After my blooper from the last hand and some further thought I decided to revisit the whole scenario of how my foe played the hand, but with a more detailed and analytical approach.
Firstly, with a short stack, his play on the flop is flat out wrong. Here he must either bet out or check raise me as he hopes to be a favourite and should want to get his stack in whilst so, with the added equity of making me pass. A check call is the worst alternative unless he knows for sure that he can contrive the play I am about to analyse, which starts to become a bit of an extensive parlay.
So we’ve got to the turn. What are his alternatives? He can bet out or he can go for a check raise – I’m dismissing a check call here for simplicity’s sake. The bet out is the straightforward play here. Assuming I’m a LAG (loose aggressive good) then betting out will make me pass all my draws, except the 15+ out ones, and of course if he’s already losing, he has to accept that he’s going broke here. It’s hard to get away from a set with a shortish stack in PLO. This wins him the pot but does it maximize his EV? Back to the Theory of Poker thing, it actually forces me to play correctly as in that I will pass if I should pass and call if I should call. It is hard for me to make an error here. But now let us look at the crafty check raise play.
The main risk, and drain of EV, in the check play is that I check back. Not only does he then give me a free card, but he’s also committed himself to calling any bet on the river as his show of weakness is more likely to encourage a bluff (I’m assuming he understands this of course.) But. He then picks up some catch bluffs equity on the river, normally from my low odd misses. And if I hit a high % draw, in a sense he was putting the money in regardless so although it feels dumber putting it in when I’ve hit, it’s not a catastrophe as he would have paid anyway. The only real disasters are he makes less money, because I would have paid but now refuse to bluff; I hit a low % draw which I would have passed.
Calculating all of these permutations is unnecessarily complicated, all we need do initially is look at the foe’s EV for the check raise turn, but understand that it would have to be downgraded for the reasons above.
Unfortunately I can't get my calculations into any kind of presentable format, but with some assumptions on the range of hands I have, mostly skewed to the weaker side, he ends up with a huge $500 EV+ on just over a $500 wager. This is truly massive and could not be turned negative by the risk of checking unless I am a high % checker on the turn, which is unlikely from the play of the hand. I also find it hard to see how simply betting out could better this either.
Interestingly, this expert play does not mean he is an expert. As I commented recently, many expert Omaha plays look identical to chump ones. It’s the thought that counts.