Since there are no faces to read as when "sittin' at the table," y' gotta play the mechanics:
Assuming equal probability of either team winning any particular game... they're equally good, in other words (that's how each of them got to the world series, after all)...
... then the probability of either team winning is P=0.5 for each of them.
For six games, the probability of guessing right for six games in a row is...
0.56 = 0.015625, is the probability of "hitting" six wins in a row just by guessing randomly. 64 to 1 odds. But it's not impossible.
Probably figured he could afford to lose the original bet amount and just let it ride.
I'm chicken. I would have just bet half my winnings from the previous guesses.