I'm IP. Villain Checks. I believe Villain will call any reasonable bet OTR.

$1 in the pot OTR

1) We have 30% equity

I bet 50c, Villain calls.

EV = (0.3 x 1.5) - (0.7 x 0.5) = 0.45 - 0.35 = +0.10

I check behind

EV = 0.3 x 1 = + 0.70

2) We have 50% equity

I bet 50c, Villain calls

EV = (0.5 x 1.5) - (0.5 x 0.5) = 0.75 - 0.25 = + 0.50

I check behind

EV = 0.5 x 1 = + 0.50

3) We have 70% equity

I bet 50c, Villain call

EV = (0.7 x 1.50) - (0.3 x 0.5) = 1.05 - 0.15 = +1.00

I check behind

EV = 0.7 x 1 = = + 0.70


Conclusion: In this simple example, if we think we are behind Villain's range then we should always check behind and when we think we are ahead of villain's range we should bet the maximum amount that we expect to be called.