After 10 heads in a row, is tails "due"? No! Each flip is independent. Three betting strategies all converge to the same result.
The gambler's fallacy is the belief that past results affect future independent events. After 10 heads, the next flip is still exactly 50/50.
Three strategies are tested: bet against streaks ("tails is due"), bet with streaks ("hot hand"), and random bets. All converge to the same expected value.