Willfull suspension of disbelief as it pertains to river play - Page 2

fizzleboink · #11 12-28-2005, 07:13 PM

Ok I'm going to try and solve this problem using some math.

Let X be the probability that Hero is ahead of UTG
Let Y be the probability that Hero is behind UTG

Let A be the probability that Button overcalls 1 BB
Let B be the probability that Button calls 2 BB

Let C be the probability that UTG calls your raise when he is behind
Let D be the probability that UTG 3-bets your raise when he is ahead

Constraint:
X + Y = 1

Equation 1: EV of calling UTG's bet = (1 + A)X - Y
Equation 2: EV of raising UTG's bet = (2B + 2C)X - (3D)Y

This is assuming you always call a 3-bet from UTG. UTG never 3-bets a worse hand and never folds a better one.

I'm going to tackle this problem from the angle where I don't know how often Hero is ahead or behind here, but I have some idea of how the calling station will act, as well as UTG.

So I will let X and Y be the unknowns.

Basically I want to find the tipping point where both raising and calling have the same EV. If they have the same EV, then I can combine equations 1 and 2 together:

(1 + A)X - Y = (2B + 2C)X - (3D)Y

Using the constraint equation (X + Y = 1) I will put Y in terms of X.

(1 + A)X - (1 - X) = (2B + 2C)X - (3D)(1 - X)

Solving for X yields:

X = (1 - 3D) / (2 + A - 2B - 2C - 3D)

If you want X in terms of percent, just multiply it by 100%.

I think this equation can be used re-used in this kind of situation all the time, and it is a situation that does happen somewhat often. I'd like to maybe try and generalize it some more later on with a variable number of possible overcallers, when I have a bit of free time.

Now just an example, here are some numbers that might be reasonable:

I will let:
A = 0.8 (= 80%)
B = 0.1 (= 10%)
C = 1 (= 100%)
D = 1 (= 100%)

If you feel that these are unreasonable assignments of the variables, you can change them and plug them into the equation above and see how the results change.

Anyways, it gives us a result that X ~ 83%. So Hero needs to be ahead of UTG greater than 83% of the time in order for raising to be superior to going for the overcall.

The next step would be to put a weighted range of hands on UTG, and to see how that range compares to X. Ofcourse you can argue the values that I chose for A, B, C, and D are wrong. You can also get into long-winded arguments about how often Hero is ahead. I think the best way to do it is to play around with the numbers and see how the result changes. Assume a bad case for Hero and if the answer is still clear cut, then fiddling with the numbers a bit is irrelevant.

I slapped together a quick spreadsheet so that you can play around with the numbers and see the result a lot quicker:

http://rapidshare.de/files/10003408/...Raise.xls.html

Stealthy · #12 12-28-2005, 07:16 PM

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I like the overcall.

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Okay, time for me to school some folks.

News flash: He just about never has a 4 here. Your hand is good >90% of the time IMO.

I want to get in more than 1 more bet. He's not bet/folding because he's not that smart. Button has a propensity to call, I want him to call 2 cold some % of the time. I also want the donk to bluff 3-bet sometimes, or 3-bet his weaker hand like an idiot.

Combine all these factors and you can earn more by raising. The overcall isn't guarantee and has a value of less than one BB. The raise is worth more than 1 BB.

Simple enough?

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Ah I see exactly what you mean!

In that case ..... I call. [img]/images/graemlins/wink.gif[/img]

They always seem to have the 4 when I raise here, damn runner runner!

Alobar · #13 12-28-2005, 08:02 PM

great post

B is a lot higher than 10% tho

fizzleboink · #14 12-28-2005, 08:26 PM

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great post

B is a lot higher than 10% tho

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Oh and just by looking at the equation, you can see that:

B makes twice as much of an impact as compared to A
C makes twice as much of an impact as compared to A
D doesn't matter too much. I mean it still makes a difference but because it's in the numerator and denominator the effect of the 3 is attenuated.

kidcolin · #15 12-28-2005, 10:02 PM

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great post

B is a lot higher than 10% tho

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D is a lot less than 100%, too.

Your equation is nice and all, but Metereon put it best:

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The overcall isn't guarantee and has a value of less than one BB. The raise is worth more than 1 BB.

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oxymoron · #16 12-28-2005, 10:14 PM

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I'd go for the overcall.

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TheMetetron · #17 12-28-2005, 11:57 PM

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great post

B is a lot higher than 10% tho

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D is a lot less than 100%, too.

Your equation is nice and all, but Metereon put it best:

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The overcall isn't guarantee and has a value of less than one BB. The raise is worth more than 1 BB.

[/ QUOTE ]

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I really think it just simplifies the whole problem to think of it that way. Your hand is just so good it's not even funny here.

fizzleboink · #18 12-29-2005, 12:57 AM

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I really think it just simplifies the whole problem to think of it that way. Your hand is just so good it's not even funny here.

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Yup you're right. I just felt the raise vs. overcall is a frequent question on these boards and that using the math I did should prove helpful in a tougher spot.

Spartan1983 · #19 12-29-2005, 02:36 AM

[ QUOTE ]
[ QUOTE ]
I like the overcall.

[/ QUOTE ]

Okay, time for me to school some folks.

News flash: He just about never has a 4 here. Your hand is good >90% of the time IMO.

I want to get in more than 1 more bet. He's not bet/folding because he's not that smart. Button has a propensity to call, I want him to call 2 cold some % of the time. I also want the donk to bluff 3-bet sometimes, or 3-bet his weaker hand like an idiot.

Combine all these factors and you can earn more by raising. The overcall isn't guarantee and has a value of less than one BB. The raise is worth more than 1 BB.

Simple enough?

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Very nice concise thorough explanation, thanks.

peterchi · #20 12-29-2005, 03:43 AM

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[ QUOTE ]

Your equation is nice and all, but Metereon put it best:

[ QUOTE ]
The overcall isn't guarantee and has a value of less than one BB. The raise is worth more than 1 BB.

[/ QUOTE ]

[/ QUOTE ]

I really think it just simplifies the whole problem to think of it that way. Your hand is just so good it's not even funny here.

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Not saying that you're wrong, but I'm not yet convinced.

Given the description, button is calling 1 bet pretty much always. 2 bets, probably not so much.

I agree that it is most likely that UTG is full of [censored]. But 90%+, I don't know. And what do we do if 3-bet? I can't fold so basically then we are losing 3 bets.

I think the question for me is, do we win 4 bets often enough to overcome the times that we lose 3? Maybe so, but I'm still pondering. Either way, I don't think this is as obvious as you say. I may come around though, don't give up on me yet.