Martingale vs bold play

Same trades, same edge, same rules. Only the bet sizing changes. Which plan passes the challenge most often?

The three plans

• Fixed fractional: risk the same % on every trade. The "safe" plan most courses teach.
• Martingale: start at the base risk and double it after every loss, back to base after a win. One win recovers the losing streak, until a streak runs into a limit.
• Bold play: size each trade so that one win reaches the target, but never so big that one loss breaks the daily limit or the max drawdown.

Every plan is kept inside the rules: no trade is allowed to risk more than what is left before the daily limit or the max drawdown (minus a small buffer). An account counts as blown when there is no room left for a meaningful trade.

Why bold play wins when you have no edge

With zero edge and no costs, optional stopping says every plan passes about D/(T+D) of the time. Once each trade costs something, or the edge is negative, every trade loses a little on average. The plan that needs the fewest trades gives the casino, here the spread, the fewest chances. That is Dubins and Savage’s "bold play" result. Martingale beats tiny fixed risk because it bets bigger, but it still needs many trades and gets cut off by the limits mid-streak.

Caveats. Daily loss limits cap how big one trade can be, so "bold" really means "as few, as large trades as the rules allow". Some firms ban this style outright: Lark Funding lists an "All-or-Nothing" prohibited strategy, and some firms cap risk per trade (use the max risk field). Breaking those rules can void a pass. And if you do have a real edge, the conclusion flips: many small trades let the edge add up. Read the full write-up: why martingale fails a prop challenge.