Reverse Engineering A Fold Equity Calculator

moldyfishmoldyfish Red Chipper Posts: 97 ✭✭
Hey y'all,

Question: Can someone show me the equation which RCP's fold equity calculator uses to solve?
https://redchippoker.com/fold-equity-calculator/

example: we are on the river. pot is $100. villain bets half-pot (50). I raise 3.5x the bet (175). I have 18% equity.

Inputs for FE calc:
Pot Before Shove (P): 150
How Much to Call (B): 50
How Much is Shove (R): 175
Equity (E): 18%

Output:
Fold Equity (F): 39%

How can I reverse engineer this? I am looking to use it in an google spreadsheet.

If you could, please use the variables above and solve for F. Thank you.

Comments

  • RoblivionRoblivion WisconsinRed Chipper Posts: 294 ✭✭✭
    edited August 8
    First, a clarification: I'm pretty sure the calculator is expecting the "pot before shove" to be 100, and "how much to call" to be 50. Otherwise, there wouldn't be a reason to enter both numbers.

    Anyway, I believe it's using something like this:

    0 = [(P + B) * F] + (1 - F)*[(P + R)*E - R*(1 - E)]

    So, equilibrium is when
    The money we make when he folds PLUS
    The money we make when he calls and loses MINUS
    The money we lose when he calls and wins
    Equals 0.

    Then, just rearrange the equation to solve for F.
  • moldyfishmoldyfish Red Chipper Posts: 97 ✭✭
    edited August 9
    Roblivion wrote: »
    First, a clarification: I'm pretty sure the calculator is expecting the "pot before shove" to be 100, and "how much to call" to be 50. Otherwise, there wouldn't be a reason to enter both numbers.

    this is unclear.

    and yes i am aware of that equation, not the rearranging.
  • TheGameKatTheGameKat Posts: 2,281 -
    moldyfish wrote: »
    Roblivion wrote: »
    First, a clarification: I'm pretty sure the calculator is expecting the "pot before shove" to be 100, and "how much to call" to be 50. Otherwise, there wouldn't be a reason to enter both numbers.

    this is unclear.

    and yes i am aware of that equation, not the rearranging.

    I seem to recall doing this once and producing a quadratic.
    Moderation In Moderation
  • RoblivionRoblivion WisconsinRed Chipper Posts: 294 ✭✭✭
    moldyfish wrote: »
    Roblivion wrote: »
    First, a clarification: I'm pretty sure the calculator is expecting the "pot before shove" to be 100, and "how much to call" to be 50. Otherwise, there wouldn't be a reason to enter both numbers.

    this is unclear.

    I'm pretty sure the pot and any bets you are facing are left as separate variables, because you may or may not be facing a bet and this would be an elegant way to separate the two numbers.
  • TheGameKatTheGameKat Posts: 2,281 -
    Roblivion wrote: »
    moldyfish wrote: »
    Roblivion wrote: »
    First, a clarification: I'm pretty sure the calculator is expecting the "pot before shove" to be 100, and "how much to call" to be 50. Otherwise, there wouldn't be a reason to enter both numbers.

    this is unclear.

    I'm pretty sure the pot and any bets you are facing are left as separate variables, because you may or may not be facing a bet and this would be an elegant way to separate the two numbers.

    That's correct, I think. By including any bet you're facing it allows a calculation of your raise size from your bet. Not the only way to set it up, but a relatively clean one.
    Moderation In Moderation
  • EazzyEazzy Red Chipper Posts: 964 ✭✭✭✭
    Ok lets develop it intuitively .

    When called your equity is %equity * final pot - your bet(not including the call)
    we will call this E (equity in final pot)

    when they fold we win the pot...or P

    so is the fold equity is X then the times they call is (1-x)
    The amount we win when they fold has to equal the amount we loose when they call)

    xp = (1-x)e
    xp = e-xe
    xp +xe = e
    x(p+e) = e
    x = e/(p+e)

    In a spread sheet I would calculate final pot, and E and then use it in this final formula.
  • Doug HullDoug Hull RCP Coach Posts: 1,779 -
    I implemented this.

    It was confusing as anything to implement because the plug-in we use was meant for "Sum these two numbers" and rather simple things like that. I do not remember the exact formula used, but I derived it from published sources and "I are an enginer" so the math is right. You will need to re-derive as has been done above.
    Co-founder Red Chip Poker,
    Author Poker Plays You Can Use
    Author Poker Workbook for Math Geeks
  • moldyfishmoldyfish Red Chipper Posts: 97 ✭✭
    be77uwewwwlb.png


    I was attempting to figure it out to build this interactive fold equity calculator.

    The formula for which was

    =(-Q2*(((3.5*A6)/(1+A6))+(1)+((3.5*A6-A6)/(1+A6)))+((3.5*A6)/(1+A6)))/(-Q2*(((3.5*A6)/(1+A6))+(1)+((3.5*A6-A6)/(1+A6)))+((3.5*A6)/(1+A6))+(1))

    Where Q2 is equity and A6 is the percentage of pot of the initial bet.

    @Roblivion and @TheGameKat , i’m fairly certain you are not correct about how to input the fold equity calculator. The pot at the decision point is the initial pot + bet. It matches up in my table.
  • RoblivionRoblivion WisconsinRed Chipper Posts: 294 ✭✭✭
    moldyfish wrote: »
    be77uwewwwlb.png


    I was attempting to figure it out to build this interactive fold equity calculator.

    The formula for which was

    =(-Q2*(((3.5*A6)/(1+A6))+(1)+((3.5*A6-A6)/(1+A6)))+((3.5*A6)/(1+A6)))/(-Q2*(((3.5*A6)/(1+A6))+(1)+((3.5*A6-A6)/(1+A6)))+((3.5*A6)/(1+A6))+(1))

    Where Q2 is equity and A6 is the percentage of pot of the initial bet.

    @Roblivion and @TheGameKat , i’m fairly certain you are not correct about how to input the fold equity calculator. The pot at the decision point is the initial pot + bet. It matches up in my table.

    You're absolutely right. When I drop the equity to 0 and I change the amount you have to call, it doesn't change the FE calculated at all, which means it's not changing the size of the total pot based on the amount bet. It must only be using that to back into the amount V would have to call to calculate what you would win in cases when you win.

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