He has said before that "the most common sequence of wins and losses is WLWLWL" or words to that effect.

If he bets small, waiting for a win followed by a loss, and then bets big, expecting a win next, he'll be right about half the time.

If you shift his big bets back two steps then he'll be right every time (since the two bets before the big one were W and L) - the big bet will land on the first observed W rather than the third hoped-for W.

Surely that explains your observed result doesn't it?  Or were you shifting in the opposite direction?