Calculate EV of preflop All-ins

    • gigenieks
      gigenieks
      Global
      Joined: 18.10.2010 Posts: 130
      For example,

      fold, fold, fold, fold, fold, Hero raises to $0.06, fold, BB raises to $0.30, Hero raises to $1.06, BB raises to $1.82, Hero raises to $2.32 and is all-in, BB calls $0.39 and is all-in

      BB shows A:spade: Q:spade: (Pre 32%)
      Hero shows K:diamond: K:heart: (Pre 68%)
      Hero wins $0.00
      BB wins $4.21

      So the calculation goes like this?

      0.68*4.21 + 0.32*(-4.21) = 1.59

      And that means although I lost that hand I "should"win on long run approximately $1.59, right?
  • 7 replies
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,904
      You need the Equilab

      So that you don't die of curiosity while installing it:


             Equity     Win     Tie
      UTG    68.16%  67.94%   0.22% { KK }
      UTG+1  31.84%  31.62%   0.22% { AQs }


      Oh, I get it -- you already have the equities.

      But I think that you have the calculations a bit skewed -- or I do ?(

      "68% equity" means that you "own" 68% of the pot.
      The would work out to $2.86

      You put in half of that pot, though (ignoring the blinds to simplify), which is 2.10
      So your net gain is 2.86 - 2.10 = 0.76
      Less rake of course.

      That seems like such a thin margin.
      I hope your calculation is correct :f_biggrin:
    • Tomaloc
      Tomaloc
      Bronze
      Joined: 17.01.2011 Posts: 6,858
      vorpal's post is mostly correct. do you think that 30+ big blinds in a result that already discounts rake is something little though :P

      where's op's mistake?
      0.68*4.21 + 0.32*(-4.21) = 1.59

      if you are calculating EV profit you are not investing $4.21, the right value to use is effective stacks ($2.21)

      0.68*2.21 - 0.32*2.21 = ~0.80 (also ignoring 1 cent of small blind)

      why the result difference? because rake is not being considered.
      without rake the pot would actually be $4.43 instead of $4.21

      since you have the final amount discounting rake though, you can just use it like
      4.21*0.68 - 2.21 = ~0.65

      how much do you hate nl2 rake now :f_biggrin:

      [edit: i missed 1 cent of small blind. oh well]
    • Schnitzelfisch
      Schnitzelfisch
      Bronze
      Joined: 08.11.2008 Posts: 4,952
      Hey,

      what you calculated is the EV of the following scenario in the long run:

      -you have KK
      -you know that opponent has AQ (he shows it to you)
      -you shove all-in and he always calls

      in that scenario, EV is:

      EV = 0.68*2 - 0.32*2.21 = 1.36 - 0,7 = +$0.66

      Of course in reality things are a bit different, since you play vs hand ranges, the equities are different. And you will usually want to know the equity of calling a shove or something similar, then again the calculation is different.

      -SF
    • gigenieks
      gigenieks
      Global
      Joined: 18.10.2010 Posts: 130
      Only $0.66?

      So if I played 1,000,000 times KK vs. AQs in the end I would won ONLY $0.66 ???
      I don't know why but this doesn't feel correct...
    • VorpalF2F
      VorpalF2F
      Super Moderator
      Super Moderator
      Joined: 02.09.2010 Posts: 8,904
      Thanks, Tomaloc & Schnitzelfisch for clarifying that.

      As you can see, even with slightly better than 2:1 edge in equity, the margin is quite thin.
    • Tomaloc
      Tomaloc
      Bronze
      Joined: 17.01.2011 Posts: 6,858
      no, you win $0.65 EV bucks (raked) each time so you'd win $0.65 * 1000000 :P

      you can make the calculations yourself :f_biggrin: you see, 68/32 is not a that massive edge
    • ExternalUseOnly
      ExternalUseOnly
      Bronze
      Joined: 30.01.2010 Posts: 3,373
      Originally posted by gigenieks
      Only $0.66?

      So if I played 1,000,000 times KK vs. AQs in the end I would won ONLY $0.66 ???
      I don't know why but this doesn't feel correct...
      I would hope to win a little more than $0.66 :D

      Yeah this means that if you play the hand over and over and over in the same scenario you will win 0.66 each time obviously that doesn't min you will win every single hand but this is the average you will win each time this scenario happens :)

      It's good to see you asking questions in the forum though. You can't learn if you don't ask right? So if you need anything else feel free to ask away

      All the best
      Carl