A betting strategy where the bettor consecutively wagers "all-ins" on single bets (or cautious doubles), with each subsequent stake being equal to the previous stake plus the winnings from the last bet, is known as the "Martingale" system.

The Martingale is a betting method that involves doubling the stake after every losing bet, hoping that an eventual win will recover all losses. However, this high-risk strategy can lead to significant losses during losing streaks. It requires careful bankroll management to avoid substantial financial setbacks.