Quote from Kevin Schmit:
Martingale betting methods can be useful, can overcome
a small negative expectation or expand a positive expectation,
when the return series being traded is antipersistent, mean
reverting, or has a variance ratio less than one. Stock index
return series at the interday time frame have, for the past few
years, had precisely those characteristics.
Intraday trading markets are a pretty poor pseudo-random
number generator and such return series fail most of Knuth's
standard tests.
The first two random number generators shipped with WinCraps
could be beaten by a number of martingale betting schemes.
Interestingly, these RNG's failed the same randomness tests
that intraday market return series do.
The trader in question may have a small positive expectation
going in due to his "Murray Math" trading method. Even with
a zero edge, martingale system "Oscar's Grind" against even
a slightly antipersistent series, has, given a sufficiently large
initial bankroll, been shown to be a recurrent Markov chain --
meaing you won't blow out trading it!