First of all I want to say, that I am not familiar with poker games other than No Limit Texas Hold'em. However, my theory should be extended to a wide class of MTT games. The information provided in my scheme is quite doubtful, i.e. it does not provide any strategies like "how to win in the MTT" or "how to beat some hand", although it could be helpful to make better decisions in marginal situations. Furthermore, I do not even know if someone has already tried something similar, because my experience in poker is poor. If anything I have written is already well known, please provide me a link. I do not have a certain question I just post my ideas (which I am going to update over time) and hope to get a feedback.
P.S. I will deal with some basic math, but I did not find an integrated LaTeX editor here. That is I will try to write as clear as possible.
Suppose we have a MTT with P0 entries and S0 starting chips. Define two functions: A(t), B(t) -- values of ante and big blind at the time t. These functions are known and can be viewed at the tournament's structure page. Suppose, P(t, r.p) = P0 * exp(-r.p * t) is a number of active players in the tournament at the moment t with an outting rate r.p>0, which is specific for a certain tournament and could be estimated beforehand. Let H(t, r.h) = r.h * t be a number of hands we have seen up to t with a handling rate r.h>0, which is specific for a certain table and could be estimated online. Now we are interested in a function S(t) -- a number of chips in our stack. In order to obtain this function in a closed form, one have to solve a differential equation:
dS = dX - [A + 1.5 * B / p.t] * r.h * dt,
where p.t is an expected number of players at your table (which depends on P) and X is a pure jump stochastic process depending on both t and S, which describes your active moves in game. I am thinking about dX part for now, however throwing it out still may give us useful information. In particular, one can estimate his place in the tournament if he starts folding each hand from some moment (using P and solving differential equation with dX=0 and suitable boundary conditions).
I hope someone find this thoughts helpful. Feel free to ask any questions, any feedback will help me. Thanks in advance!