At 600-1200/1200, I raise the button with As5d to 2500, with 22000 behind.  The BB calls.  He has me covered at least 4x.  We are in the mid to late stages of the tournament; 18 left 7 get paid.

Flop is A97r.  Villain check calls 2K

Turn is Ad, bringing back door diamonds.  Villain check calls 4K

River is Jd (completes flush).  Villain jams for 16k.  Should I call?

PIO thinks the flop is a mix, but does bet my hand about 2/3 of the time.  When I gave it 1/3 and 2/3 pot sized bets, it mixed those as well, but preferred my sizing.  It has Villain 18/47/35 for R/C/F.  It raises AT+, 97,77 for value.  For reasons I don’t understand, it check calls 99 and raises 77.  I guess 99 blocks my 9x, and that is more important than blocking 7x?  It bluffs almost all of its straight draws at some frequency, but does not bluff JTs with BDFD.  It’s most common bluff raise is 85.  It does bluff T8 as a mix, but mostly check calls.

The Ace of diamonds turn is a clear bet for my hand.  When I gave it bigger sizing, it mixed 4K, and 8K.  I also let it jam, but it did that less than 1% of the time. Villain defends 11/64/25 to my raise.  Once again it is check raising Ax, some straight draws and a lot of diamond flush draws that somehow called the flop.

The river jam is where we leave PIO territory, since it jams less than 1% of its hands.  I don’t think it is instructive to see that we call when it does jam but FWIW it calls down to TT.  How should we think about whether to call the jam?

One metric we can use is Minimum Defense Frequency.  In theory we need to call at least 1/2 of our hands on the river.  Is A5o in our top half of hands? PIO thinks I get here with about 150 combos, and 68 of them are trips or better.  So, for chip ev, this is probably a call.  What about blockers?  Of course an Ace is a good blocker to Villains Full houses.  The 5d is a minor blocker to Villains flushes.  We don’t block 8s, which Villain can be turning into a bluff (86).  We don’t block Ts which can be value betting straights.  

In game, I did call.  The tipping point for me was that some player types like to bluff odd flushes, so, even though I have more hands that are better than trips on this river, I think the bluffing frequency is higher than for an off suit Jack.  I think the math on MDF and where my hand is in my distribution make this a Cev call, but Tev fold.  

I gave myself a 43% range of openers, down to J5s.  I gave Villain 53%, and assumed he’d 3 bet TT+, AQs, AKo.