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If the sequence of Xs are outcomes in successive trials of a game of chance and fn is the fortune of a gambler after the nth trial, then the martingale condition says that the game is absolutely fair in the sense that, no matter what the past history of the game, the gambler's conditional expected fortune after one more trial is exactly equal to his present fortune.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com