Let be a probability measure on Cantor space , and let .

1. A --supergale is a function that satisfies the condition

   (1)

   
   for all , the set of all finite strings of 0's and 's (including , the empty string).
2. A --gale is a --supergale that satisfies the condition with equality for all .
3. A -supermartingale is a -1-supergale.
4. A -martingale is a -1-gale.
5. An -supergale is a --supergale, where is the uniform probability measure.
6. An -gale is a --gale.
7. A supermartingale is a 1-supergale.
8. A martingale is a 1-gale.

Put in another way, a martingale is a function such that, for all , .

Let be a --supergale, where is a probability measure on and . We say that succeeds on a sequence if

succeeds on 

Intuitively, a supergale is a betting strategy that bets on the next bit of a sequence when the previous bits are known. is the parameter that tunes the fairness of the betting. The smaller is, the less fair the betting is. If succeeds on a sequence, then the bonus we can get from applying as the betting strategy on the sequence is unbounded. If succeeds strongly on a sequence, then the bonus goes to infinity.