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9:24 am
February 18, 2008
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threads13
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| posts 343 |
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Here is something that I have in my head taht I have never had a 100% confident grip on .
Laying odds vs. getting odds
For example:
Say that me and my opponent just have $1 behind in a $1 pot and he bets the pot at me. I am getting 2:1 ona call and I can call if I have at least 33% equity. Cool… got it
Now flip it around… say I bet $1 into the $1 pot. That means I am risking $1 to win $1 which means I have to win 50% of the time. Correct? This includes the equity I have when an opponent calls PLUS the fold equity I have.
So, say when I bet $1 my opponent will fold 20% of the time and will call 80%. The times that he calls I have 30% equity. Does this mean that it is a break even cbetall (20% + 30% = 50%) or is it -EV. If he calls 80% of the time and I have 30% equity then that means I will only win (.8*.3 = .24) 24% of the time total. Add that to my 20% of fold equity and that gives me 44% equity total.
I believe I am looking correctly in that I only have 44% equity, but I have never seen it jotted out anywhere.
Just looking for some confirmation here.
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12:31 pm
February 18, 2008
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Todd
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You are risking $1 to win $1 sometimes and $1 to win $2 other times. His call is your money if you win that pot.
In your example, the pot is $1, your bet is $1 and his call is $1. The final pot will be $3.
If he folds 20% of the time, then you have 100% equity in the $2 pot which is $.40 for that portion of the line.
If he calls 80% of the time and you have 30% equity on average when he calls, then you have (.8*.3)*$3 = $.72 in equity on that part of the larger pot.
In total, your $1 bet yields $.40 + $.72 = $1.12 or $.12 in profit.
So you really don’t have 44% equity in the pot, you have equity in 2 different pots depending on whether he puts in money or not. You can use the call/fold ratio to sum the two equities together.
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3:39 pm
February 18, 2008
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threads13
Member
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| posts 343 |
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Todd said:
You are risking $1 to win $1 sometimes and $1 to win $2 other times. His call is your money if you win that pot.
In your example, the pot is $1, your bet is $1 and his call is $1. The final pot will be $3.
If he folds 20% of the time, then you have 100% equity in the $2 pot which is $.40 for that portion of the line.
If he calls 80% of the time and you have 30% equity on average when he calls, then you have (.8*.3)*$3 = $.72 in equity on that part of the larger pot.
In total, your $1 bet yields $.40 + $.72 = $1.12 or $.12 in profit.
So you really don’t have 44% equity in the pot, you have equity in 2 different pots depending on whether he puts in money or not. You can use the call/fold ratio to sum the two equities together.
If he folds we only win a dollar, right? We don’t really win our own bet back. I think that would be the same as saying he bet a dollar into a dollar pot and then saying we are getting 3:1. Maybe I’m looking at it wrong? Not sure really.
I do agree with most of the rest though. I think you forgot to subract out your loss in the EV equation.
It should be something like 20% of the time he folds, 24% of the time he calls we win, 56% of the time he calls and we lose. (Using your numbers for the fold scenario that I still need some clarity on  )
(.20)*(2) + (.24)(3)+ (.56)(-1) = .40 + .72 - .56 = .56EV
Yeah?
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4:05 pm
February 18, 2008
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Todd
Member
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threads13 said:
Todd said:
You are risking $1 to win $1 sometimes and $1 to win $2 other times. His call is your money if you win that pot.
In your example, the pot is $1, your bet is $1 and his call is $1. The final pot will be $3.
If he folds 20% of the time, then you have 100% equity in the $2 pot which is $.40 for that portion of the line.
If he calls 80% of the time and you have 30% equity on average when
he calls, then you have (.8*.3)*$3 = $.72 in equity on that part of
the larger pot.
In total, your $1 bet yields $.40 + $.72 = $1.12 or $.12 in profit.
So you really don’t have 44% equity in the pot, you have equity in
2 different pots depending on whether he puts in money or not. You can
use the call/fold ratio to sum the two equities together.
If he folds we only win a dollar, right? We don’t really win our own bet back.
Really, we do. Once we put the $1 in the pot, it’s gone. 20% of the time, the dealer will push us $2.
I do agree with most of the rest though. I think you forgot to subract out your loss in the EV equation.
I’m not sure that’s quite right. We account for the loss in our total
equity. When called, 30% of the time the dealer pushes us $3, the rest
of the time he pushes us $0. We spend the $1 once. the key is that we
account for it at the end when we net the whole thing out.
It should be something like 20% of the time he folds, 24% of the
time he calls we win, 56% of the time he calls and we lose. (Using
your numbers for the fold scenario that I still need some clarity on
)
(.20)*(2) + (.24)(3)+ (.56)(-1) = .40 + .72 - .56 = .56EV
Yeah?
I think it’s this:
.2*$2 + .24*$3 = (.4 + .72) - $1 = $.12
We account for our bet at the very end.
We could also account for the bet by saying (.2 + .8)*$1, but we
leave that out because it always has to equal 1 if we are betting and
not the one considering the fold.
We could also calculate it like this, which is what I think you are trying to do:
.2($1) + .24($2) - .56($1) = $.12
Here
we win $1 net 20% of the time, a portion of $2 net and a portion of -$1
net. I prefer to deal in the size of the actual pot and deal with the
bet at the very end. I think it makes the calculations a little more
straight forward.
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7:35 pm
February 18, 2008
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threads13
Member
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| posts 343 |
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I don’t know if that is right about the dealer pushing us 0. Look at it this way, say you bet $5 into a $5 pot and you know you will get call 100% of the time and you will lose 100% of the time. Using the approach you are suggesting that would give us an EV = 0, but clearly the EV = -$5.
On the same note, if we know that he will fold 100% of the time and we bet $5 into a $5 pot we should expect to win $5 on average. It’s not a $10 win.
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8:13 pm
February 18, 2008
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Todd
Member
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threads13 said:
I don’t know if that is right about the dealer pushing us 0. Look at it this way, say you bet $5 into a $5 pot and you know you will get call 100% of the time and you will lose 100% of the time. Using the approach you are suggesting that would give us an EV = 0, but clearly the EV = -$5.
I think we’re getting caught up in semantics somewhere. We are talking about 2 different numbers, our equity in the pot and our EV. For instances where we are betting, our EV is our total pot equity minus out bet.
In this case, your equity in the pot is 0. You’re EV is -5 expressed as 0 - 5.
On the same note, if we know that he will fold 100% of the time and we bet $5 into a $5 pot we should expect to win $5 on average. It’s not a $10 win.
You are correct, it is not a $10 win. Our equity in the pot is, however, $10. The dealer pushes us $10 in chips. Once the money is in the pot it’s gone, it’s easiest to talk about equity in those terms. Our EV is our total equity in the pot minus our bet. In this case $10 - $5 = $5.
We can account for our bet in each leg of the calc, but it tends to be a bit more complicated because the pot sizes are all different. For example, here we are talking about net amounts:
.2($1) + .24($2) - .56($1) = $.12
20% of the time we net a $1. 30% of 80% of the time we net $2, and 70% of 80% of the time we lose our bet and net -$1.
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5:53 am
February 19, 2008
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threads13
Member
| | Florida | |
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| posts 343 |
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Todd said:
threads13 said:
I don’t know if that is right about the dealer pushing us 0. Look at it this way, say you bet $5 into a $5 pot and you know you will get call 100% of the time and you will lose 100% of the time. Using the approach you are suggesting that would give us an EV = 0, but clearly the EV = -$5.
I think we’re getting caught up in semantics somewhere. We are talking about 2 different numbers, our equity in the pot and our EV. For instances where we are betting, our EV is our total pot equity minus out bet.
In this case, your equity in the pot is 0. You’re EV is -5 expressed as 0 - 5.
On the same note, if we know that he will fold 100% of the time and we bet $5 into a $5 pot we should expect to win $5 on average. It’s not a $10 win.
You are correct, it is not a $10 win. Our equity in the pot is, however, $10. The dealer pushes us $10 in chips. Once the money is in the pot it’s gone, it’s easiest to talk about equity in those terms. Our EV is our total equity in the pot minus our bet. In this case $10 - $5 = $5.
We can account for our bet in each leg of the calc, but it tends to be a bit more complicated because the pot sizes are all different. For example, here we are talking about net amounts:
.2($1) + .24($2) - .56($1) = $.12
20% of the time we net a $1. 30% of 80% of the time we net $2, and 70% of 80% of the time we lose our bet and net -$1.
Now I’m with ya! Now all the lines are together at this point. I guess I should have noticed that my calculation came to the same as you put in one of your first posts…
There isn’t a "poker math" book out there, is there?
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