Hey guys,

Two questions about GTO approach.

1. There is a simple formula how much does we need to defend vs various villains bet sizes so he is not making automatic profit 1-(bet/(bet+pot). Let’s say he bets full pot, so we should defend (1-(1/(1+1))=50% of our range. So say that we defend only 40%. Out of 100 hands he makes 60 times +1, 40 times -1 (even if he loses every single time we call him), so he is +0.2/hand. Does that mean that he makes automatic profit? On the other hand, we win 40 times 2 (pot size 1 + 1 his bet) if we win every time, so we make +0.8/hand. My point is that his +0.2 is not automatic profit, it’s just small part of realized equity from the pot, which he build in the first place (if we call 40% of our range with 100% equity vs his betting range, we split the pot 20% for him and 80% for us). What am I missing everywhere is callers vs bettors equity in the formulas.

2. There is another formula which is ratio value/bluffs based on our betsizing. If we bet full pot on the river, we should have 2/3 value, 1/3 bluff. This works fine in polarized scenarios. Because our value range wins always. However this is usually not the case and again, we need to add equity of our value range vs villain calling range to equation. Let’s say, that our value range has 90% equity. If we get called 100 times we get:
   33 * -1 + 67 * 0,90 * 2 = 88, way less than 100 which we get if our value range has 100% equity. So if our value range has less than 100% equity, we need to add less bluffs than the ratio we get based on our bet sizing or we are (way) overbluffing. Is there a formula which takes this into account?