# Is there a way to calculate if my bets are + or - EV?

Jacksonville, FloridaRed Chipper Posts: 21 ✭✭
Maybe this is a dumb question but I've crammed so much into my brain lately that I feel like I've completely overlooked something simple.

I was doing some hand history earlier, trying to see if my plays were +EV or -EV when I realized I have no idea how to calculate that when I'm the one doing the betting.

It seems like I've spent so much time learning the math involved in calling someone else's bet or raise that I have no idea if my bets can even be calculated that way.

I'm going through core now but I feel like I've overlooked that part. What sort of math is used when Hero is the one making the bets/raises? I know we want to give the villain -EV when possible but is that it?

• Posts: 2,858 -
The short answer is the more money and streets there are left to play, the more difficult it is to directly calculate EV. Think of it this way. In an ideal world we'd have some silver bullet. We'd punch numbers in our super special EV calculator and we'd get back a number. +EV good, -EV bad.

Now cast this in the context of multi-street NLHE. We raise pre from LP and only the BB calls. We're 150bb deep. Flop comes something and the BB checks. How would our super special EV calculator work?

In principle it has to follow an almost infinite number of ever-branching trees. In fact the only reason the problem is finite is because like quarks, chips are indivisible. So we have a finite number of bet sizes we can make between 0 (a check) and our remaining stack. In response, our opponent can fold, call or raise any number up to their stack. If the last option, we then have all 3 choices. So that's one tree and then it bifurcates (multifurcates?) again on the turn.

I mean honestly this is why I took up Hearthstone.

Anyway, this is where solvers come in, but even here it's a daunting task to probe a range of bet sizes to figure out the most +EV line. Ideally one wants an iterative algorithm in which bet size is one of the variables, and I've never seen this discussed but I really start to wonder whether we might get all sorts of nasty mathematical artifacts produced by local but not global minima in the Nash equilibrium wotsit... but I've wandered off the path.

The issues you raise do crop up throughout CORE and in terms of a practical approach to poker I hope that suffices. As I've mentioned elsewhere, there are general poker principles such as range advantage and the reasons for betting that can, with work, be applied by humans. Experimenting with solvers can be a huge help within that framework.

Finally... watch this space. I have a new product announcement coming out this month that I am very excited about which I think will interest many of you asking these kinds of questions.

Moderation In Moderation
• Red Chipper Posts: 142 ✭✭
edited October 2019
Short answer is no. Only solvers are able to build the decision trees Kat mentions. However there are general guidlines when deciding when to bet and what sizing to use. The biggest factors are # of players, position, range advantage and nut advantage. Range advantage is basically equity advantage. Nut advantage is whose range has the highest percentage of nut combos which is typically overpairs + and sometimes TPTK depending on situation and board texture.

When you have the range advantage and nut advantage you want to bet frequently and small. When you have the range advantage and nut disadvantage you want to bet infrequently and large. When you are at a disadvantage you want to check a lot.

Cramming all the math into your head is good but as you mention can be disorienting. I've found the best way to build a good foundation is to study ranges on different boards with flopzilla and become familiar with who has the range and nut advantages. This also helps build hand reading skills which is extremely important.
• RCP Coach Posts: 1,798 -
No.

If we could, then we could try every option and see which is best. This is essentially what a GTO solver does, but you must assume a complete strategy for the Villain.

Often the Villain will play a wildly different strategy than we assume. For this reason we assume he will play the toughest possible strategy. Our play is based on this, so any other Villain strategy we do better.

Our best response to his best strategy can look silly vs real players.

Even us trying to say what our complete strategy is against all possible villain actions is impossible. Trying to guess the complete strategy of someone else is even harder.

For this reason, we just assume they play best in a solver, or we make a reasonable assumption about their ranges and hope.
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• Red Chipper Posts: 4,908 ✭✭✭✭✭
edited October 2019
Here's maybe the best way to look at it.

There are some river situations where you can calculate your EV, making some assumptions. For example, you can guess the probability your opponent will fold based on your bet size, and then you multiply that by the amount in the pot. (\$100 pot, 50% chance he folds, that's \$50). Then add to that the probability that he wins if he calls (you lose your bet) or he loses if he calls (you win his call plus the pot).

That's not a super hard calculation. (We'll ignore getting raised, and then you raising that, and then him folding or raising that, etc.)

Once you've got that down, play the rest of the hand in such a way as to lead to +EV river situations. It's unrealistic to calculate this from preflop, but essentially that's how you plan your hand and strategize.
• Jacksonville, FloridaRed Chipper Posts: 21 ✭✭
Thanks for all the advice! I'm happy that I didn't overlook anything.

But given all your responses I think my recent infatuation with the math of poker should be a little lower on my priority list. Which is awesome because I've got the basics down at this point and I'm dying to start honing my hand reading skills.

Thanks again guys!
• Red Chipper Posts: 142 ✭✭
MrFuss wrote: »
When you have the range advantage and nut advantage you want to bet frequently and small. When you have the range advantage and nut disadvantage you want to bet infrequently and large. When you are at a disadvantage you want to check a lot.

When you have the range advantage and nut advantage you want to bet frequently and use a sizing based on how well the board connects with the opponents range. If it misses opponents range use a small sizing. If it connects use a larger sizing.

When you have the range advantage and nut disadvantage you want to bet infrequently and small. This means you want to bet small with only your best made hands and draws.

When you are at a disadvantage you want to check a lot.
• RCP Coach Posts: 859 ✭✭✭✭
yeah multiples streets is hard but a simple EV calculator (RCP/ Split should have one) but doing one street is more straightforward based on how much equity/ worse in their range their is

in general you could assume your EV is less across multiple streets unless its true, your opponents give up more (fold) then they should and/or they dont deny you your own equity as you are the aggressor
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• Red Chipper Posts: 43 ✭✭
CREV is a good software tool for this. Comes free when you buy GTO+. Used to be the other way around because CREV came first. Some find the interface clunky, but I like it because I find it easier to put in population exploits.
• Red Chipper Posts: 1,426 ✭✭✭✭
Cloutier wrote: »
What sort of math is used when Hero is the one making the bets/raises? I know we want to give the villain -EV when possible but is that it?

You can use a solver to look at EVs in the solution. Then you can import(node-lock) your assumptions about how the opponent plays and look at those EVs.