The player begins with a single unit-if that hand is won,
the player has turned a one-unit profit, and the series
ends.
If the player loses a hand, the wager remains the same
until another hand is won, at which point it's increased
by one unit. This continues until the player winds enough
hands to recoup all previous losses, and come out one unit
ahead, at which point the next hand is considered the
beginning of a new series.
Here is an example of a series that persists for a dozen hands
# BET RESULT BALANCE
1 1 LOSS -1
2 1 LOSS -2
3 1 LOSS -3
4 1 WIN -2
5 2 WIN 0
6 3 LOSS -3
7 3 LOSS -6
8 3 WIN -3
9 4 LOSS -4
10 4 LOSS -8
11 4 WIN -4
12 5 WIN +1
In this sequence, the player wins 5 out of 12 hands - slightly
less than the expected average - but concludes the sequence
with a one-unit gain. The consistent-wager player would have
emerged at a net loss of two units, and the Martingale player
would have emerged with a net gain of five, but would have been
required to bet as many as eight units on a single hand.