Cbetting the flop, Fold equity and hand equity etc

[DJAbacus]

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.

[Timlagor]

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).

[MadMojoMonkey]

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

[Timlagor]

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.

[MadMojoMonkey]

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.

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?

[DJAbacus]

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