Wednesday, June 04, 2008

Increasing Expection Value of Big Hands in MTTs

As your stack gets short relative to the blinds late in MTTs you are faced with the pressure of "Blinding Out". Your successful deep stacks approach to playing hands will start to lose some expectation as the depth is no longer there for proper implied odds. With a deep stacks approach you are really letting the chips come to you vs. going out and getting them when you want or need them. All good MTT players will at some point in an MTT abandon the safer deep stacks approach and start fighting for pots late when the stacks get short, to avoid blinding out or attempt to build a stack for a late run. An extreme example is "push or fold" mode, where you will look at your hole cards and then either push all in or fold preflop as you don't have the chips to play any hand post flop anymore. Lets look at ATo as an example. Below is the chart for my cash game expectation value. I fold ATo preflop over 75% of the time. I lose a bit in the blinds, and win a small pot from time to time from a blind or when in position. Overall with a small chance at a decent pot, and almost no chance of getting stacked, I have a very small expectation of +0.10% for this hand.

AT0 Deep Stacks Expectation Value
Now lets imagine it is late in an MTT and your stack is 5x the BB. If we are not into antes yet your M is about 3. You are in push or fold mode, and look down at the powerful ATo. With an M=3, I am going to just assume you push this no matter what, even if the pot was opened up before. About 30% of the time you will be able to open push or push over a limper and take it down right there. About 70% of the time you will open and get called from behind, or not be able to open and call all-in or push over an opener who will auto-call you. Since you will likely be behind when called in these situations lets say you are called and lose 40% of the total times dealt ATo, and get called and still win 30% of the times. A rough calculation shows the EV for the hand is now -1.0%, and the curve looks radically different than before.

AT0 Push or Fold Mode Expectation Value
So I am playing ATo, now in a way the forces the action. 60% of the time I will pick up chips, and 40% of the time I will be going home. Before I never went broke with this hand. By playing it this way I am giving up a small amount of expectation value (+.1% to -1.0%), but I am willing to do this because the fold and get blinded away option is worse from a MTT equity perspective. Lets just say that when you get into push or fold mode or any other huge departure from ideal deep stack cash game play, you are giving up a bit of expectation by doing so.

But not so fast!

If Mr. Push or Fold Donkey is giving up Expectation Value, who gets it? The game is not played in a vacuum. MTTs are zero sum, chip-wise so somebody is picking up this expectation. Who?

The guy who wakes up with AA-JJ, AK, AQ late. These hands go up in expectation value late as the other players get desperate and there hand values go down. Think of it as a sliding scale with some hand value in the middle (not sure which one). The top hands pick up the most expectation value, and the bottom hands lose the most expectation values when MTTs get late and the pressure builds to fight. When the table M is low AA has its highest expectation possible, and T8s expectation starts to plummet.

So take some comfort in that the big hand you have been waiting so patiently for all MTT, will get paid off even better when you finally catch it. Busting before you got dealt it would not let you take advantage of this.



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