PokerJuice analysis

PokerJuice shared report - hh only (no assumptions filled in) 

Putting BTN on a generous $FI50!AA range. He probably opens much wider, but folds some to the 3-bet multiway, so we use this. We assume he is committed when he pots. 

1. Baseline analysis (no bluffs)

http://hh.pokerjuice.com/report_35b76fb6-e5ca-4641-8b6d-01779ceb659e

7+ 

EV (shove) = -$1.20

We are breaking even. Then we add some reasonable semibluffs on top:

2. Adding tight semibluff range

http://hh.pokerjuice.com/report_023e3b29-d983-4099-95a7-d0afc9166594

7+,(T+,98):Ass

EV (shove) = +$72.88

We make some money. A quick combo count:

7+ = 7862
7+(T+,98):Ass = 9497

So the semibluffs add around 20% to his range. Does it make sense to call and dodge bad turns here? Then we check-fold when we don't have the required 24.98% EQ for getting it in profitably on the next street.

Only Js, 8s, 6s don't make the cut. We are still 22%+ on these:

3. Adding looser semibluff range

http://hh.pokerjuice.com/report_a8a8039f-d386-4f32-a456-6b703595b02e

7+,Ass

EV (shove) = +$223.48

A tidy profit, but perhaps we can do better? Villain now raises 13633 combos, a 73% increase relative to the baseline. With all NFD's in his range, it becomes much more relevant to dodge spades. So we look at turn cards again.

Now there are eight bad turns: Ks, Qs, Js, 8s, 6s, 5s, 4s, 3s (our worst EQ is 19% on 8s):

Villain's range translated to OO syntax is $fi50!AA:((7,T7,TT,77),Ass). We put this into Odds Oracle and calculate our EV for calling the raise, planning to check-fold bad turns and GII on good ones (the Peel & Stack-Off line):

Peel & Stack-Off EV analysis:

- We have > 24.98% EQ on 83.47% of turns
- Our average EQ is then 54.61%

We'll do the EV math in term of Hero's final effective stack size, because this is simplest. Effective stack before flop betting is $938 and pot is $198. When we get raised, our stack is $791 with $273 to call. 

When we Peel & Fold, we ends up with $791 - $273 = $518. When we Peel & Stack Off and win, we end up with $198 + 2*$938 = $2074, and when we lose, our stack is zero.

Our stack increase with P&SO line is then:

EV (P&SO)
= (Expected final stack) - (our stack in moment we get raised)
= (0.8347*(0.5461*2074 + 0.4539*0) + 0.1653*(518)) - 791
= +$240.02 

Relative to shoving, EV has increased with $240.02 - $223.48 = +$16.54. This is an almost +3bb edge that we happily take.

Conclusion:

- We jam and break even against 7+ (or rather, it doesn't matter what we do)
- We jam and make +$79 against 7+,(T+,98):Ass
- We Peel & Stack-Off (folding on 8 spades) and make +$240 against 7+,Ass

Extending this analysis to other raising ranges is straightforward. We have learned that jamming against trips+ is break-even, and that Peel & Stack-Off is the highest-EV line when Villain is semibluffing all NFD's. Making an additional +3bb/hand compared to shoving is not to be sniffed at in games where 5 bb/100 is a good win rate.

Adding the actual outcome of the hand to our knowledge database, P&SO appears to be a useful strategy against this Villain for the future (decides to semibluff, commits his stack, and lets us choose when). We make a note of that.