help me understand math from application of nlhe - Beginning Poker Questions

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help me understand math from application of nlhe

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12-29-2023 , 01:33 AM

tiltmonster12

stranger

Join Date: Dec 2023 Posts: 1

on page 47 there is an example of calculating our expectation by multiplying our equity vs villains range times the final pot. In the example equity is .45 and pot is 201.5 and then its written like this:

-9.325 = (0.45)(201.5) - 100

But it doesn't explain where the -100 comes from.

There is also another equation of winning 12.5bb 60% of the time when our 3bet bluffs get through and winning 7.5bb on average:

7.5 = (0.6)(12.5)

It kind of seem like they both should be written the same way. I dont get where the - 100 comes from.

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12-29-2023 , 12:34 PM

slyless

Hand Evaluation Expert

Join Date: Dec 2021 Posts: 2,744

Can you provide a screenshot or photo of this page?

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12-29-2023 , 12:35 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 5,033

I haven't checked the book but it seems clear to me that the following is the case:

The general EV equation for calling a bet is

EV = Pr(win)*$ Won - Pr(lose)*$ Lost

= eq*(Pot + Bet) – (1-eq)*Bet)

=eq*(Pot + 2*Bet) – Bet

where Pot = amount prior to a bet of Bet

For the equation

9.325 = (0.45)(201.5) – 100

100 has to be amount of the bet so 201.5 has to be the Pot+2*Bet making the pot = 1.5

Therefore the equation has the blinds of 1.5 as the pot and bettor bets 100 which his opponent has to call.

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01-03-2024 , 03:21 PM

stremba70

old hand

Join Date: Aug 2020 Posts: 1,330

Hard to tell without other information but the equation is consistent with a problem like “My opponent bet $100 on the river into a $101.50 pot. My holding has 45% equity vs villain’s range. Should I call or fold?”

If that is the problem, then we profit $201.50 when we win. This happens 45% of the time, so we expect a profit of 201.50 x 0.45. It costs 100 to make the call, so the EV of the call is 201.5 x 0.45 - 100. Since it is less than zero we should fold.

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01-03-2024 , 03:24 PM

stremba70

old hand

Join Date: Aug 2020 Posts: 1,330

Your second equation is fine as far as it goes. You will win 7.5 bb on average from your 3! bluffs preflop (given that fold percentage). This implies that betting more than 7.5bb when you 3! will give a -EV. It really isn’t quite that simple of course since that would assume that you never win when you three bet bluff and get called, which is unrealistic.

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01-05-2024 , 05:34 AM

sixfour

should be called sevenfour

Join Date: Dec 2005 Posts: 75,238

Quote:

Originally Posted by stremba70

this seems quite wrong

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01-05-2024 , 11:33 AM

stremba70

old hand

Join Date: Aug 2020 Posts: 1,330

Quote:

Originally Posted by sixfour

this seems quite wrong

That’s because it is. I had a bit of a brain fart (now that I look at it again) while trying to figure out where the original formula might have come from. In reality you would expect to win 45% of 301.5 in the scenario I posted, which makes the call easily +EV.

I guess it would have to be modified to a question of calling a bet of 100 into a pot of 1.5. In that case the formula originally posted is right and it is a correct fold
.

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02-04-2024 , 11:47 AM

rivercitybirdie

Pooh-Bah

Join Date: May 2012 Posts: 4,726

interesting discussion

and from someone who does alot of math in work/life, it is easy to confuse or mix/match "gross" and "net"

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