Deterministic MTT Example #1

Above is my first example of what a deterministic MTT model would look like. The X-Axis shows the Big Blind Level, and the Y-Axis shows stack size. The blue bars show what the average stack size is at that point in the MTT. This one is simplified to show only two hands per level, and I left a bunch of hands out as well (where the blue bars remain). Its a bit hard to read, but this is what is going on. The Hole cards for the hand are shown at the top of the white bars. The white bar is the Expectation Value Graph for the hole card rotated 90 degrees. It is centered on the starting stack size for that hand, and the white bar represents the range of possible ending stack sizes. The EV graph indicated the likely results within the range of possible outcomes. The horizontal black line between hands represents your stack size.

For the first two hands shown you have about 1500 in chips with a BB of 20. You are 75x deep (close enough to 100x). The graphs at this point are not stretched out. When you pick up AA on hand 5, the BB is 40 and your stack is about 2k. You are 50x deep, and as a result the EV graph gets stretched vertically by a factor of 2x. This means that increasing your stack by say 30% on this hand becomes twice as likely as it was in round 1. For the AK hand you are 40x deep and the EV graph is stretched by a factor of 2.5x. When you catch 55 late the graph is stretched by a factor of 5x. Losing about 20% of your stack is the most likely result if you chose to play this hand normally at this point. Since you have an average stack, push or fold mode for this hand is probably not a great move just yet.

There are several takeaways from this very simple example. First off, the early hands played in an MTT are of little importance. The EV graphs are not stretched out yet, and you can't accumulate a significant amount of chips. As the MTT progresses, it becomes easier and easier to get big hands paid off in a big way. The range of possible stack size outcomes becomes much, much larger than before, and the stretching out of the EV curves make large percentage stack size moves much more likely. On the first hand of the MTT your ending stack can be 0-3000, but will tend to be little changed. For the 55 hand that comes late your stack size result will be 0-19,000 and a percentage change of +/-20% becomes a likely result. A minus 20% move here would negate a full-double up on an early hand. This also shows why the order of cards received in an MTT is so important (possibly the most important factor in determining the winner). If you are going to catch some big starting hands like AA or KK, you will be able to chip up easier, and by larger amounts later in the MTT vs. earlier. You would prefer to get these hands late if you had a choice.

What does this say about basic MTT strategy?

It really validates that tight early, loose late approach to MTTs. If you play tight and conservative early in an MTT it helps to keep you alive for later when larger percentage swings become much more likely. There is simply not much to be gained in the early stages of an MTT by risking your stack. The best MTT players have the best looking late game EV graphs, and play tight early on so that they will be alive to exploit their EV advantage later on. Its when the stacks and swings get larger late in an MTT that the winner is determined, and if your end game is good, you want to be alive when this happens. When you see top pros like Helmuth and A.C. strolling into a WSOP event two hours late, it is for a reason. The MTT can't be won in the first few rounds, and these guys can improve their hourly win rates, by skipping the early rounds and focusing on when their EV advantage gets largest over the field. This advantage kicks in when the stacks start to get short relative to the blinds.

This model is fully deterministic. It says you can't will your way into a win. All you can do is play your hole cards better on average than the rest of the field (improve your EV Graphs). Doing this will give you an edge, but in no way guarantees a win. When you play your hands better than others, get good starting cards, and get them at the right times (preferably late), that is when you will get the win. The most likely result for the best player in an MTT is that they will not win. This is because hole cards and hole card order are the primary factor in MTT success.