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Our new sequence of numbers would be; When all bets lose, the total loss is. For example, players should ordinarily stand when holding 12 against a dealer 4. Following is an analysis of the expected value of one round. Blackjack games almost always provide a side bet called insurance, which may be played when dealer's upcard is an ace. It will limit losses when you go on a bad run, but in turn will not produce large winning sessions. None of the gamblers possessed infinite wealth, and the exponential growth of the bets would eventually bankrupt "unlucky" gamblers who chose to use the martingale.

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