I re-modelled as a nuts-or-air game with 3 streets of pot bets. Ie, AA never bets, PP never improves, and PP potbets with all his nuts and gives up bluffs street by street.

Given a range of 1/8 nuts and 7/8 complete PP:s optimal strategy then is to bet his nut hands for 3 streets and

For simplicity we’ll say that PP has 8/64 nut hands and 56 air hands. He obviously bet his nut hands for a psb every street.

His optimal bluffing then is to bet 19 air hands on the flop, 10 on the turn (giving up 9) and 4 (giving up 5) on the river.

Then PP:s value for the game is 27/64 of the flop pot. So assuming the earlier street cost him 3bb he roughly loses about 46bb/100 hands.

Since the more complex game will involve suckouts I think we can assume that PP will improve his win-rate from this estimate, but I have a really hard time seeing he would get it into.

If AA always check calls and PP never bluffs I get PP:s value as roughly 100bb/100 hands.

Doing a very, very rough estimate I get that the PP guy will be able to continue from the flop on with 1/6 of his range and making AA indifferent to his betting. Which is the same thing as saying that he folds 5/6 and wins 1/6.

Since the pot never is going to get to 200bb (AA can bet very small on the flop to make 2-out draws indifferent and then go into call-down mode making bluffs indifferent) the deep stacks doesn’t really help the pocket pairs.

Ie, he’s better off just folding pre and AA gets 75big blinds/100 hands assuming the button rotates.

Interesting! I’ve been wondering about it many times how deep would stacks need to be for calling w/ pocket pairs to become profitable in scenarios almost exactly like this, so I can’t wait to hear the answer (but don’t feel pressured to reveal it before everyone who wants gets a chance to guess).

I will start by guessing that it would be profitable for hero (the player with small pocket pair) to play the game with these stack sizes, but I can’t really guess by how much. If I have to put a number on it I’ll say 25bb/100.

Heh, turns out my intuition is somewhat wrong …

According to my tool (*) if SB open-raises to 100% and can then only choose from { fold, 4-bet-to-55-and-call, 4-bet-to-55-and-fold, 4-bet-all-in } then he loses ~$1.3/hand when BB 3-bets (60%) for a total profit of $0.02 per hand (or 1bb/100) assuming BB folds if not 3-betting (**).

But if SB raises 75% and BB plays the same then he makes $3.8 per hand. So that makes a huge difference.

(*) Homegrown and somewhat tested (it ~ agreed over a small set of comparisons with StoxPoker’s tool).

(**) If BB 3-bets the top 60% then obviously he has to fold if not 3-betting. I haven’t run the calculations for if BB 3-bets a polarized 60% (allowing a not-obviously-negative-EV calling range!) because I’m too lazy to type all those hands in!

Err sorry with 75% SB makes $0.575 per hand  (+$0.5/hand when BB 3-bets + $2 when BB folds, times 75% – $1 the 25% time SB open folds) …

In the 75% case SB’s optimal play is to 4-bet/call 17% and 4-bet-shove 30% of his 75% open (you’d probably get ~the same either 4-bet-calling or 4-bet-shoving the entire range); and BB shoves/calls-shove ~33% of the time of his 60% 3-bet.

In the 100% case SB 4-bet/calls 7% and 4-bet-shoves 31%; and BB shoves/calls-shove the same 1/3rd of his 60% 3-bet.

The moral of the story is that SB needs to call BB and use position to punish him (or tighten up and hope BB doesn’t adjust ).

Well, normally people never learn and just keep playing too few hands hoping their poor luck will end.

I don’t think the red line *should* be close to zero when you’re exploiting somebody (and if you’re not, you’re very unlikely to be +ev against him). For instance, if you’re playing against an extreme calling station bluffing isn’t so appropriate so letting him have small pots and winning medium pots and bigger is ok.

Similiarly if I am exploiting somebody who folds too much, of course I’m going to take a hit once we show down, because his hands will be so much stronger on average.

I don’t really know an appropriate adaption against somebody playing very loose (while not being a complete monkey) from the button. Reraising and donking should be a part of it, as should getting rid of hopeless hands early. The strategy where somebody always checks the flop, then checkraises rarely and always checking the turn after calling allows the button to get value from the flop and see five cards with his crappy hands for only a preflop raise and flop bet.

It would be cool to see the results of the program you’re using. So please post the results, and certainly the name of the program if it’s not home made.

I’ve been really careful to check for folds under the current session tab when playing OOM, to make sure he’s not folding hands. But it turns out PT thinks he’s actually folding 20% of his hands on the reraise and playing 80% for a re-pop. I can’t figure out how that got by me.