So this could get slightly complicated, but I will try to keep it as simple as possible. So first off, equities are something that, at the table, are hard to calculate. They are usually learned over time by analyzing spots in equilab, like you are doing. You just start to get a feel for what you average equity is in a given spot. You also need to make assumptions about the range you are against and the equity can change based on the range.

So in the spot you are talking about it is slightly different than the counting the outs to estimate your equity. When counting outs, you typically have a drawing hand and you are using the rule of 4 & 2.

So in the above you have a medium strength made hand and you are more in a calldown situation and are deciding, if facing a bet, if you should call with your hand or not. Not really gonna get into if you want to donk or not or what happens when they check back. So you said the guy was opening ~22% from the BU, which is pretty nitty. So we will look at the extreme cases. If villain was only to ever bet his value hands, then you probably wouldn't have enough equity on average to call. Your pair of 9s is not doing good against only his value range, which would consist of stuff like top pair, 2 pair, sets, maybe some 9x as well. I put some of that in an equity calculator and you basically have 17% eq. If you somehow knew villain was only ever betting value hands, than you could just fold your weaker 9x and move on. On the other spectrum you said you had 63% against his entire 22% opening range. So if you somehow made the assumption that he opened 22% of hands from the BU and opted to cbet all of them on the flop. You would have an easy call. In fact, you could almost consider raising, but won't get into that either.

So, using the extreme cases, you can see how your equity varies based on the assumptions of what range you give villain to bet with. Typically people are some where in the middle. The well bet most of their value hands, but might opt to check a few back to have some strong hands in their check back range on future streets. They will then bet some draws like flush draws, strong straight draws and combo draws. Some of those are kind of for value against you, as some of them have a ton of equity against your entire calling range. Then they might add in some more bluffs, like gutshots or some hands that have backdoor flush draws or back door straight draws or some over cards that block some of your value hands in your calling range. Some guys will merge in some middle pair and bottom pair for protection as well. So when you start to add all of those things in, the equity of your 9x starts to go up. I have a formula I use, its kind of complex, so won't go into it here, but I would say that a hand like J9 in this scenario would have somewhere in the neighborhood of 35-40% eq, maybe slightly less or slightly more. I think it would be too strong to fold to one bet, so you would probably just check call and see a turn card.

The main thing with equities post flop, is you need to figure out your equity vs the range of hands that they will take that action with on the given street, not the entire range of hands they get to that street with. So in your case you want to put villain on a range of hands that they will actually bet with, not the entire opening range. Then figure out your hands equity vs the betting range. Likewise, if you are the preflop aggressor and want to figure out if you have more than 50% equity with a given hand to be able to make a value bet, you need to figure out the hands equity vs the calling range of the villain, not the entire range they called with preflop. Unless you somehow knew they were always betting or always calling with their entire range.

As for calculating what to do vs a shove, you basically have to use the risk/risk+reward formula and compare that to the equity you think you have. So lets say that villain is ~50bb short stack and opts to just open shove the flop. So if he opened for 3bb and you called 3bb there would be ~6bb in the middle. Maybe slightly more with the blinds, but will use this to keep it simple. if he shoves 50bb on the flop the pot would now be 56bb and you have to call 50bb.

The 50bb you have to call is what you are risking and the 56bb pot is the reward. so 50/56+50=47.17%. So now you would need to put villain on an flop shoving range and calculate your hand's equity vs that shoving range. If your hand has 47.17% eq or more than you call. If it doesn't then you fold.

Based on the the little bit of math we did above he would need to be shoving pretty wide for you to have more than 47% eq in order to call.

Thanks so much for taking the time to explain this for me ..... you really did make it easy to understand.

Cheers

Andy

You're Welcome.

There was another piece that was left out and that is minimum defense frequencies or MDFs. I use this to construct my default ranges for each street and then based on assumptions I make about villains I can adjust from there. It is kind of used to prevent your villains from being able to auto profit from you and to make yourself less exploitable.

The premise is basically this: Versus a given bet size you need to defend x amount of combos that you arrive on that street with, so that your villain can't just bet any two cards and make profit from you long term by you folding too much.

So the math that you use is the same as risk/reward formula. So for example we will say it is BBvBU and the BU is cbetting on the flop half pot. So the pot size is 1 and the bet size is .5. So to calculate the bluff equity that your villain has, you would divide his .5 bet by the pot and his bet. So .5/1+.5 which comes out to .33 or 33%. So essentially if you are folding to a 1/2 pot cbet more than 33% of the time, then your villain can exploit you by cbetting vs you a ton. So to take it a step further that means you need to be defending ~67% of your preflop calling range that you get to the flop with. So in simple terms lets say you get to the flop in that BBvBU scenario with 400 combos then you would want to be defending ~267 combos to a half pot cbet. Unfortunately, it is not that simple and the process of constructing the ranges is more involved than that as you have to take into account things like the fact that in this spot BB, on most flop textures, is going to have an equity disadvantage before anything even happens. So I wouldn't recommends just counting total combos and multiplying by MDFs and using that as a defense. You would probably be calling to much. It also doesn't quite work the same way when the preflop aggressor is OOP. Thats why people use solvers. Essentially this is what a solver is doing.

You can do this with any bet size:

2/3 pot - .66/1+.66=~40% so your MDF is ~60%
3/4 pot - .75/1+.75=`43% so your MDF is ~57%

So basically I use these as a baseline and if i have a villain that i feel is underbluffing in a spot then I will call less and fold more and if I have a villain that I feel is bluffing way too much, I can float more or bluff raise more. You will find the underbluffing one quite a lot at the micros on Ahigh boards. A typical 3 street calldown will require you to defend some of your weaker Ax, depending on the runout, but at the micros they are rarely 3barreling with anything weaker than a big A and at the micros they tend not to bluff enough on the river, so you can lean towards overfolding on those rivers with some of your weaker aces.