Ah, of course. Thanks heaps :)

Follow up question, are these numbers exact when playing real poker?

It's a good rough estimate though

Ok, that makes sense. Thanks heaps :)

It's fairly accurate on a bunch of flops though

Ok, I've got a lot of study to do it looks like

Good luck with it all ��

So this is calculated for the nuts/air vs bluff catcher game. It comes from the fact that in constant sum 2 player games (such as poker), at Nash Equilibrium neither player can unilaterally increase their EV. We know that when player betting holds air they will bluff sometimes and not bluff other times. Therefor if we are at Nash Equilibrium then the EV of both these lines must be the same. The EV of checking is 0 (as when you check back air you lose), therefore the EV of betting must also be 0.

EV of bluffing = (pot size)(1-calling frequency)-(bet size)(calling frequency)
0=P(1-C)-BC
0=P-PC-BC
PC+BC=P
(P+B)C=P
C=P/(P+B)=1-B/(P+B)

There are alternative ways of thinking about it when you’re playing though. You could also look at the odds they’re getting on their bet. When your opponent bets half pot, the pot it twice their bet so they’re getting 2:1 on a bluff. Hence you need to call 2 times for every time you fold.

And you could do a similar thing when your betting as well. If you bet half pot then your opponent is getting 3:1 so you need to bluff once for every 3 value bets

The odds method is a much easier way to look at it. Thanks dude