Sunday, June 8, 2014

Let it go, Let it go...

I can't, but I don't want to bother the CC thread anymore:

There was a question of whether Selbst played this hand properly or soundly:

And the suggestion was that her 4-bet shove was too aggressive or not well thought out ("unsound"). I am mostly calculator-dependent, and don't know much about hyper-aggressive play (light four and five betting etc), but was curious to look into the hand as a learning experience.

One person said that the 4-bet shove was fine if she suspected a light 3-bet from Fee. The problem with that is I don't think a player like Fee would ever 3-bet light from the big blind with only 21BB against a player as aggressive as Selbst who has him well-covered. The reason is he puts himself in the spot of having to 3-bet\fold for 25% of his stack, which is horrible.

Approximate starting stacks:

1654000 - Selbst
338000 - Fee

So Fee's stack is about 20% of hers.

If we start with the assumption that he's never 3-bet\folding there or 3-betting light, then what does his range look like? I'm thinking this, which is top 6.64%:

Selbst's 9d8s has 28.26% equity against this range according to Equilab. Her equity increases a few % if we add some lower pairs, AJo, and AT combos.

In this range, there are the following combos:

36 combos (6*6) of the six individual pairs 99 to AA.

48 combos (3*16) of AK, AQ, KQ.

4 combos of AJs.

Total possible hands from Fee's estimated range: 88

Roughly 41% of his range consists of the paired hand combinations, while 59% of his range consists of unpaired combos.

When Fee calls the 4-bet shove and shows up with an unpaired combo, Selbst has 35-36% equity at the start of the hand, while investing only 20% of her stack.

I turned the hand around a bit and suggested that Selbst might be justified in calling if Fee overplayed and 3-bet shoved with AKo, but I forgot to do the pot odds. 

Selbst has 35000 invested in the hand. If Fee were to 3-bet shove (a mistake imo with 20BB behind, and may only get him fold equity), Selbst has to call 325000 to win 685000, or 1 to 1.1.

At best she is slightly better than a 2 to 1 underdog. At worst, she is slightly better than a 3 to 1 underdog. She needs around 47% equity to call a 3-bet shove there. At best she has around 36% against any individual unpaired combo, while on average she has around 28%. At worst she is crushed with an average of only 16% equity when Fee shows up with a pair, and only 12% equity when his pair is 99.

So overall, is a 4-bet shove there unsound or overplayed? Mathematically, I think yes because she rarely gets fold equity and is a 72% underdog in the race against his 3-bet range in that spot. But it's hard to fault her or anyone for gambling with only 20% of their stack. 

Time to calculate the EV (expected value) of making the 4-bet shove in that spot:

EV= (probability of winning * amount we can win) + (probability of losing * amount we can lose)

Plugging in the numbers (I subtracted Selbst's initial raise from the amount she could lose, because we're calculating the EV for the 4-bet shove, not the initial raise + the 4-bet):

EV= (.28 * 360,000) + (.72 * -303,000)

Expected Value of 4-bet shoving in that spot without fold equity = -117360

(Caveat emptor though about EV in tournaments.)

As for how Fee played the hand? Apparently he 3-bet to an amount that could give an impression of fold equity, induced a shove from a worse hand, and got unlucky. 

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