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Cbetting the flop, Fold equity and hand equity etc

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  1. #1

    Default Cbetting the flop, Fold equity and hand equity etc

    I understand that if we cbet 50% pot OTF then we need a Villain to fold more than 33% of the time for it to be +EV.

    I understand that when calculating fold equity we need to consider what our Villain PF calling range is and the types of hands they are likely to continue with vs a 50% cbet OTF.

    So we can use Flopzilla to calculate our fold equity.

    However, this assumes we have 0% hand equity, (or does it?)

    So how can you add your hand equity OTF vs their range into the equation?

    Here's an example:

    Villain is a Fish who calls PF with 100% of his range and calls a 50% cbet OTF with any slightly made hand which includes stuff like A high and Overs.

    I hold AK

    Flop: Q65

    Our fold equity is calculated at 34.5%.

    so purely considering fold equity EV cbet = 0

    However our hand equity vs Villains range OTF is 50%, so how can we add this into the equation to calculate our EV and therefore how we should plan to proceed in this hand?
  2. #2
    This does assume 0% hand equity: it makes the action profitable in isolation and is usually stated as doing so.

    Once you get into hand equity you raise the question of how much of that equity you can actually expect to realise (are you likely to call Turn if he bets his AQ?) -and how much extra you're in danger of giving away.

    If you think 50% is the actually realisable value then it's fairly easy: just add 50% of the pots he calls to your equity: EV= 2P/2 = one flopped pot of pure profit.


    The point of working out when an action is profitable in isolation is that you can CB 100% of your hands at that point giving villain no information at all and knowing that you are making a profitable play (there's probably a better strategy still but that one is +EV) ...provided that you don't mess up later on the inflated pots he calls to the extent that you give away more than you won: it's +EV if you never put another chip in but not necessarily so if it leads you into (more expensive) mistakes

    Naturally you're looking for a higher FCB than 34% (and you're mostly going to find it). Once you have that I tend to view hand equity a a bonus that just makes it all more profitable; if I'm betting for hand equity then that's my primary concern and the fold equity is a bonus. I'm not looking for marginal plays because:
    + there's plenty of fat value to be had
    + I want a comfortable margin of error when putting my chips into the variance-hole (both for the variance and because I am going to miscalculate my odds and misjudge my opponents ..also Rake).
  3. #3
    Quote Originally Posted by Timlagor View Post
    This does assume 0% hand equity: it makes the action profitable in isolation and is usually stated as doing so.

    Once you get into hand equity you raise the question of how much of that equity you can actually expect to realise (are you likely to call Turn if he bets his AQ?) -and how much extra you're in danger of giving away.

    If you think 50% is the actually realisable value then it's fairly easy: just add 50% of the pots he calls to your equity: EV= 2P/2 = one flopped pot of pure profit.


    The point of working out when an action is profitable in isolation is that you can CB 100% of your hands at that point giving villain no information at all and knowing that you are making a profitable play (there's probably a better strategy still but that one is +EV) ...provided that you don't mess up later on the inflated pots he calls to the extent that you give away more than you won: it's +EV if you never put another chip in but not necessarily so if it leads you into (more expensive) mistakes

    Naturally you're looking for a higher FCB than 34% (and you're mostly going to find it). Once you have that I tend to view hand equity a a bonus that just makes it all more profitable; if I'm betting for hand equity then that's my primary concern and the fold equity is a bonus. I'm not looking for marginal plays because:
    + there's plenty of fat value to be had
    + I want a comfortable margin of error when putting my chips into the variance-hole (both for the variance and because I am going to miscalculate my odds and misjudge my opponents ..also Rake).
    Thanks for this. Good stuff.

    I don't really understand your formula 2P/2 here or how to apply it though.

    So back to the example: let's add in some $.

    EV (fold-win) = 0.345 x 0.12 = +0.0414
    EV (not fold-lose) = 0.655 x -0.06 = -0.393

    so effectively zero.....

    Now how do we add in that we have 50% hand equity (that we assume to actualise) to the equation?

    I'm trying to establish a mathematical framework for these types of scenarios so I can think about how I would then proceed on later streets if I decide to cbet here.

    If I know that cbetting is +EV then I can then hopefully 'repeat and rinse' OTT, making the necessary adjustments to my fold equity and hand equity.
    Last edited by DJAbacus; 02-25-2015 at 07:29 AM.
  4. #4
    Ok, think I may have this....

    First, the equity I stated in the OP was our equity OTF before we decide whether to cbet or not...

    Second, We are assuming to keep things simple that fold equity of 35% is the same whether IP or OOP (which I know is not necessarily the case)

    So our hand equity if Villain calls (all those 'made hands') is now 37%

    So...

    EV = EV (fold-win) + EV (not fold -lose) + EV ( not fold win)

    EV (fold-win) = 0.35 x 12c = +4c
    EV (call -win) = 0.37 x 0.65 x 12c = +3c
    EV (call-lose) = 0.63 x 0.65 x -6c = -2.5c

    Total EV = 4 + 3 - 2.5 = +4.5c

    So it is +EV at this point to cbet 50% pot based on our reads.

    Is this correct?

    Once, I know this we are moving this hand onto The Turn because as Timlagor rightly points out that this cbetting is only good for us here if we are able to play the next street correctly. i.e. understand how the turn card affects our 'fold equity'' and our 'hand equity vs the Villains calling range' OTT.
  5. #5
    MadMojoMonkey's Avatar
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    You guys are doing well here.

    One thing I want to point out is that you've maybe said more than you've heard.

    The statements divined from the math can be understood on their own as well as in the context of a specific question.
    This tells us truths we were not necessarily aware we needed to know.

    ***
    Not once is the street mentioned here:

    EV = EV (fold-win) + EV (not fold -lose) + EV ( not fold win)

    EV (fold-win) = 0.35 x 12c = +4c
    EV (call -win) = 0.37 x 0.65 x 12c = +3c
    EV (call-lose) = 0.63 x 0.65 x -6c = -2.5c

    Total EV = 4 + 3 - 2.5 = +4.5c
    Or even the game of poker, or even cards.

    There are a few variables here, but you've started to really explore 1/2 PSBs as well as the "fit-or-fold" behavior.
  6. #6
    MadMojoMonkey's Avatar
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    Quote Originally Posted by DJAbacus View Post
    EV = EV (fold-win) + EV (not fold -lose) + EV ( not fold win)

    EV (fold-win) = 0.35 x 12c = +4c
    EV (call -win) = 0.37 x 0.65 x 12c = +3c
    EV (call-lose) = 0.63 x 0.65 x -6c = -2.5c

    Total EV = 4 + 3 - 2.5 = +4.5c
    Wait up a minute.

    This one's not right:
    EV (call -win) = 0.37 x 0.65 x 12c = +3c

    You forgot to count Villain's call.
    EV (call -win) = 0.37 x 0.65 x (12c + 6c) = +4c

    ***
    EV (fold-win) = 0.35 x 12c = +4.2c
    EV (call -win) = 0.37 x 0.65 x (12c + 6c) = +4.3c
    EV (call-lose) = 0.63 x 0.65 x -6c = -2.5c

    Total EV = 4.2 + 4.3 - 2.5 = +6.1c
  7. #7
    Quote Originally Posted by MadMojoMonkey View Post
    You guys are doing well here.

    One thing I want to point out is that you've maybe said more than you've heard.

    The statements divined from the math can be understood on their own as well as in the context of a specific question.
    This tells us truths we were not necessarily aware we needed to know.

    ***
    Not once is the street mentioned here:


    Or even the game of poker, or even cards.

    There are a few variables here, but you've started to really explore 1/2 PSBs as well as the "fit-or-fold" behavior.
    Is my EV (call-win) calculation correct? Maybe it should be E(call-win) = 0.37 x 0.65 x 18c) = +4.5c

    ...and not 12c...as we have to include the 6c that Villain calls our cbet with...
  8. #8
    MadMojoMonkey's Avatar
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    Quote Originally Posted by DJAbacus View Post
    Is my EV (call-win) calculation correct? Maybe it should be E(call-win) = 0.37 x 0.65 x 18c) = +4.5c

    ...and not 12c...as we have to include the 6c that Villain calls our cbet with...
  9. #9
    Ok....so we are still OTF here...

    Let's compare our 'betting 50%' EV to our 'Checking' EV.

    1. We are IP and we check-back. Our hand equity is 50% (this is our equity vs Villains whole PF range)

    EV (win) = 0.5 x 12 = 6
    EV (lose) = 0.5 x 0 = 0

    EV (checking back) = + 6c

    2. If we are OOP and we check and Villain bets 50% pot and we call. Our hand equity is now 37% vs Villains betting range.

    EV (win) = 0.37 x 18 = +6.7
    EV (lose) = 0.63 x -6 = -3.8

    EV (check-call) = +3c

    Compare to our EV of cbetting (IP or OOP) 50% which is +6c

    If we are OOP we want to bet.

    If we are IP we can either bet or check.
    Last edited by DJAbacus; 02-25-2015 at 12:10 PM.
  10. #10
    Quote Originally Posted by DJAbacus View Post
    I don't really understand your formula 2P/2 here or how to apply it though.

    That's ok it was wrong anyway
    P=Pot (12c in this case)
    ..but in the case you call 'call-win' you win 18c not 24c as your bet isn't won. so it should be
    3P/2*P(call)*P(win|call) =3P/2 * X * 1/2

    It's not at all clear to me where you are getting your 0.37*0.65 (*18c).

    That looks like (1/2 * 0.65) * 0.65 which is P(call&win)*P(call) ..an extra P(call).
    Last edited by Timlagor; 02-25-2015 at 02:19 PM.
  11. #11
    Quote Originally Posted by DJAbacus View Post
    1. We are IP and we check-back. Our hand equity is 50% (this is our equity vs Villains whole PF range)
    That should be our equity against his checking range. Hand equity after he checks doesn't include hands he wouldn't check. Whether that's higher or lower than our equity against his IP range is going to be villain-dependant
  12. #12
    Quote Originally Posted by Timlagor View Post
    That should be our equity against his checking range. Hand equity after he checks doesn't include hands he wouldn't check. Whether that's higher or lower than our equity against his IP range is going to be villain-dependant
    which includes his 'check/folding' range, his 'check/calling' range and his 'check/raising' range.....
  13. #13
    MadMojoMonkey's Avatar
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    Quote Originally Posted by Timlagor View Post
    That's ok it was wrong anyway
    P=Pot (12c in this case)
    ..but in the case you call 'call-win' you win 18c not 24c as your bet isn't won. so it should be
    3P/2*P(call)*P(win|call) =3P/2 * X * 1/2

    It's not at all clear to me where you are getting your 0.37*0.65 (*18c).

    That looks like (1/2 * 0.65) * 0.65 which is P(call&win)*P(call) ..an extra P(call).
    35% is fold equity 65% is call equity
    37% is Hero's hand equity to win against Villain's calling range 63% is Hero's hand equity to lose against Villain's calling range
  14. #14
    MadMojoMonkey's Avatar
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    Quote Originally Posted by DJAbacus View Post
    which includes his 'check/folding' range, his 'check/calling' range and his 'check/raising' range.....
    but not his bet/fold, bet/call or bet/raise ranges.

    You DID assume that Villain would check 100% of his pre-flop hands, when he checks.... meaning you expect Villain to NEVER bet.

    EDIT: Every action tells you something about Villain's range. If Villain checked, then Villain does not hold a hand Villain would bet.
    Last edited by MadMojoMonkey; 02-25-2015 at 04:42 PM.
  15. #15
    Quote Originally Posted by MadMojoMonkey View Post
    Every action tells you something about Villain's range. If Villain checked, then Villain does not hold a hand Villain would bet.
    Yes and No...

    I think fish are pretty random in their decision making at 2nl. Sometimes they might check TP. Another hand they might bet with MP. Sometimes they slow play AA and then 2 hands later shove KK. When a fish has a range of say 40/5, I don't think it means that they bet 40% of their range of which they raise the top 5%, it mean they bet 40% of the time of which they raise 5% of the time.

    So when I think about fish calling/checking I think we have to keep the ranges pretty wide but when a fish raises then we can narrow their range down considerably.

    If Villain is a known Aggro LAG, LAG, TAG or Nit then their VPIP/PFR are more reliable.
  16. #16
    Quote Originally Posted by MadMojoMonkey View Post
    35% is fold equity 65% is call equity
    37% is Hero's hand equity to win against Villain's calling range 63% is Hero's hand equity to lose against Villain's calling range
    As I understand it the 37% is the chance that you get called and win anyway. (also the chance of getting called and losing)
    I fail to see why this being is multiplied by the chance of getting called* again.

    * which is already factored in afaics


    If you said that you assume V checks 100% then I missed it.
  17. #17
    MadMojoMonkey's Avatar
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    Quote Originally Posted by Timlagor View Post
    As I understand it the 37% is the chance that you get called and win anyway. (also the chance of getting called and losing)
    No.

    37% is the equity Hero's actual specific hand has to win against Villain's range.
    How Villain got that range (betting, calling, whatever) is irrelevant.

    I didn't actually check to see if the 37% was accurate in the example in this thread.

    Quote Originally Posted by Timlagor View Post
    I fail to see why this being is multiplied by the chance of getting called* again.

    * which is already factored in afaics
    EV = (%chance of call)*(value of call) + (%chance of fold)*(value of fold)
    (All options need to be accounted for.)

    NOW:
    value of call is this
    (value of call) = (%chance to win)*(value of win) + (%chance to lose)*(value of loss)

    SO, plug that into EV
    EV = (%chance of call)*((%chance to win)*(value of win) + (%chance to lose)*(value of loss)) + (%chance of fold)*(value of fold)

    So the distributive property applies to the big parentheses, and we have

    EV =
    (%chance of call)*(%chance to win)*(value of win)
    + (%chance of call)*(%chance to lose)*(value of loss)
    + (%chance of fold)*(value of fold)

    Do you see it now?
  18. #18
    Quote Originally Posted by MadMojoMonkey View Post
    No.

    I didn't actually check to see if the 37% was accurate in the example in this thread.
    Based on this info:

    Villain is a Fish who calls PF with 100% of his range and calls a 50% cbet OTF with any slightly made hand which includes stuff like A high and Overs.

    I hold AcKh

    Flop: Qd6s5d
  19. #19
    Ahh. I was getting confused by so many similar numbers (much clearer if you use formulae with variables in!) and in particular this "However our hand equity vs Villains range OTF is 50%," from the original post.

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