Martingale System Calculator

Defaults: Base Bet $10, Loss Streak 5, Payout 1 (even money), Wheel Type European (37 pockets). The engine walks a recovery Martingale: after each loss it sizes the next stake so that a win at the stated payout would recoup all losses plus one base unit. With even money that is classic doubling. Sequence of bets through five losses: $10, then $20, $40, $80, $160. Sum — Total Exposure — is $310.00. The next recovery bet, the sixth stake, is $320.00. If that $320 even-money bet wins, you recover 310 + 10 = 320 of losses-plus-target and sit one base unit ahead of the start of the streak. If it loses, the hole is $630 and the following stake would be $640.

Loss-streak probability on a European wheel for even-money chances (18 winning pockets out of 37) is ((37 − 18) / 37)^5 = (19/37)^5 ≈ 3.5707 percent. About one session in twenty-eight sees five reds in a row if you camped on black, ignoring the zero as a “neither.” American double-zero raises that to (20/38)^5 ≈ 4.0386 percent because two zeros sit against you. Neither figure is the chance you go broke on a casino visit; it is only the chance this specific length of losing even-money trials occurs in five independent spins.

Common mistakes: believing the 3.57 percent “won’t happen tonight,” ignoring table maxima that cap the $320 stake, and treating payout 1 as if it cancelled the zero. Even-money bets on European roulette still lose 19/37 of spins, house edge 1/37 ≈ 2.70 percent. Martingale never touches that edge. It only rearranges variance into many small wins and rare catastrophic sequences. Next, flip Wheel Type to American and watch streak probability tick up; raise Loss Streak to 8 and watch exposure explode (classic 10 × (2^8 − 1) = $2550 through eight losses, next bet $2560). Do not read $310 as a budget you “need to beat the wheel.” It is the money already in the hole after five doubles.

If the $320 recovery bet is above the table limit, the system is already dead: you cannot take the one spin that would have squared the book. If your bankroll is $300, you cannot even complete the five-loss path the defaults assume. Type the streak length you could actually fund, not the streak that looks pretty on a chalkboard.

This page sizes a negative-progression recovery Martingale on even-money (or other) roulette bets and reports how much you have already risked after a given losing run, what the next stake must be to get one unit ahead, and how often that run occurs on a 37- or 38-pocket wheel. It is for people who have heard that doubling after losses “must win eventually” and want the cash and the probability in the same screenshot. Pit bosses, mathematicians, and every casino from Monte Carlo onward have used the same arithmetic to set table limits: the limit exists specifically so this sequence cannot be ridden to infinity.

The Martingale is eighteenth-century gambling folklore, popularised at Monte Carlo after François and Louis Blanc’s casino era, though the doubling idea is older than the Blancs. It was never a proven edge. It is a stopping-time trick: you win one unit whenever the streak ends before the table or the bankroll does, and you lose the entire geometric pile when it does not. Probability textbooks use it as the canonical example of a strategy with positive probability of a huge loss and a high probability of a small gain whose expectation remains negative.

Who uses a calculator like this: writers debunking systems, players who want to know whether five doubles fit under a $500 max, and students comparing European 2.70 percent edge with American 5.26 percent edge on even money. Who should not: anyone looking for a way to beat roulette. The engine will not find one. Changing payout away from 1 lets you inspect recovery sizes on non-even bets (the code sets nextBet = (total + base) / odds), which is even more hostile because those bets have worse probabilities.

What it does not do: simulate a session, include 0 and 00 as separate even-money results beyond the pocket count, or model French-rule en-prison / la partage, which cut even-money house edge in half on some tables. It does not track consecutive wins. It is a loss-streak exposure tool. It will not tell you to bet $320. It will tell you that after five losses at $10 even money you already have $310 in the fire and a 3.57 percent European chance of having arrived there in five spins from a standing start — educational accounting, not a forecast, not financial advice.

Doubling recovery is the lecture form of Martingale on an even-money chance. A base of 10, five losing steps, payout 1, and a European wheel of 37 pockets generate a geometric pile. After each loss the next stake is sized so that a win at even money recoups all prior losses plus one unit. The posted amounts through five losses are 10, 20, 40, 80 and 160. Exposure, the sum of those five stakes, is 310 dollars. The next recovery stake, the sixth, is 320 dollars. If that 320 wins, the session sits one base unit ahead of the start of the streak; if it loses, the hole is 630 and the following stake would be 640.

Closed form for even money is elementary. After k losses the next stake is 10 × 2^k and the sum of the first k stakes is 10 × (2^k − 1). For k = 5 that is 10 × 31 = 310 of exposure and 10 × 32 = 320 next, matching the walk. Loss-streak probability on the European even-money chances, eighteen winning pockets out of thirty-seven, is P(streak) = (19 / 37)^5 ≈ 3.5707 percent. An American double-zero wheel would replace the fraction with (20 / 38)^5 ≈ 4.0386 percent. Neither figure is the chance of ruin over an evening of overlapping windows; it is the chance of five specified even-money misses in a row from a standing start.

House edge on those even-money bets is 1 / 37 ≈ 2.7027 percent European and 2 / 38 ≈ 5.2632 percent American. Martingale does not change either number. Optional stopping on the first win produces many small plus-10 outcomes and rare catastrophic minus-(2^n − 1)×10 outcomes whose expectation remains minus house edge times money turned over. Finite bankroll and a table maximum truncate the right tail that the “sure” recovery required. If 320 exceeds the posted maximum, the system is already dead after five losses. If the wallet cannot fund 310, the five-step path was never available.

Folklore, not a theorem, attached the name to eighteenth-century France and to the Blanc family at Monte Carlo in the nineteenth. The doubling idea is older than François and Louis Blanc; the casino made the roulette application famous and then set table limits precisely so the sequence cannot be ridden to infinity. Measure-theoretic martingales, which borrowed the name later, are a different object: a true martingale has constant expectation. A casino even-money bet is a supermartingale for the player, expectation drifting down. Confusing the staking plan with the mathematical object is a standard essay error.

Assumptions: independent spins, constant even-money payout defined as eighteen pockets, no la partage, and the ability always to post the next stake. Over hundreds of spins, runs of five are expected several times; 3.5707 percent is not a talisman that “will not happen tonight.” The system rearranges variance. It does not cancel the 1 / 37 edge. Exposure 310, next stake 320, and P(streak) = (19 / 37)^5 ≈ 3.5707 percent are bookkeeping for base 10, five steps, payout 1, European 37, nothing more.