Hi.
Basically, I would like to know the formula to know when a jam over a flop c/r is profitable.
Let´s say we are 20 bb deep and we have 9h7h,
We minraise pre, villain calls.
We cbet 1/2 pot on a Ks6h4h board, and villain c/r to 5 bb.
Flopzilla says we have 36% equity over his check-raising range.
What´s the math, here?
Thanks! 
You can adjust the equations I derived here to answer this question:
http://www.husng.com/content/jumped-35s-7s-twice-twice-i-get-crushed
You just need to add in the villain c/r and adjust the amount hero jams to reflect there has been an additional raise after the cbet.
Deriving and solving these equations will help your understanding of the math underlying these spots.
Happy to check your result & working once you or another poster have had a go at it.
I'm interested to hear what % of the time you need to get a fold for the jam to be profitable based on us having 36% equity if they call......
In general though in these spots I won't make these kind of calculations, my rule is just generally:
If I believe they are check raising light = jam (as long as they have enough chips behind them to fold and I think they will give my jam credit)
If I believe they are check raising tight = flat call as long as the pot odds / implied odds are there
Use your intuition to work out if they are check raising light based on how often villain is check raising, their general level of aggression in the match, how long they took to check raise, game flow, bet sizing compared to other times they have made larger or smaller bet sizing etc.....
On top of this you don't just want to work out what their check raising range is, but what part of their range you think they will fold to your jam. Are they the type who might check raise 2nd pair here and call your jam? or will they fold it? Two Check raisers with the exact same check raising range will produce different results for you depending on what parts of their range they are willing to fold to your jam / how spewy they are.
The math here will be helpful especially when you work out what %% of the time you need to get a fold, but there is no formula which is going to tell you whether you should jam or not.
So...
pot on flop, P0 = 4.0 BB
cbet = 2.0 BB
pot after cbet, P1 = 4.0 + 2.0 = 6.0 BB
villain c/r = 5 BB
pot after villain c/r, P2 = 4.0 + 2.0 + 5.0 = 11.0 BB
hero jam, J = 20 - 4 = 16.0 BB
final pot when called, P2 = 20 * 2 = 40.0 BB
villain has to call, C = 20 - 2 - 5 = 13.0 BB
EV(c/r jam) = f * P1 + (1-f) * [ P2 * e - J ]
or in terms of effective stacks (S),
EV(c/r jam) = f * 11.0 + (1-f) * [2*S*e - (S-4)]
@ S = 20BB * e = 36%
so...
0 = f * 11 + (1-f) (40*0.36 - 16)
0 = 11f -1.6 + 1.6f
f = 1.6 / 12.6 ~ 13%
Is this correct?
Yep.
Other than your notation of repeating P2, thats correct.
But that's being a bit picky because your answer is right.
You risk 16BB to win 11BB and have 36% equity in a pot worth 40BB when you get called.
If villain folds > 13% of the time you are better jamming than folding.
So villain needs to have 1 c/r fold to jam hand for every (87/13) = 6.7 c/r call jam in his c/r range to be able have better expectation jamming over villain's c/r than folding to it.
Another way to frame it is to look at the stack you expect to end up with at each end of branch of the decision tree:
If you fold after cbetting, you will end up with a stack of (S-4).
If you jam, you end up with a stack of
(S+7) if villain folds,which happens with a frequency of 'f'
(2Se) if villain calls, which happens with a frequency of (1-f)
So you are better off jamming when your expected stack after jamming is worth more than your stack if you fold:
f(S+7) + (1-f)(2Se) > (S-4)
which for S=20 and e=0.36
f(27) + (1-f)(14.4) > 16
27f + 14.4 - 14.4f > 16
f > 1.6 / 12.6 ~ 13%
Hey, knoxxxy, thanks for the advice. Yes, I agree.
In the end, math is only right if our assumptions are right.
Great lessons, cdon3822.
I guess that, with some adjustments, this equations can be aplied in almost every spot in a poker hand.
That´s my bigest leak, understanding the math behind some spots.
I´m eager to learn all that and you gave me a great help, thank you so much.
Yes, with enough branches of a decision tree and assumptions about ranges & corresponding frequencies you can use math to model poker.
How many folds you need when you jam over villain's 5BB c/r in a single min raised pot after cbetting 0.5P and you have 36% equity vs his c/r and call jam range is a fairly specific question.
Building up a fundamental understanding of common spots will allow you to play better in them as well as provide more discrete reference points from which you can think about new spots which you encounter & correct adjustments vs particular player tendencies while playing.
Some spots which come up far more frequently, which you may want to explore:
Pre flop
- open jam vs calling range [C] @ S
- call open jam vs range [R] @ S
- min raise call vs 3b jam range [3b] @ S
- min raise fold vs 3b jam range [3b] @ S
- attacking limps vs [limp call] : [limp fold] ratios
- effect of limping on postflop SPRs
- 2 street limp stab expectation vs one street preflop only game models
Post flop
- cbet call vs cbet fold on various board textures within the context of which lines villain allocates his hands into (c/f, c/c, c/r)
- 2barrel & 3barrel bluffing @ (S, SPR) vs [c/c] : [c/f] ratios on various board run outs
- c/r jam semi bluffs vs [cbet fold] : [cbet call] ratios @ SPR on various board textures
- turn & 2barrel river bluff probes vs flop check back ranges on various board run outs
Ok, thanks!