@ Cornholio:
Against BB-s x/r range ofc. KQ is around the top 40% of BU-s range. That means if you fold KQ here, you fold nearly 60% of the time, and if we are starting off from that then I gladly x/r every single hand that I have here, and you can go for TP for my bunghole, cause I wont give a poop if you raise back. Reasons :
a) Due to your overfold I have already made a massive profit with the hands I will fold to your bet/3bet
b) You wont be able to re-bluff enough
You cant fold more than 26.66666.% of the time otherwise I can raise(.../fold) any2.
So Kx is an obvious call here. The x/r -er's goal is to make this call at least 0EV, and also the call of weaker hands if necessary,the bottom is at 27% as already mentioned.
The x/r-er needs to make the c-better indifferent between (at least) four options:
a) calling the flop or folding instantly
b) calling the flop and folding the turn
c) calling the flop+turn and folding the river
d) calling all three streets
The x/r-er can do this by x-ing at each decision point as if the hand was ending there (because if the x/r-er does not overbluff b/c-er's winnings can be maximum 0 on further streets and so forth...), and he needs to do this at least in a frequency according to the previous decision point's pot odds.
For example just examine point a). For flop the c-better to have a break even call vs a x/r on the fop he needs to win the pot 11.7% of the time according to the immediate odds, so the x/r-er needs to x the turn at least 11.7% of the time. But to be more precise he also needs 11.7% equity vs the range that is x-ed down and it also needs to be x-ed down in this %. Otherwise his flop call wont win the pot enough times to be at least BE.
So if you x/r as the BB and give up something with 11.7% frecuency that has say 10% equity you still win the pot 10% of the time when it goes x-x, the BB-s flop call will have something like -0,1 EV so you rather have to x 12.7% of the time and so he'll be BE.
But that was only point a). If you only have 13% bluffs and give em all up on the turn your turn bet range will contain only value. So you obviously have to bluff more, and this is where the stacking model gets into question.
If we consider all three streets betting down as a x/r-er bluffing goes something like this
>11,7% >> 16% >>> 12%
( I denote > as a street: > is flop, >> is turn, >>> is the river)
You only bet down the core of your value range because on future streets you'll have to x with value hands that turn below 50% equity (either by the narrowing or improving of the opponent's calling range) plus you'll also get raised ( tho this is not included to the indifference equations of this model, still have to count with it somehow) , BUT we can still include a parameter to represent this range, say because of this core range is 100% value we make this represented by 100 combos.
So on the river the x/r-er has value 100 combos and he needs to bluff 12% of the time 100/(1-0.12)=100/0.88 =113.636 comos in total so 100 value +13.5 bluffs. Just test this if its right: 113.636*0.12 =~ 13.6 so indeed 13.5 bluff combos is OK.
And it goes all just like this back on the turn and the flop :
100/ ( 1-0.12) / (1-0.16) / (1-0.117) =~ 153.2
And this leads us to 53.2 pure bluff(!) combos on the flop when we make that x/r. In % that is 53.2/153.2= 34.7%
This means if the flop c-better has a pure bluffcather facing that x/r on the flop , that can't beat anything else but a bluff, then this bluffcatcher must have there at least 34.7% equity just due to the number of pure bluff combos that the x/r-er has in his range. IF he has a bluffcatcher that has only something like 32 % equity there, he can muck it it right away, because he just simply wont win the pot enough times.
So if we return back to the case of KQ and we see that it has I'd say around 15% equity vs the x/r range you designed on the coaching, then BU can simply dump that and exploit the x/r range that simply does not contain enough bluffs. As mentioned above that's a top 40% hand and this is a massive overfold cause BU need's to continue with top 73%
The range I designed counts with around 160 value hands I started off considering that you'll x/r and bet down your Ax-s quite frequently (that's roughly 12x12 combos=144) plus some pocket pairs, sets, improved bluffs, so even if you x sometimes on the turn or on the river or if you get a raise, +card removel +whatever 150-160 hands might a good approximation ,tho I dont really have good methods for this. And this makes up to 240-250 hands in total so 80-90 bluff combos.
Even vs this quickly designed range a weaker Kx has only like 27-29% equity, which seems a bit lower than it should be, but it may also be OK because :
- BB will have to x more than what the model dictates and this makes your future investments lower
- despite the dry board the hand still has a little implied odds and this makes your expected winnings increase
So I think you can go below 35% equity, but not too much, and something like 15-20% is certainly wrong IMO.
