If you had a heads up flop pot of $100 and you ran a simulation of an infinite betting sequence from 1 player that always went 2/3barrel on the flop then 2/3 barrel on the turn followed by a 1/3 bet on the river and it did this 50% of the time and the other half of the time it did an infinite betting sequence that went 2/3, check and then 1/3 on the river my question is: if the other player had 5 outs on the flop would it be long term profitable for him to call that $66?

And for simplicity sake we are assuming both are deep stacked, no one can reraise at anytime and no deviation form the sequence can occur

I don’t think you need to do a simulation if my understanding of the problem is correct. The decision point for the opponent is the flop. With opponent having 5 outs and the assumed future betting fixed, opponent has a showdown equity of about 20% using the 4x rule.

If you assume no folds, you can calculate the total opponent investment and how much he might win. Then apply the 20% equity value in the standard EV win/lose equation to get his EV. I did a quick calculation and got a -89 but the arithmetic was a little messy so no guarantees on the accuracy of this result.

So let me get this straight, did you find the avg number of chips that will go in post flop (about 215ish more chips) and then applied this info and calculated the ev based on a 4-1 flop decision?

I calculated the chips that will go in from the stated flop turn and river actions. Between the two 50/50 betting schemes, it averaged over 600 chips and the opponent put in an average of about 270, if I didn't mess up the arithmetic.

The point of my response was not so much the result but to point out that your question was how one can evaluate a situation where you know the showdown equity at some point and fix how future betting will occur from that point on.

Even though odds and equity will change as cards are dealt and bets are made, I claim that under the given conditions, it is appropriate to use the initial estimate of flop showdown equity to do the EV analysis for making the flop call decision assuming the fixed action/bet sequence supposed does take place.

If you wanted to include some randomization such as one of the players folding at some point, then I could see using simulation, but then some more factors would have to be given.

I thought maybe you could find the ev of the first sequence assuming you have 8-1 on the flop. The ev is negative 1

Then you work out the ev of the second sequence using 4-1 on the flop and it comes to -4.6.

Add the two outcomes together and divide by 2 to find the avg and get -2.3

Consider the second betting sequence.

Pot is 100. A bets 2/3 pot and B calls. Pot is now 232. Check - check on turn. A bets 1/3 pot on river = 77. B calls. Pot is now 232+154= 386. A and B each bet 143 and winner wins that plus initial pot of 100. With 20% equity on flop B has EV = 0.2*243 – 0.8*143 = -66. ( I had mistake earlier, included B’s invest as part of winnings.) Similarly, for first sequence B EV = -220, so average = -143

I may not be understanding this correctly, but I think you have to determine Villain's optimal decision on turn and river in the two scenarios. It makes no sense to "fix" these in the case of future Hero bets (of differing amounts).

Clearly if Villain makes his hand by the river, he will call the 1/3-pot river bet in both scenarios. And Villain will fold if he does not.

If Villain makes his hand by the turn, he will call Hero's turn bet (2/3-pot) in one of the scenarios. And Villain will fold to that bet if he does not. Of course, if Hero checks Villain will see a river card for free.

So in calling scenario in which Hero checks turn (w/50% prob), Villain nets +143 with prob 10% (half of 20%) and nets -66 with prob 40% (half of 80%).

In the other calling scenario in which Hero bets 155 on turn (w/50% prob), Villain nets -66 with prob 45% (half of 90%) and nets +402 with prob 5% (half of 10%).

Adding these all together, Villain's EV of calling Hero's flop bet is -21.7. Of course, Villain's EV of folding to Hero's flop bet is 0. So Villain should fold to Hero's flop bet.

I hope this makes sense and that I didn't totally misunderstand the question.

**** guys I forgot to say Hero always folds if he faces another bet on the turn when he hasn’t hit. Sorry about that important detail

That "fact" was included in my analysis, though regrettably my use of Hero and Villain is flip-flopped from yours.

Yeah I was assuming hero to be the caller/folder not the bettor. So if I just switch that around your analysis still stands right that my hero should fold to the flop bet because long term he loses 21.7 chips if he calls in this simulation.

Hang on he loses 21 every how many simulations? Every 5 or every 9?

Ignore that. Thanks for the replies everyone