cross-posted with this thread from the theory forum

A common situation, especially in agro games: you've got some small PP and villain is an agro 3better. you don't want to make a small 4bet because you think hero could well shove T7s and force you to fold. At what point does it become +EV to 4bet your small PP AI?

I've outlined the calcs below. I believe them to be correct, but would be grateful if someone could check. I've picked hero's hand as 22.

Assume 100 BB stacks,3x raises and 10x 3bets

what 3bet % is it ok to push 22 after?

how much we lose when called: (.36 x 106BB) - (.63 x 97BB) = 38-61= -23BB

how much we win when villain folds: 13BB

for every time that villain calls, he has to fold around 1.7 times

probable 3bet+call AI 4bet range is 8.3% of total hands. (see below- I've included half of all KQo hands and all KQs hands in villain's calling range)

Text results appended to pokerstove.txt

1,130,120,640 games 0.814 secs 1,388,354,594 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 63.188% 62.84% 00.35% 710146116 3957660.00 { 77+, ATs+, KQs, AJo+, KcQd, KcQh, KcQs, KdQh, KdQs, KhQs }
Hand 1: 36.812% 36.46% 00.35% 412059204 3957660.00 { 22 }



therefore villain has to 3bet more than 8.3% x 2.7 = 22.5% of the time for an AI push to be +EV

What about if you include AQ in your 4bshoving range too?

Text results appended to pokerstove.txt

9,071,786,592 games 6.464 secs 1,403,432,331 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 59.527% 57.73% 01.80% 5237191632 162959397.00 { 77+, ATs+, KQs, AJo+, KcQd, KcQh, KcQs, KdQh, KdQs, KhQs }
Hand 1: 40.473% 38.68% 01.80% 3508676166 162959397.00 { 77-22, AQs, AQo }

how much we lose when called: (.40,5x 106BB) - (.59,5x 97BB) = 43-58= -15BB

how much we win when villain folds: 13BB

for every time that villain calls, he has to fold around 1.15 times

2.15 x 8.3= 18%

wow this seems interesting. any math guy here who can approve this?

Why makes you think he is calling with KQ+? Do that same calc from his perspective now and work out villains break even calling range vs your 4bet range.

Does not compute.

Edit: Or maybe it does. Could you please explain this? Perhaps with an example?

I think he means in the specific example where we have 22 and not in general/w value type hands to induce spew.

I mean our equity on bluffs increased considerably when villain doesn't bluff us back.

That's nice, imo.

we loose a LOT of value if we shove w AQ... Fwiw villians are polorised to 22-77 a LOT when they do this..

Ok. So you write that, then you follow up with this:
Yeah, and a lot of players knows that as well. Think about those two statements now and think about what range the OP gave as calling range, because you contradict yourself.

yes i know there is a contradiction.

do u still call off w AJ/KQ when there is a 3bb open and you 3b to 10bb and he OTT ships 4 the rest of 100bb? I have not come across many people who have in my experiance, It allowes them to play too perfectly with their much trashier hands.

(i am not saying its a bad play, i just feel you loose too much value playing it THAT way, then possibly flatting/4bing.. its all oppnant specific)

I have been cought with snapping off w KQ and AJ/A10 kinda hands too. and then loosing but then i found the villian to stop 3bing so much and the game dynamics changed a lot. So i dont know how much you could use it as part of your general strtagy.

How about having 78ss in that range too? What about AA?