My poker theory math is screwed up, can someone please clear these doubts?

    • maheepsangari
      maheepsangari
      Silver
      Joined: 08.06.2010 Posts: 2,163
      I've been avoiding fully understanding these calculations for a long time and just used short cuts but now when I'm trying to understand theory I have some weird doubts cropping up in my head.

      Lets say we're on the river and the CO bets into the BU for 1/2 PSB.

      x(1)-(1-x)0.50=0

      This equation is used to calculate FE, I understand that where x is the % of the time the BU should fold when CO bluffs ATC.

      So,
      => x-0.50+0.50x=0
      => 1.5x=0.50
      and x=33%

      So when CO bluffs ATC the BU needs to fold more than 33% of the time and the CO makes instant profit.

      Q1. In the above equation if x is the % of time CO needs to win and say CO's betting range on river has value hands and bluffs and the BU has bluff catchers and is indifferent to calling or folding so say he's always calling. So when BU calls a 100% of CO's river bets and when CO bets the river according to the equation CO need to win 33% of the time, right? I know my conclusion is completely wrong as CO needs 33% of his range to be bluffs and rest to be value so where am I screwing this up?

      Moving on, from the same equation above we can work out that the BU needs to defend 67% of his range at least.

      Using the equation,

      x(1.5)-(1-x)0.50=0
      we can find out the % of time the BU needs to win on the river.

      So,
      => 1.5x-0.50+0.50x=0
      =>2x=0.50
      so x=25%.

      Q2. So this means that the BU needs to win 25% of the time to breakeven after he calls. And we determined that the BU should call 67% of the time so thats a total of 0.67x0.25=16.75% of the range that he sees river with needs to win. That has to be wrong cause thats too low a number. So again where am I screwing up?

      My whole problem is that when I view all of this as an observer and not the CO and BU, it doesn't make sense.

      If I am the CO I know that betting 1/2 pot on river means I have 33% FE. And I know that if I am the BU and face a 1/2 pot bet on the river, if I call I need to win atleast 25% of the time. But if I view as an observer then its like ok CO can have 33% bluffs in his range and BU needs to win atleast 25% of the time so the BU needs CO to have 25% of bluffs in his range to breakeven. Shouldn't these number be exactly linked? As in if CO needs to win 33% of the time then the BU should need to win 67% of the time right?

      Someone please help me, I am so screwed up with basic poker theory math.
  • 6 replies
    • maheepsangari
      maheepsangari
      Silver
      Joined: 08.06.2010 Posts: 2,163
      bump
    • ZeDawning
      ZeDawning
      Bronze
      Joined: 27.02.2011 Posts: 204
      I'll address a part of your question,

      Originally posted by maheepsangari
      So when BU calls a 100% of CO's river bets and when CO bets the river according to the equation CO need to win 33% of the time, right? I know my conclusion is completely wrong as CO needs 33% of his range to be bluffs and rest to be value so where am I screwing this up?
      CO needs 25% of his range to be bluffs actually, in order to make BU's bluffcatchers indifferent to calling or folding.

      Eg. If CO bets 50 into 100 pot, and he is bluffing 1/3 of the time, BU should call 100% of the time w his bluffcatchers as its +EV. BU should only be right 1/4 of the time.
      If CO is bluffing 1/4 of the time, calling or folding bluffcatchers is the same for BU.

      Hope this helps.
    • maheepsangari
      maheepsangari
      Silver
      Joined: 08.06.2010 Posts: 2,163
      Can you show this with an actual equation? Like I showed you how I came to the fact that CO needs 33% folds and BU needs to win over 25% when he calls using the equations I did, can you show me why you say that its 25% and not 33% for CO?
    • mkjmkjmkj
      mkjmkjmkj
      Bronze
      Joined: 05.02.2012 Posts: 159
      question 1
      the 33% is how often opponent needs to fold for your bluffs to be succesfull
      if he calls 100% you win more on your value hands so it equals out. but your ev calculation is only shows the EV of your bluffs if you want to see your overall EV you should extend the equation to include valuehands

      its the value to bluff ratio that is 33% 25%/75% =0.33

      0.25 is bluffs and 0.75 is valuehands

      x(1)-(1-x)0.50*0.25 + (1-x)*1.5*0.75=0

      question 2
      your calculation is right the number is not too low
    • mbml
      mbml
      Black
      Joined: 27.11.2008 Posts: 20,698
      With a half pot bet

      1a. The bettor needs at least 33% FE in order to breakeven on his bluffs
      b. Thus, the defender must look to defend 67% of his range to deny the bettor the opportunity to auto-profit on his bluffs

      2a. The caller is receiving 25% pot odds on a call
      b. In order to make the caller indifferent between calling and folding, the bettor must design his betting range such that the caller's bluffcatchers have exactly 25% equity on a call (75% value, 25% bluffs)

      These 2 numbers are not directly related.

      If defender knows the aggressor's actual betting ranges or can make a very strong educated guess, his decision is simple.
      Call if equity >25%
      Fold if equity <25%

      If defender is not sure about the aggressor's actual betting ranges, then he looks at his own ranges and defend the top 67% of his bluffcatch range to deny the bettor an opportunity to autoprofit with his bluffs.
    • maheepsangari
      maheepsangari
      Silver
      Joined: 08.06.2010 Posts: 2,163
      Originally posted by mbml
      With a half pot bet

      1a. The bettor needs at least 33% FE in order to breakeven on his bluffs
      b. Thus, the defender must look to defend 67% of his range to deny the bettor the opportunity to auto-profit on his bluffs

      2a. The caller is receiving 25% pot odds on a call
      b. In order to make the caller indifferent between calling and folding, the bettor must design his betting range such that the caller's bluffcatchers have exactly 25% equity on a call (75% value, 25% bluffs)

      These 2 numbers are not directly related.

      If defender knows the aggressor's actual betting ranges or can make a very strong educated guess, his decision is simple.
      Call if equity >25%
      Fold if equity <25%

      If defender is not sure about the aggressor's actual betting ranges, then he looks at his own ranges and defend the top 67% of his bluffcatch range to deny the bettor an opportunity to autoprofit with his bluffs.
      This really helped clear things up. Thanks a lot.

      So the primary purpose of the first equation is to figure out what % the BU needs to defend basically (not just what FE CO needs, just another way of looking at it basically) and work accordingly.

      The second equation helps us determine what bluff:value ratio the CO needs and what equity the BU needs to make the river call.