Two Plus Two Newer Archives - Theory of Stack Sizes---Hypothetical Response to the Gigabet Dilemma

Ok, boys and girls, this here may be the most -ev post I have ever written. The Q3 push thread received quite a few responses from players who were confused about the validity of it, while I thought that it was a fairly standard play for most of us here(read independent.) Even if the players do not know why they do it, I thought that at least they would understand intuitively the value from plays such as these. Before I get into the actual dynamics of that individual hand, let me see if I can explain the "Gigabet Dilemma."

For those that do not know, there was a very long and controversial thread(in the MTT forum) about another hand that I had played. Basically, I had made a -ev call because I had felt that the positive ev I would gain later in the game, if I win the hand, outweighs the negative ev of the specific hand. Because you cannot mathematically prove the positive equity of future happenings with any certainty, this is all theory. The controversy surrounding the argument of whether or not to take the immediate negative expected value or make the "correct" play has been coined the Gigabet Dilemma.

If you are on my side, and agree with my reasoning, then you have to take these negative situations and use them to your advantage. But the real question is, how do you recognize when you can get on the negative side of the situation and know that if you lose that individual hand, your stack will still be able to contend with the fields? Understanding that every situation is one long stream of events, and the results of any single hand mean nothing in the long run isn't enough. Because of Gamblers Ruin(cannot recover from zero) you are forced to recognize that each situation is independent, and have to be results oriented for that hand. It is counter-intuitive to make a move based on one situation, rather than 100s of thousands similar situations, but because you cannot recover from zero, there has to be a plateau in each situation that you can recover from. Since each situation will involve different stacks, you have to depend on your results from the texture of that individual setting to decide whether to make that -ev move. You cannot create hard and fast guidelines to make that decision, rather, you have to go by your feel for the situation at hand.

Here is where it gets interesting. Although you cannot make guidelines, you can create one "model" that you can look at, and decide what the best decision would be in that model. If you decide that your model calls for avoiding the -ev situation, then adjust the sizes of the stacks until you find a model that calls for embracing the negative situation.

If you think you would have troubles actually finding a correct model, here are some things that may help you. Put everyone at near the same stack size, except for one player, who has around 1/3 the rest of the field, and gradually increase the blinds, if you still cannot get it, gradually increase your stack, while leaving everyones the same, including the small stack.

Once you get your model, use it as a relative comparison to some past stts you have played, and see if you cannot see actual game situations that are relatively close to that situation that is represented by your model. Read through enough hand histories, and you will start to intuitively see the situations as they arise.

In my mind, I see each stack as a "block" that fits into a complete mold that encompasses all of the chips in play. I cannot comprehend what "one" chip is, because that is too small of a unit for my mold. Here is a very loose description of what I mean. At the beginning of a tourney, everyone has a block that is the same size, imagine 10 blocks sitting next to each other, with a bold face line running across the top of all of the blocks. I actually envision a pie type mold, with the blocks pieced in the pie evenly, however that is too difficult to put into words, so I will try and analagize it. Ok, so your bold face line is just a guideline that represents the saturation point of the chips in play, basically, the average stack, but the line could go above or below avg, if one of the stack gets excessively larger or smaller than the fields. As the tourney goes on for a time, and the blinds get to a certain point, your line will get very erratic, and there will be times, when the size of the blinds will equal, or nearly equal the size of a "block" that is near the level of your line. When situations like these occur, and your stack hovers above the line, then any part of your stack over the line is essentially meaningless. However, because the line is erratic at that level of play, using those meaningless chips to capture a "block" will make your stack a real force that controls the level of that line. Basically, capturing a block is nearly equivalent to doubling up.

Here is a kicker, if your stack is flush with the line, and the size of the pot is nearly flush with the line, then you have an ideal situation to take alot of negative ev to call an all in from another player. If you can understand that statement, then you will understand alot more than just what I have written so far.

There will be situations where math tells you to push with any two cards to pick up the pot(preflop, of course), however, if you are using my model, you will see that because the "line" is relatively stable, and your stack hovers above the line, than taking down that pot is very nearly always wrong. This is working on the opposite side of the coin, and recognizing when +ev situations should actually be avoided, because it would be more positive to wait until either the line moves, or your stack moves closer to the line.

Now that you have read this, go back and look at the hand history, and see if you can see why I pushed all in with Q3, knowing I was going to take the worst of it in a showdown. If need be, I will go through and explain that hand in detail, and try and put together a more easily identifiable model that represents the stacks at that table.

I have never put this theory into words before, however, I have put them in use enough times to know that there is no doubt in my mind that they are true. I hope that this isn't too disjointed to read, and while I know that understanding it may be difficult, please read through it a few times before asking questions that may have an obvious answer. Obviously newer players will benefit from this more, since they have less "preconceived" notions of how to play. More experienced players may actually intuitively understand it more, but find it hard to believe that this is any kind of poker, and never really incorporate it into their game.

Gigabet