Pocket 9s

Edit: I still don't get why blogspot is so crappy with editing posts (read: why I don't get how to properly use it), so I am writing in the formulas by hand.

I do remember a friend and very good poker player saying that when players got out of line with their 3betting, he would sometimes 4bet shove 100 bbs deep with a medium pp, and said it would show a profit. So I decided this morning to do some math and see if my 4bet shove BvB w/ 99 was nearly as poor as I thought it was. A key difference here of course is how often the villain will fold relative to the limits my friend played and also the difference in the calling range of players at the limits.

The first thing I did was make some approximations of a few calling ranges for villain. These calling ranges and my estimated equity against them include:

· JJ+, AQ+: 38%
· JJ+, AK: 32%
· TT+, AK: 30%

I figured the formula to determine my required fold equity would be as follows:

Win when called - Losses when called + Win when he folds = 0

The first term is what I win when I get called. Simply put, this is just my equity share of the pot multiplied by $100 and then multiplied by the probability that he calls my 4bet shove. In mathematical terms, it is:

100 * E * Pc

Okay then, what about the second term? The loss term for when I get called and lose is going to be villain’s equity share of the pot in place of my equity share in the term above.

100 * (1 - E) * Pc

Finally when villain folds, I win the $8 in the pot every single time and never lose, so that term is defined as:

8 * Pf

The probability he calls though is simply the same thing as the probability he folds subtracted from 1, so substitution and combining everything leads to the following equation:

100 * E * (1 - Pf) - (100 * (1 - E) * (1 - Pf)) + 8 * Pf = 0

At this point we can easily plug in our estimated equity share of the pot and calculate our breakeven fold equity required. Here is what I calculated:

· JJ+, AQ+: 38% à Fold equity needed: 75%
· JJ+, AK: 32% à Fold equity needed: 82%
· TT+, AK: 30% à Fold equity needed: 83%

We can see, it isn’t really all that pretty. Was it profitable though? Does he fold enough? Well, I think in this spot, he most likely calls with JJ+ and AK. So let’s use 32% equity for our analysis. Let’s follow that with assuming in this particular spot, versus me, villain is most likely 3betting about 10% of the time. What percentage of hands constitute JJ+ and AK? Well, I have to think a little, since I don’t have poker stove with me and I know that there are 1,326 combinations of hands possible. I know that JJ+ and AK have 40 combinations, so that would mean that JJ+ and AK are ~ 3% of hands. So he is folding 70% of the time when I 4bet shove here.

That means my play is going to show a negative expected value. However, by how much? Plugging in a fold equity of 70% yields an expected value of -$5.20.

What if he does actually call with AQ? Well, my equity share of the pot increases but my fold equity decreases. Let’s see what happens. My equity share is now 30% and villain will fold 5.8% of the time. Plugging these values in the other equation yields an expected value of -$5.44. This is not really surprising when you think about it. My equity share goes up, but my fold equity goes down. We are adding in hands that flip with us, so it shouldn’t have too much of an impact on our bottom line, since it constitutes 25% of his range and not something like 90% of it, which would have a significantly larger impact.

Therefore, it was not a good play to 4bet shove 99 in that spot. However, it wasn’t the worst play ever and not nearly as –EV as I thought it would be. And these are all estimations of calling ranges and how often villain is 3betting. Obviously if his calling range is wider, I am in more trouble and if he is 3betting more often (very possible), it isn’t as poor of a play. It isn’t something I should lose sleep over, I should just focus on improving my play and not letting emotions get the best of me. I ran into KK but I easily could have gotten a fold or ran into AK and won a flip or heck, maybe sucked out! My point is that my actual value was far worse than my expected value for the play and I just need to learn from this and move on. There is nothing wrong with some 4bet bluffing and I do that from time to time with certain situations and better hands to do it with via card removal and whatnot, but this is not a play I need to have in my arsenal for these games.

Continuing to do analyses like this and think about how to exploit my opponents will lead to success, so the exercise is worth the time I spent and I can learn something from it. That is what is important. Next session, I will focus on playing solid poker and be mindful of the present and that should lead to a well-played session which is all I can control and need to be thinking about. That’s all for now!