ok, so I have had some time to sleep and think about this and I think I know where I went wrong. It had a little bit to do with the numbers logun thrown out, and a bit to do with me just being stupid. Here is what I came up with after some rest.
When we bet out at this pot, we are spending $147 to win $249. of the times we bet, I figure that he folds 20% of the time. The other 80% of the time he calls, we have him on a range of hands that leaves us with a 32% equity.
So with that, if we bet it should look something like this:
.20 * $249 = $49.80
(or 20% of the time we will win the pot of $249)
.80 * .32 * $534 = $136.7
(or, 80% of the time we will win 32% of the total pot of $534)
If we add these two together, we get $186.5. so we are risking $147 to win an expectaion of $186.50. For a net expectation of $39.50
In this scenario, we might want to change the numbers a little too. maybe he never folds here, maybe our range was wrong etc. These things will effect the outcome of your EV and are why your reads must be so precise.
Now, let's look at if we check call. If we check there is a chance he will check behind. If this happens his range cannot be the one we had given him before. It will change, and in this situation we are favored a lot more, since hands that beat us will deffinetly bet the end. There are a range of hands that we should but the villain on here, but I am getting late for work, and I do not want to do a whole call down range. I said before that we were a slight dog, but I know feel that was a mistake on my part. I feel if he checks behind we are about an 80:20 favorite.
So with that, chek, check looks like this.
.20 * .80 * $249 = 39.84
(or, 20% of the time we will win 80% of the existing pot of $249 when he checks behind.)
**Note that him checking behind is simular to him folding to our bet.
If villain bets we already agreed that we are calling 100% of the time. There is also a different betting range for him than the one we had before as well, but I think I going to leave it as is, and just factor in a bluff %. I get a little slipped up here though and I think this is were I need some advice. I feel the situation should look like this.
.80 * .05 * $534 = $21.36
(or, 80% of the time he bets, 5% of those times will be a bluff and we will win the pot of $534)
.80 * .95 * .32 * $534 = $137.99 (it's a bargain from $138 )
(or, 80% of the times he bets out, 95% of those time he will have a hand that is within our range and we have an equity of 32% of the $534 pot)
So when we Check with the intention of calling his AI, we are risking $147 to win $199.19. This number benefits from the fact that sometime he checks behind when we check and we get to control the pot.
So checking nets us an EV of: $52.19
These numbers again are heavily subjected to reads though, and can be thrown in any direction.
I feel I have done a better job of explaining this this time, but there may still be some flaws. Hopefully someone can give me feedback.
