The Notorious Ed Miller 'Backdoor Two Pair'

[JacksonTens]

For those of us who have read SSHE there is one line that cracked me up 'They will call with flush draws, runner runners, one overcard, even backdoor two pair draws.'

I'm not sure if thats the correct writing but you get the idea. My question is how big must the pot be for you to call with 2 undercards? This is primarily an odds theory question and although you will most likely never get the chance to implement it. This post may make you think a little more about playing to odds and potsizes. Take this hand for example

$5-10 at the Banana Inn (10 players)
Hero is Button with 8 /images/graemlins/heart.gif7 /images/graemlins/heart.gif
All call, Hero calls, SB calls, BB raises, all call, Hero calls, SB 3bets, UTG+1 caps, all call

Flop: (10players) 40SB 3 /images/graemlins/spade.gif Q /images/graemlins/club.gif 2 /images/graemlins/diamond.gif
SB bets, all call, hero???

Do we call getting 49:1???

JT /images/graemlins/spade.gif

[thirddan]

your odds aren't 49:1, you have to consider your effective odds in this situation, not just your immediate odds, since if you hit one of your cards on the turn then you will have to pay a certain number of bets on the turn in order to see the river...your odds are probably closer to 15/20:1 because you have no idea what the flop action will be since you don't close the action and such...

[Harv72b]

Raise preflop. /images/graemlins/tongue.gif

When considering whether or not to continue, you have to take other things into account besides just the immediate pot odds: the possibility, albeit unlikely based on the action so far, that you're already drawing dead to a set or drawing very thin to queens up or Q7/Q8. Or that you catch your runner runner two pair while someone else catches their runner runner flush.

I honestly can't think of a situation where it would be correct to peel with two undercards/no draw, except possibly HU vs. an aggressive opponent.

[ebranig]

Uhm, where do I get into this game?

[JacksonTens]

We are closing the action so we are getting 49:1 to call.
If we don't pair the turn, we fold. If we hit the turn we call. Once we've hit the turn this is an esay call, getting such enormous odds. The turn call will be profitable. as we are about 9:1 to make a pair on the turn I think this is a call, if someone can pull out numbers to prove otherwise. ALso please note the non-aggressiveness of the players thus far, this adds further to the benefits of calling a bet...perhaps the turn will be checked through. Does anyone want to call now??

JT /images/graemlins/spade.gif

[TheHip41]

no

[TheHammer24]

[ QUOTE ]
We are closing the action so we are getting 49:1 to call.
If we don't pair the turn, we fold. If we hit the turn we call. Once we've hit the turn this is an esay call, getting such enormous odds. The turn call will be profitable. as we are about 9:1 to make a pair on the turn I think this is a call, if someone can pull out numbers to prove otherwise. ALso please note the non-aggressiveness of the players thus far, this adds further to the benefits of calling a bet...perhaps the turn will be checked through. Does anyone want to call now??

JT /images/graemlins/spade.gif

[/ QUOTE ]

You are incorrect. 49:1 on flop, first we'll assume two pair is good always to win river and that the turn will always be unraised to you with about 4 players in.

First you will make a pair on the turn 13% of the time. You will make two pair or trips on the river 1.3% of the time. (6/47)(5/46). Do I need to go on you're a 76:1 dog to make your draw? Say you do, the pot will be about 29 BB. You will be getting 29:1 to go on and see the river. At which poitn you will have paid 1.5 BB for a 29 BB pot making you 29:1.5 pot odds, you were a 98:1 Dog on the flop.

[Jake (The Snake)]

I'm not positive, but I don't think everyone around here is using the term "effective odds" correctly.

That post Jason made a week or two ago also kept using the term, and I don't think it is correct.

We estimate our outs (like BD flush draws) based on the entire hand, which take effective odds into account. Who cares if we pick up a draw that we will have to call on the turn? All that means is that our turn decision is +EV. Our choice is RIGHT NOW. We have to figure out if the flop call is +EV. So we estimate our outs (keeping in mind what might happen on the turn and river) and then make a judgement based on pot and implied odds.

The only time I see where effective odds really matter is when you are deciding on the turn whether or not you will also call a river bet even if you dont improve.

If I'm mistaken, please enlighten me.

[JacksonTens]

Firstly, thankyou for your statistical input.

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

[/ QUOTE ]

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 /images/graemlins/spade.gif

[thirddan]

i think you are right about the terminology, i don't have my copy of TOP with me...

but i don't think in this case taht villain is getting 49:1 since if he hits on the turn then he will be putting in some number of bets on the turn that must be considered...is this possibilty negated by the times where he misses on the turn and can just fold?

[Jake (The Snake)]

Perhaps we are just thinking about it differently. I just tried to write out a long response and it didn't work so I am thinking maybe I am wrong. I need to go to sleep but tomorrow I'm going to look over that other thread and think about it some more.

Edit: Yeah, I think the difference might be that I usually take effective odds into account when estimating outs by discounting them. Perhaps you and others do it with the pot odds or something. IDK, it's a tough subject for me.

[JacksonTens]

[ QUOTE ]
I think the difference might be that I usually take effective odds into account when estimating outs by discounting them. Perhaps you and others do it with the pot odds or something. IDK, it's a tough subject for me.

[/ QUOTE ]

Can you show me your thinking in number form so we can understand your line on this topic?

JT /images/graemlins/spade.gif

[TheHammer24]

[ QUOTE ]
Firstly, thankyou for your statistical input.

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

[/ QUOTE ]

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 /images/graemlins/spade.gif

[/ QUOTE ]

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.

[jason_t]

[ QUOTE ]
I'm not positive, but I don't think everyone around here is using the term "effective odds" correctly.

That post Jason made a week or two ago also kept using the term, and I don't think it is correct.

We estimate our outs (like BD flush draws) based on the entire hand, which take effective odds into account. Who cares if we pick up a draw that we will have to call on the turn? All that means is that our turn decision is +EV. Our choice is RIGHT NOW. We have to figure out if the flop call is +EV. So we estimate our outs (keeping in mind what might happen on the turn and river) and then make a judgement based on pot and implied odds.

The only time I see where effective odds really matter is when you are deciding on the turn whether or not you will also call a river bet even if you dont improve.

If I'm mistaken, please enlighten me.

[/ QUOTE ]

Effective odds are the odds you are getting from the pot with more than one card to come.

The classic example is drawing to a backdoor flush. It's about 24:1 to come in but if the pot is laying you, say, 25:1 on the flop it's not profitable to draw to it even though if you did hit another card of your suit on the turn calling a turn bet would be profitable. The reason is because the combined action of calling a flop bet and turn bet would not be profitable.

Say that we are playing 1/2 and the pot is $24. Villain bets $1 laying you 25:1. The likelihood that the board comes runner runner of a certain suit when there is one on the flop and you hold two in your hand is (10/47) * (9/46) = 4.16%. There is no card of our suit on the turn 37/47 = 78.72% of the time. The board comes one of suit and then we miss 100% - 4.16% - 78.72% = 17.11% of the time. So our EV is

EV = .0416 * (24 + 1 + 2 + 2) - .7872 * (1) - .1711 * (1 + 2) = -.09.

I also use the term effective odds to refer to the possibility of having to call more than one bet on a single street. The reason for using this terminology here is simple: the methodology for figuring out your real odds in both cases is you add up all the calls you'll to make and add up all the money you expect to make if you hit your hand.

[JacksonTens]

[ QUOTE ]
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.

[/ QUOTE ]

If the turn is checked through? We're getting
24.5+19=52.5BB on a 0.5 about 104:1. Granted this is a extremely rare scenario. So the turn needs have a 55% chance of getting checked through to make this worthwhile.
With this many players all passive (its a scientific scenario only) This 55% is very achievable, as who wants to bet into 8 players? So Hammer can I yet convince you of the value of the "Backdoor Two Pair Draw" yet? Becuase I think I may have even convinced myself! /images/graemlins/smile.gif

JT /images/graemlins/spade.gif

[Jake (The Snake)]

Right, ok, thanks for the examples.

But I think, for me at least, it is much easier to take effective odds into account when estimating outs.

For the BD flush example, isn't this why we usually count it as 1.5 outs instead of 2 outs? Or is is becuase we sometimes hit it and still lose?

[jason_t]

[ QUOTE ]
Right, ok, thanks for the examples.

But I think, for me at least, it is much easier to take effective odds into account when estimating outs.

For the BD flush example, isn't this why we usually count it as 1.5 outs instead of 2 outs? Or is is becuase we sometimes hit it and still lose?

[/ QUOTE ]

A one-outer comes in 1 - (46/47) * (45/46) = 4.24% of the time which is roughly equal to the amount of time a backdoor flush comes in. So actually 1.5 outs in overestimate. I suspect we do this because we can often get a raise in on the river because people don't fear backdoor flush draws? I'm not sure.

[Jake (The Snake)]

Yeah I just reread the explanation in sshe and Ed says it's because both the extra river bets we collect and because we can usually save a bet by folding on the turn when the 4th flush card doesn't come in.

Thanks for clearing everything up for me.

[JacksonTens]

[ QUOTE ]
I suspect we do this because we can often get a raise in on the river because people don't fear backdoor flush draws?

[/ QUOTE ]

I think when they talk about in SSHE. They justify it with:
1. The extra bet, because its unexspected.
2. If you miss it on the turn you don't have to follow to the river.

Although after reading replies to this post I'm not so sure about (2).

Can someone quote the book??

JT /images/graemlins/spade.gif

[jason_t]

[ QUOTE ]
Yeah I just reread the explanation in sshe and Ed says it's because both the extra river bets we collect and because we can usually save a bet by folding on the turn when the 4th flush card doesn't come in.

Thanks for clearing everything up for me.

[/ QUOTE ]

I don't see what not having to a call turn bet has do with anything. If we call for a gutshot on the flop in an 11 SB pot then we can fold the turn when we miss. That doesn't mean we should count a four-out gutshot as 4.5 outs.

[JacksonTens]

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

[/ QUOTE ]

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

JT /images/graemlins/spade.gif

[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]

[ QUOTE ]
[ QUOTE ]
Firstly, thankyou for your statistical input.

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

[/ QUOTE ]

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 /images/graemlins/spade.gif

[/ QUOTE ]

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.

[/ QUOTE ]

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.

[/ QUOTE ]

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

JT /images/graemlins/spade.gif

[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]

[ QUOTE ]
[ 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.

[/ QUOTE ]

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

JT /images/graemlins/spade.gif

[/ QUOTE ]

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]

[ 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?

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

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

[/ QUOTE ]
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]

[ QUOTE ]
[ 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?

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

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

[/ QUOTE ]
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.

[/ QUOTE ]

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.