Financial Physics - Probability of Winning

May 2012
United States
1. The problem statement, all variables and given/known data

In game A the probability of winning at time t is determined by success (in any
game) at the previous two timesteps t-2 and t-1. A win (W) earns one unit of cash,
and a loss (L) results in paying one unit of cash. Following a sequence of outcomes (L;L)
at time steps (t - 2, t - 1), the probability of winning at timestep t is p1. Following
(L;W) it is p2, following (W;L) it is p3 and following (W;W) it is p4. Let D1(t) be
the probability of the sequence (L;L) at timesteps (t - 1, t), D2(t) be the probability
of (L;W), D3(t) be the probability of (W;L), and D4(t) be the probability of (W;W).
Find expressions for the Di in the steady state, for i = 1 to 4. Show that a player loses
on average when
p1p2 < (1 - p3)(1 - p4)

2. Relevant equations

No other equations are given!

3. The attempt at a solution

Im taking a class on Financial Physics and have no previous knowledge of probability. I have not taken statistical mechanics or Quantum yet. I am completely lost on this one. I been learning more about it but this is just over my head. Can someone help! Dont know where to start!