By 4betting we risk an additional $18 to win a total of $31.5 (including the blinds), but in case he shoves we call.
So in those cases we effectively risk $97.
It's hard to say what his shovingrange looks like exactly, but {TT+,AQs+,AKo} should do it.
I just included AQs to have some AQ combos in there.
Our equity against that range is:
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 64.162% 62.90% 01.26% 290811564 5824662.00 { TT+, AQs+, AKo }
Hand 1: 35.838% 34.58% 01.26% 159861192 5824662.00 { TT }
or roughly 35%.
His range makes up for 3.8% of total hands.
When we look at the formula for calculating the breakeven point, we have:
EV = Pfold * Pot + (1 - Pfold) * (Equity * (Win + Investment) - Investment)
We can set the EV to 0 as we want the breakeven-point.
We have to solve this for Pfold (i'll skip the detailed fomula transformations):
Pfold=1 / 1 + ( -Pot / (Equity * (Win + Investment) - Investment) )
Putting in the numbers:
Pfold = ~0.46 = 46%.
So he has to fold more than 46%.
We estimated his total_callingrange to be 3.8% which should be 1-0.46=54% of his range in this spot, therefore with the rule of three we get:
3.8/54 = ~0.0704
0.0704 * 46 = ~3.24
So he has to have an additional 3.24% of total hands he folds., therefore his total 3bettingrange needs to be ~7%.
This is actually a lot tighter than the last one I calculated.
I guess the reason is, that the last time I assumed we were up against a looser opponent. In general this means he shoves more hands like AQ, so our foldequity is decreased. That is because we have a flip against AQ, so when he folds his equityshare in the pot it's better for us than if he shoves it in, therefore we still need him to have the same ~4% foldingrange - if he gets it in with 5%-6% of hands we're in this 10%-11% region I mentioned above).
♠_rolleyes:> ♠_confused:> ♠_cool:
