This post is a deeper theoretical dive into the hand I discussed in this weeks’ newsletter. The hand where I defend T9dd from the small blind versus his Hijack open and check call three barrels on KTxxQ.

In game my logic was something like this: 

– He’s opening very very wide, cbetting almost always

– He has the table covered, there are 5 hands left, he may play this hand as if it had bubble pressure.

– The only time he might not c-bet is if he has something with showdown that he is “mixing it up” with, therefore ALL air will cbet

– He will check back river with marginal showdown hands like top pair weak kicker or decent second pair like QJ

– Therefore, if he bets the river is polarized between strong top pair or better versus hands that T9 can beat.

– Given the end of the night dynamic he will be more inclined to fire a third barrel with air than to check back a hopeless hand. So I just need to figure out how often he is arriving at the river with a hopeless hand, if it’s “often enough” I should call.

That was the process that lead me to call in game. When I busted early on day 3 I had the leisure time to run some software analysis which I concede will be very hard to get right. It’s hard to know what assumptions to work with, but here is what I tried. Even though he was in the HJ position I gave him a button’s opening range to simulate how wide he was opening. For obvious reasons I can simulate my own calling range in the SB accurately :). I ran it first in PioSolver just with these basic assumptions.

My first pass showed flop and turn call totally standard, river call slightly losing but almost indifferent. However, when I look at a Pio’s solution it is obviously way off what would happen in the real world. Pio had him checking back a lot on the flop because given how wide he is and how tight my range is, he wouldn’t theoretically have a range advantage and should check back a fair amount. But I know he is cbetting at a high frequency, in fact he’s cbetting at an almost absurdly high frequency. To simulate this I can do something called “node locking” where you force the solver to certain frequencies and then solve for equilibrium from that point onwards. So I up his cbetting considerably, lock his flop action and solve again. I repeat this logic on the turn also. With each iteration of this process it makes sense that you have to call wider and wider on the river, and given these assumptions calling with T9s on the river is +EV.

But there are a number of ways in which this could all be flawed most of them to do with real world considerations. I didn’t know for sure he was opening that wide, I was guessing based on the frequency I had seen. Maybe he just hit a rush of cards?

The other consideration, and I think this one is very important, he was intelligently varying his play based on his opponents. I think, but I’m not sure, that he had concluded I was one of the tougher opponents and that might make him less likely to do something wild here. I might be super imposing the way he played against someone else on how he would play against me, and this is very likely not a good assumption. Also, he was smart enough to see this board as one that would be good for my range, maybe I didn’t give him enough credit to pull out of a flop and turn bluff on the river.

I think I was over-consumed with the idea of him abusing the “last few hands” factor. I did know he had just flown in that day, that he was on east coast time and that he had expressed fatigue. Perhaps this would indicate he was less inclined to go berserker in the last few hands. Maybe I just imagined this for him. These are things, of course, that are impossible to know and its what makes poker so awesome.

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