Simplified math

    • Gabinr1
      Gabinr1
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      Joined: 05.04.2009 Posts: 7,755
      I want to ask a question, but I will start by adding some value to this thread.



      * To know if a call is profitable we have to calculate our pot odds and compare it to our equity vs our opponents range (we get the equity with the pokerstrategy equilab)

      - If villain bets pot 10$ into 10$, then we have 33% pot odds. We have to pay 10$ to win a total pot of $30. 1/3 or 1:2, however you want to note it.

      We calculate this way: $10 (investment) / $30 (total pot) = .33 (aka 33%)


      To verify this we can take 9 cases:
      . in 6 we lose to a best hand
      . in 3 we are right and win
      - 6 times we lose 10$ = -$60
      - 3 times we win a total of $90 (in pots), we extract our investment (10$*3) and get $60 pure winnings.
      - So from 9 showdowns we have 0 loss/profit. This verifies the equation.

      That said, we need at least 33% equity to make the call profitable. So if we win in half the time we are +EV.

      If villain's bet is half the pot, then we have to be right with our call in at least 25% of the time to be +EV. (ex. villain bets 5$ into 10$... 5/20= .25 [pot odds] )



      * To know how often a bluff has get a fold we just have to know the pot and our bet size. If on the river we bet pot $10 into $10, villain has to fold in at least 50% of the time to make the bluff profitable.

      We calculate it this way: $10 (investment) / 20$ (total pot won. our bet included) = .5 (aka 50%) [for BE]

      To verify this we can take 10 cases:
      . 5 times villain calls our bluff and wins
      . 5 times our bluff succeeds and we take the pot
      - 5 times we lose $50
      - 5 times we in $100 (in pots), we extract our investment (10$*5) and we get $50 pure winnings.
      - So from 10 cases we have won 5 times 10$ and lost 5 times 10$ = 0$ profit/loss. This verifies the equation.

      This means that if from 10 cases he folds 6 times and 4 times he calls and we lose, it's +EV to bluff.

      If we bet with half the pot then we have to get a fold in just 33% of the time to be +EV. (ex. we bet 5$ into 10$... 5/15= .33 )



      *OK, what I want to ask is how do we make the math (in a simplified way) to find out how often do we need to get a fold from villain when we shove on the flop with equity if called? Please give several examples.

      Lets say we shove on the flop $10 into a $10 pot, if called we win 20% of the time at SD. How often do we have to get a fold for the semibluff to be profitable? (if 0 equity then that would be 50% of the time, but here we also have equity to include in the math) How do you do the math to find out?
  • 18 replies
    • clawindsouza
      clawindsouza
      Bronze
      Joined: 08.12.2009 Posts: 7,085
      examples....dam....sorry im too tired to do it today...will let you know tomorrow alright? thought id post and let you know instead of just leaving it blank so that you know ppl are reading your post....:D
    • 101aj
      101aj
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      Joined: 16.10.2010 Posts: 170
      r we allowed to use equilab while playin at the tables... ?
    • eXtremeACE
      eXtremeACE
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      Joined: 22.02.2011 Posts: 267
      Originally posted by 101aj
      r we allowed to use equilab while playin at the tables... ?
      Of course! How would they even know if you're using it or not?
    • nathanrenard
      nathanrenard
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      Joined: 09.02.2009 Posts: 816
      Originally posted by eXtremeACE
      Originally posted by 101aj
      r we allowed to use equilab while playin at the tables... ?
      Of course! How would they even know if you're using it or not?
      I am pretty sure PokerStars can find out if you are using ICM trainer while playing SNGs...
    • Gerovit
      Gerovit
      Bronze
      Joined: 16.01.2011 Posts: 1,308
      Ill repaire this

      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -0.8x*10 + 0.2X*20 + 10*(1-x) = 0
      -8x-10x + 4x = -10
      -14x = -10
      x= 10/14= 5/7

      or if he call you 5 out of 7 times your shove is be.

      So he has to fold only two out of seven times for shove to be break even.

      Hope this helps.
    • eXtremeACE
      eXtremeACE
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      Joined: 22.02.2011 Posts: 267
      Originally posted by nathanrenard
      Originally posted by eXtremeACE
      Originally posted by 101aj
      r we allowed to use equilab while playin at the tables... ?
      Of course! How would they even know if you're using it or not?
      I am pretty sure PokerStars can find out if you are using ICM trainer while playing SNGs...
      I don't know anything about ICM trainer, and don't know if you were being sarcastic or not, but Equilab is basically a software independent of poker platform and stuff..

      It's not scanning tables or anything. If they were able to find you're using it, then imo they are doing something against your privacy and I'm pretty sure they aren't allowed to do so.
    • Gerovit
      Gerovit
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      Joined: 16.01.2011 Posts: 1,308
      Originally posted by eXtremeACE
      Originally posted by nathanrenard
      Originally posted by eXtremeACE
      Originally posted by 101aj
      r we allowed to use equilab while playin at the tables... ?
      Of course! How would they even know if you're using it or not?
      I am pretty sure PokerStars can find out if you are using ICM trainer while playing SNGs...
      I don't know anything about ICM trainer, and don't know if you were being sarcastic or not, but Equilab is basically a software independent of poker platform and stuff..

      It's not scanning tables or anything. If they were able to find you're using it, then imo they are doing something against your privacy and I'm pretty sure they aren't allowed to do so.
      You can use equilab but not sng wiz you have a list of forbidden and allowed software on pokerstars

      http://www.pokerstars.com/poker/room/prohibited/
    • gadget51
      gadget51
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      Joined: 23.06.2008 Posts: 5,622
      Two questions guys.

      1. Why do we lose -$8 and not -$10?
      2. We don't seemt o take rake into account anywhere, is that ok?
      Sorry for being a bit simple. :(
    • Wriggers
      Wriggers
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      Joined: 21.07.2009 Posts: 3,250
      Don't we lose $8 because 20% of the time we win the pot. If we have 20% equity in the $10 pot then our EV longterm is -$8.

      And yes, I was wondering about the rake as well.
    • Gabinr1
      Gabinr1
      Bronze
      Joined: 05.04.2009 Posts: 7,755
      Rake is 0, for simplicity.

      Why -$8? We win 20% of a $30 pot, not a $10 pot.


      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -8*x + 10*(1-x) = 0
      -8x-10x = -10
      -18x = -10
      x= 10/18 = 5/9

      or if he call you 5 out of 9 times your shove is be.

      Hope this helps.
      Can you post some examples? And maybe verify it like I did on the first 2 points.
    • Wriggers
      Wriggers
      Bronze
      Joined: 21.07.2009 Posts: 3,250
      Originally posted by Gerovit
      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -8*x + 10*(1-x) = 0
      -8x-10x = -10
      -18x = -10
      x= 10/18 = 5/9

      or if he call you 5 out of 9 times your shove is be.

      Hope this helps.
      I think gadget was referring to the above post, where the pot is $10, meaning with 20% equity we would lose $8 in this pot. Either that or i've missed something completely :D
    • Gabinr1
      Gabinr1
      Bronze
      Joined: 05.04.2009 Posts: 7,755
      Haha, I think I got it, this is gold, will post after further verification. I will explain it like no other.


      A sample:

      It seems that with 20% equity with a pot shove on the flop we need to get at least 30% folds to be profitable (instead of 50% with 0% equity if called).

      It goes like this:
      In 100 cases...
      - 30 times we take the 10$ >>> +$300
      - 14 times (20% of 70% when called) we take a profit of 20$ >>> + $280
      - the rest of 56 times we lose $10 >>> - $560

      Results, 300+280-560=+$20. This means that we have an EV of (20/100) +$0.2 per shove with this exact odds.
    • Gabinr1
      Gabinr1
      Bronze
      Joined: 05.04.2009 Posts: 7,755
      With 25% equity if called we only need to see folds in at least 20% of the time for the semibluff to be profitable. (we 20% exact FE we are BE)

      Again, we verify it by taking 100 cases:
      - 20 times we win $10 (the pot) with the semibluf >>> +$200
      - 20 times (25% of 80% we get called) we get a profit of $20 >>> +$400
      - 60 times we lose $10 >>> -$600

      Results, 200+400-600=0... BE.



      I will post later when I understand it better how I got to find how many % of folds we need.
    • Gerovit
      Gerovit
      Bronze
      Joined: 16.01.2011 Posts: 1,308
      Originally posted by Wriggers
      Originally posted by Gerovit
      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -8*x + 10*(1-x) = 0
      -8x-10x = -10
      -18x = -10
      x= 10/18 = 5/9

      or if he call you 5 out of 9 times your shove is be.

      Hope this helps.
      I think gadget was referring to the above post, where the pot is $10, meaning with 20% equity we would lose $8 in this pot. Either that or i've missed something completely :D
      This
    • Gabinr1
      Gabinr1
      Bronze
      Joined: 05.04.2009 Posts: 7,755
      Originally posted by Gerovit
      Originally posted by Wriggers
      Originally posted by Gerovit
      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -8*x + 10*(1-x) = 0
      -8x-10x = -10
      -18x = -10
      x= 10/18 = 5/9

      or if he call you 5 out of 9 times your shove is be.

      Hope this helps.
      I think gadget was referring to the above post, where the pot is $10, meaning with 20% equity we would lose $8 in this pot. Either that or i've missed something completely :D
      This
      Sorry but that is wrong. If we get called 5/9 times the shove will not be BE, but highly profitable. If we get called 3/10 times the shove will be slightly above BE. I explained it above.
    • Gerovit
      Gerovit
      Bronze
      Joined: 16.01.2011 Posts: 1,308
      Originally posted by Gabinr1
      Originally posted by Gerovit
      Originally posted by Wriggers
      Originally posted by Gerovit
      Ill make this as simplest as possible

      every time villain calls you you loose in average -8$
      Every time he doesn't you win 10$
      x times he calls you (so 1-x times he doesn't), we want to see when are you break even:
      -8*x + 10*(1-x) = 0
      -8x-10x = -10
      -18x = -10
      x= 10/18 = 5/9

      or if he call you 5 out of 9 times your shove is be.

      Hope this helps.
      I think gadget was referring to the above post, where the pot is $10, meaning with 20% equity we would lose $8 in this pot. Either that or i've missed something completely :D
      This
      Sorry but that is wrong. If we get called 5/9 times the shove will not be BE, but highly profitable. If we get called 3/10 times the shove will be slightly above BE. I explained it above.
      Im sorry i made a mistake didn't take a win into account it should be like this :f_cry:
      (when we win we get 20$ (10$ pot+ 10$ villains)

      0.8*(-10)*x + 0.2*20*X + (1-x)*10 = 0
      14x=10

      x = 10/14 or 71.42% of a time

      So

      10 times we get called and we loose 8 times -80$
      10 times we get called we win 2 times +40$
      4 times we dont get called +40$

      Sorry for confusion pretty sure this is ok now :f_p:
    • Gabinr1
      Gabinr1
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      Joined: 05.04.2009 Posts: 7,755
      This adds a new dimensions to my game, I got a lot of new insights in the game of poker after what I just realized today here. I almost don't want to write it, but this thread made me think about it and the feedback from the posters helped in the process. So here it is:


      1. We need to find out how much we lose when we get called.
      2. Use that number as the investment, for taking down the pot (as a bluff).

      You get it? Instead of using $10 to win $10 (10/20... FE equation), we use loss from equity to win $10 ( loss/10+loss).

      Here are the two examples from above, with 20% equity and 25% equity:

      A) 20% equity if called.
      - 80% of the time we lose 10$
      - 20% of the time win get a profit of $20
      ... that means we win $4 ($20*0.2) and we lose $8 ($10*0.8). We get 4-8=$4 loss if we would have no fold equity (if we got called every time).

      Now what we do is making that loss be our bet to take down the $10 pot. Because that's the most we are losing in this pot, not $10 but $4. So we do 4/14 (14 pot to take down =10 initial pot + 4 our bet ) and we get 28.6%... this is how much villain has to fold for our semibluff to be at least BE. The more he folds the more we win.


      B) 25% equity if called.
      - 75% of the time we lose 10$
      - 25% of the time we get a profit of $20.
      ... that means we win $5 ($20*0.25) and we lose $7.25 ($10*0.75). We get 5-7.5= 2.5 loss.

      2.5/(10+2.5) = 0.2 aka 20% ... If villain folds at least 20% of the time we have a profitable shove.


      To be clear and to be no confusion, the hand/problem has the next hypothesis:
      - Pot is $10
      - We shove for pot $10
      - Villain to act.
      - No rake. For the simplicity of the example.


      Insights:
      * If we get a positive number from our equity equation, than the bet is profitable even if it's called 100%.
      * If we have at least 34% equity if called, then a semibluff shove for pot will be profitable no matter what. This is like calling a bet, but with added benefit of FE.
    • gadget51
      gadget51
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      Joined: 23.06.2008 Posts: 5,622
      Thank you very much for making the effort to explain it.

      Now.......about that rake. :)