Basic fold equity question

[muffins]

Hi all,

Just a question about the concept of fold equity. I understand that a push has a lot more expected value than a call since you have fold equity as well as showdown equity, and I understand how to use a calculator to work out a $EV figure, and if this is positive then the push is the correct move. I have seen this called an unexploitable strategy. My question is this: The reason this strategy is unexploitable is that you are including the fold equity in your calculation, and your opponent has no fold equity once you have pushed. But can't your opponent change this by deciding to call every push, reducing your hand value to showdown value alone, where you could be effectively 50/50 to win or lose?

[Slim Pickens]

An unexploitable push is one against which there is no range of calling hands that makes a push incorrect. If the calling range is too small, the pusher has enough folding equity that it makes up for the times he is called and is crushed. As the calling range opens up, the pusher's hand increases in showdown value enough to compensate for the decreased folding equity. A hand like 88 or ATo often behaves like that.

[drzen]

Slim, I understand that my equity increases by the share of the prize pool that the blinds represent, if I push and they fold, and by the share of the prize pool that double my stack represents when I push, they call, but I suck out.

So I take A (times they fold*increase in equity) + B (times they call*times I win anyway*increase in equity)/ C (times they call * times I am beaten) as my EV for the hand. And you're saying that there's no range of hands they can call with that will make C big enough to make this negative? (Because if they call too with too many, B is increased, and if they call with too few, A is increased. And we call it "unexploitable" because even if we villains knew what we were doing, they couldn't find a good range to call with.)

So is 88/AT the cutoff at this blind level? What would be the best way to figure this out? Do I need to sit down with paper and pencil and work out equities against ranges until I figure it out? (Is cutoff even the right idea? If 88 is unexploitable, does that mean 88+ is unexploitable too? Would 88-JJ, AT+ be if you did something else with QQ+ and, say, AKs?)

And okay, this might be unexploitable, but is it best? Could you give a tip on how I can figure that out?

[Finnisher]

[ QUOTE ]
So I take A (times they fold*increase in equity) + B (times they call*times I win anyway*increase in equity)/ C (times they call * times I am beaten) as my EV for the hand. And you're saying that there's no range of hands they can call with that will make C big enough to make this negative? (Because if they call too with too many, B is increased, and if they call with too few, A is increased. And we call it "unexploitable" because even if we villains knew what we were doing, they couldn't find a good range to call with.)

[/ QUOTE ]
That's it but there's also the NE ranges which are such that villain can only be 0-EV at best with his calling ranges. But our NE pushing range doesn't mean that we're always +ev, but if we push NE and villain calls too loose they lose also eg spitecalling. But unexploitable ranges are always +ev and against those ranges villains won't even be 0-EV.

In the 88 hand unexploitable range is 88+, AJ+ (NE was 16% about iirc). SNGWiz's graphs are very useful for determining unexploitable ranges.

And obv unexploitable isn't always best, usual example is shoving AA first hand. Calculating the EV of shoving is fairly simple cos there's not too many permutations but raising and getting rr'd/playing a flop gets complicated. If someone's constantly restealing behind you raise/calling the top of your range is a good start and the more they shove the worse hands you should raise/call. But with 10-15bb against players who just call shoving 88 and AJ is usually much simpler at least.

[IFoldPktOnes]

It should be A + B - C:
[ QUOTE ]
A (times they fold*increase in equity) + B (times they call*times I win anyway*increase in equity) - C (times they call * times I am beaten * decrease in equity)

[/ QUOTE ]
As Finnisher said you can see this in action if you have SnGWiz and look at the equity vs calling range graphs, equity>0 for all calling ranges.

"Unexploitable" can be misleading since, in this case refers to the hand itself and not the hand range you are playing. For example, if I knew that someone only pushed unexploitable hands then I would adjust by calling tighter, in some sense exploiting them (since I am reducing their potential EV and they could unilaterally improve their strategy vs me by pushing wider).

If one hand (eg 88) is "unexploitable" then so is any hand of greater value (eg 99+).

[drzen]

Hold on, hold on. If you can "in some sense" exploit me by calling tighter, then my strategy is not "unexploitable". It must be that *nothing* you do can lessen my EV, right? Because if you tighten up, I get more fold equity (increase A) to compensate for losing more often when called, so we're saying that 88 is exactly where the balance is.

[IFoldPktOnes]

You don't get dealt unexploitable hands every time, thats the point. So you are giving up potential value by only playing strictly "unexploitable" hands.

I was just trying to point out that an "unexploitable" hand is different to an unexploitable/optimal range.

[drzen]

Thanks so much, btw, for answering this. I'm often in this spot, about 13BB at t100, waking up with a decent but not monster hand, and thinking, I could shove, should I?

I know I can use SNGwiz to give the answer, but I like to understand why it's the answer. I really appreciate the time you guys have taken to explain it. You just can't find the answers anywhere online but here. STTF FTW innit!

[drzen]

[ QUOTE ]
You don't get dealt unexploitable hands every time, thats the point. So you are giving up potential value by only playing strictly "unexploitable" hands.

I was just trying to point out that an "unexploitable" hand is different to an unexploitable/optimal range.

[/ QUOTE ]

Do you agree though that in this spot, which is pretty common for players who use the "standard" strategy (about 13BB at t100, so we've pretty much folded everything), there's rarely going to be a better play than just shoving your whole unexploitable range?

I know, I know. I need to sit down and figure it out. But what do you think?

[IFoldPktOnes]

Yup your right, your unexploitable range should always be pushed (or raised if thats higher EV).

Learning what is unexploitable in a given situation will give you the minimum range of hands to push, it's then up to you to decide what other hands you will also add to your pushing range to maximize your EV.