See below for the EV discussion! Basic to EV calculations, however, is estimating our equity fairly closely. Just on inspection, I’d say that the villain had a middle pair or something like AK. It turns out that he had 99 so my wild guess wasn’t totally wrong!
Using magic tools and a bit of pixie dust, we can look more closely at what villain might be holding on the river. First up, let’s give our villain a super wide range that is guaranteed to hit pretty much every board!
I’m going to say that villain would raise and call your 3! every time with:
AA-22,AKs-A2s,KQs-K4s,QJs-Q8s,JTs,AKo-A7o,KQo-K7o,QJo-QTo,
Because our villain, in this analysis, is a bit of a loose canon and probably has a few screws loose, I’m going to say that he will raise and call your 3! 50% of the time with:
[50.0000]K3s-K2s,Q7s-Q2s,J9s-J2s,T9s-T8s,98s-97s,87s-86s,76s-75s,65s-64s,54s,A6o-A2o,K6o-K2o,Q9o-Q2o,JTo-J2o,T9o-T8o,98o-97o,87o-86o,76o-75o,65o-64o,54o[/50.0000]
I’ll also assume that villain will play on with anything that has a direct hit, overpairs etc and all “decent” draws.
Preflop: Hero has 63% equity, we’re good to go!
Flop: Absolutely no surprise to discover that our hero now has 78% equity (against villains continuing range). It should also be no surprise that villain has an absolute bucketload of hands to continue with here.
Turn: Villain has a load of Ax diamonds that might have continued from the flop, overpairs, top pairs and so on - the standard stuff. Nothing exciting and our equity against his turn continuing range is 78%.
River: We can assume that our villain is going to bet or call a reasonable bet with any made hand at this stage. Hero is still looking good with 78% equity.
Villain is likely to have:
straight: 16%
set: 18%
two pair: 18%
overpair: 24%
top pair: 24%
What about if our villain is stupid tight? We’ll assume, as previously, that he only continues with overpairs, direct hits and “decent” draws and his preflop range is: 88+,ATs+,KJs+,AQo+
Seems pretty tight to me!!!
Our heroes equity on the river against villains made hands is 82%.
The final possibilities are:
set: 17.65%
overpair: 70.59%
top pair: 11.76%
Notice that, in this scenario, our villain is playing so tight that he just can’t have a straight or flush!
The danger of these sorts of numbers, though, is that I have been assuming that our villain isn’t going to bluff with air!
These numbers may not be right for you, please consult the product disclosure statement or your poker consultant. Past performance is not a guarantee of future performance. These figures are generated using standardised tests in a controlled environment, your mileage may vary.
The basic EV equation is (%win * $win) - (%lose * $lose).
%win = hand equity, %lose = 100 - %win (obviously), $win = pot + your call amount, $lose = your call amount
If I have rearranged things correctly, we get required equity: %win = (100 x $lose) / ($win + $lose)
Interestingly, required equity using this formula is only 20%! I certainly hope that someone clever will double check me on this!
A more interesting, to me, formula that you might enjoy playing with calculates the EV when hero wants to shove. This is particularly useful in tournaments where our hero is down to about 25BB. It’s quite amazing just how little equity is required to justify a shove provided, this is important, you get your fold equity estimate fairly close!
(C2xB24) + (1-C2)x((B2x(B24+B5))-(1-B2)xB5)
C2 = fold equity
B24 = pot size
B2 = heroes hand equity
B5 = heroes stack size
There you go, no need to pay for a solver
There is an affordable solver, GTO+, that is $75 for a lifetime license. I am nowhere near needing anything more sophisticated than fingers and toes but those of you in the upper echelons may find that this is good value.
If you don’t already have it, I would strongly recommend getting Flopzilla Pro for $25 - it is, pretty much, a surgically enhanced, steroid junkie version of Equilab.
I have no idea what I’m doing with it but all the pretty colours keep me entertained for hours!
Hope this helps
Regards,
TA