The Allure of the Doubling Progression
The intuition seems appealing: "It is impossible to lose 10 rounds in a row at a 50% probability." Mathematically, this intuition is completely false.
Across an active session of 1,000 rounds, the mathematical probability of experiencing at least one 10-loss streak exceeds 72.8%. When this inevitable streak arrives, the player hits either their bankroll limit or the casino maximum wager ceiling, resulting in an unrecoverable 100% loss of capital.