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Oscar’s Grind

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

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.

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