'm interested to hear Hammers reply.

JT [img]/images/graemlins/spade.gif[/img]

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I guess he will say : "you stupid moron, you forgot to multiply flop with 47, making it 963.5 BB's (lost)..." so....

963.5+492 = 1455.5 BB's lost

6x5x50 = 1500 / 100 = 15

1455.5 / 15 = approx. 97...

So you would need to be approx. 97 % sure you hand helds up on river...

My bad.

[SeaEagle]

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You call flop
For a total of 41 times, you will miss and fold turn
For a total of 6 times you will see the river, lets say approx. 1.5 BB put in on turn
For a total of 41 times, you will miss and fold river
For a total of 5 times, you will hit the river, paying lets say 1.5 BB on avg, and winning 60 % of the time
Lets say avg profit when winning is 50BB's. Lets add up the numbers:

41 X 0.5 BB = 20.5 BB's (lost)
6 X 41 X 2.0 BB = 492.0 BB's (lost)
(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

This looks like a pretty easy call to me given those assumptions. Am I doing everything wrong here?

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I'm not sure how many samples you're trying to use in this example but your math is badly off.

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(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

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For you to make 2 pair 30 times (which is what this line shows) you'd need a whole lot more samples than you're showing.

And to win 50bbs, you'd need to get your opponents to put in 25 more BBs during the last 2 rounds, which isn't going to happen.

If you redo the math correctly, I think you'll see this is a trivial fold.

[FlyingSumo]

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[ QUOTE ]
You call flop
For a total of 41 times, you will miss and fold turn
For a total of 6 times you will see the river, lets say approx. 1.5 BB put in on turn
For a total of 41 times, you will miss and fold river
For a total of 5 times, you will hit the river, paying lets say 1.5 BB on avg, and winning 60 % of the time
Lets say avg profit when winning is 50BB's. Lets add up the numbers:

41 X 0.5 BB = 20.5 BB's (lost)
6 X 41 X 2.0 BB = 492.0 BB's (lost)
(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

This looks like a pretty easy call to me given those assumptions. Am I doing everything wrong here?

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I'm not sure how many samples you're trying to use in this example but your math is badly off.

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(6 X 5 X 50 BB)*0.6 = 900 BB's (won)

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For you to make 2 pair 30 times (which is what this line shows) you'd need a whole lot more samples than you're showing.

And to win 50bbs, you'd need to get your opponents to put in 25 more BBs during the last 2 rounds, which isn't going to happen.

If you redo the math correctly, I think you'll see this is a trivial fold.

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Read my reply at 10:01. I sometimes get a bit "fill_in" when doing math.

[FlyingSumo]

Oh... Yeah, It's probably one or two more tiny mistakes, but your hand needs to hold up at about 95-100 % of the time with the assumption, that you need 2 pair or better, to make it correct to call the flop.