Math problem...

    • Kombaiyashii
      Kombaiyashii
      Bronze
      Joined: 24.04.2012 Posts: 5
      I am really bad at math, so please be easy on me.

      Lets say we are short stacked, I want to shove pre-flop my 300 stack into a pot of 450.

      My opponent will fold 40% of the time.

      How do I work out what minimal equity I need for this shove to be profitable?
  • 5 replies
    • InsanityOnFire
      InsanityOnFire
      Bronze
      Joined: 09.01.2011 Posts: 120
      Hey!
      you win 450 40% of the time when he folds
      you win 300+450 with a probability of 0.6*x, where x is your equity against his calling range.
      you loose 300 with a prob of 0.6(1-x).
      That assumes he made no bet before you shove (when he calls he calls the full 300 you push)

      Your EV = 0.4*450 + 750*0.6*x - 300*0.6*(1-x)

      put EV = 0 and rearrange:

      1050*0.6*2*x = 300*0.6 - 0.4*450

      Example is not very good, as we get x=0, meaning you don't need any equity. That is, your push is profitable with just foldequity alone, even if you loose the flip 100% of the time.
    • UPAY4DINNER
      UPAY4DINNER
      Bronze
      Joined: 27.09.2009 Posts: 21,922
      Thank you InsanityOnFire :)
    • iThinBetRiver
      iThinBetRiver
      Bronze
      Joined: 06.06.2012 Posts: 12
      In simpler terms (lets assume you lose every time he calls),

      Your opponent calls 6/10 times -> You lose 300 * 6 = 1800 chips

      Your opponent folds 4/10 times -> You win 450 * 4 = 1800 chips

      I.e. As Insanity stated, you don't need equity since you would still be break-even even if you are drawing dead every time he calls.
    • InsanityOnFire
      InsanityOnFire
      Bronze
      Joined: 09.01.2011 Posts: 120
      Exactly.
      I just showed a general way of calculating this minimal equity you need if he doen't quite fold enough.
    • UPAY4DINNER
      UPAY4DINNER
      Bronze
      Joined: 27.09.2009 Posts: 21,922
      Thank you guys :)