Let's say I bet 100 into a 100 pot and villain will always call.
How often do I have to win to be +EV?

Is it 50%? Or only 33%?

I think I have some sort of dyscalculia because I get SO confused by these things.


I bet 100 into a 100 pot, I know I'm getting called, so I'm betting 100 to win 300? Or am I betting 100 to win 200?

If I actually think about this, I'm putting in 100 and when I win I'm getting 300, so I'm betting 100 to win 300 right?

So if I win 33% of the time, that puts me at 0EV right?


Let's do this 999 times:
100 * 666 (times I lose) = 6660
300 * 333 (times I win) = 9990
So this is wrong?

If I win 200 instead it does work out:
100 * 666 = 6660
200 * 333 = 6660

So I am betting 100 to win 200? Can someone explain this to me? Because I'm getting 300 when I win right?

So does this mean when I value bet all-in I only have to win 33% of the time to break even?
Does this work for bets that are not all-in too?

Your question might be more general than this, but let's start simple.

If you are in position on the river and can check behind to show down for free, it is 50%.

Here is why. When you are thinking about the EV of betting you need to compare it to checking.

Now, how often you are good actually doesn't matter for this calculation (because you are always getting called on the river, so the percent of the time you win is the same for both). The important thing is there are 2 cases: either you are good or you are no good.

If you check behind, you win the pot every time you are good, and nothing when you are no good.

If you bet and get called, you will win the pot plus an extra $100 the times you are good, and you will lose an extra $100 the times you are no good.

When you look at it this way, the money you bet is going in at 1:1 odds. So you need to be good 50% of the time for betting to be better than checking.

That makes sense.
So you're saying the EV of betting must be higher than the EV of checking.
While interesting that doesn't really answer my question

The situation I have in mind is OOP on the flop.

It's exactly the same math as calling an allin.

Did you see the part about how math confuses me?

It is? What if our opponent has a checking range if we check to him, even though they call with everything?

I'm really just wondering if my math is correct.
Obviously you're right about betting EV needing to be higher than checking EV to bet.

OK well I know how to reconcile the “betting to win” thing.

There are 2 ways to do it. One is that you are betting 100 to win 200. That is one correct interpretation. By that logic, you need to be getting 2:1 odds.

Another correct interpretation is that you are building a pot of $300, and you are paying $100 to build it, so your equity in that pot has to be at least $100. 100 out of 300 is the same break-even point as 2:1 odds. As it should be.

EV of bet = 200*equity - 100*(1-equity)
Ev of check = 100*equity

The problem with this is understanding that something being EV > 0 doesn't make it good.
33% makes it EV = 0, but checking is still much higher EV (33 chips)

50% makes it EV = 50, which is the same EV as checking, 50 chips

So for jamming to be a good play when you get called all the time you need >50% equity, assuming you're closing action.

As for your confusion. When you win, how many chips does your stack have compared to before?

Yeah it pretty much always comes down to comparing the EV of a bet vs a check.

In position on the river:
You can either check back and realize your equity, or bet. For a value bet to be higher EV than a check, it needs to have at least 50% equity against the calling range. In other words, a value bet needs to be getting called by worse more often than it's getting called by better. For a bluff to be higher EV than checking, you need to be gaining more EV in fold equity than you would have had checking back.

Out of position is more complicated. This is because you don't necessarily realize your equity when you check. When the EV of a check is lowered, the EV required to bet is also lowered, meaning you can sometimes "value bet" with hands that have less than 50% equity when called. This largely ties into the idea of block-betting rivers.

That’s outside the scope of the question.

Is that supposed to mean re-framing the problem doesn’t help? That’s basically what math is. Calculating the equity required to call an allin is something every serious poker player learns to do early on.

How much do you win when you win? The amount won/lost is the difference between your final and initial stack.

Edit: I see the last question was already asked. Oops.

The frame of reference is really important here too, in most scenarios we say that folding is zero EV because that makes the math easiest. So no matter what action you take with a "value bet" other than folding, it is going to be "+EV" in this reference frame- thus you can't just say "oh it's +EV I'm gonna do it", you have to compare it with the EV of checking or other sizings.

It is the exact same for bets that are not all in, but for simple models we typically just say all-in because then we don't have to make the additional calculation of the bet/fold and bet/call scenarios if we get raised (which isn't too hard to do if we must).