Do Betting Systems Work? Martingale, D'Alembert and the Rest

Where these figures come from

The 97.3% figure in 'Why no staking plan changes the edge' is a closed-form identity on a named wheel layout, not a dataset, and it holds for every bet on the wheel, not just one type: a single-zero European wheel has 37 pockets, and every standard bet pays as though there were only 36. A straight-up number pays 35 to 1 on a 1-in-37 chance, returning (1/37) x 36 = 36/37 on average; an even-money outside bet (red, black, odd, even, 1-18 or 19-36) pays 1 to 1 on an 18-in-37 chance, returning (18/37) x 2 = 36/37 on average by that separate construction. Neither figure follows from the other, they are two different bets landing on the same ratio because the wheel prices every bet the same way, which is why the claim above is stated for the wheel as a whole rather than scoped to outside bets: 36/37 = 97.297%, rounded here to 97.3%. That construction is not derived on this page; it is this site's own House Edge tool's single-zero row (2.70% edge, the same number the other way up) and Roulette Payouts, which computes it from the same 37-pocket wheel model rather than a transcribed percentage, and roulette-payouts' own sourceVerification independently cross-checks it against Pragmatic Play's published 97.3% RTP figure for European Roulette (retrieved 2026-09-14; roulette-payouts also checked it against Play'n GO's matching figure until Play'n GO withdrew the page that figure was read from). The settled distribution figure in 'What each system actually does' (bust rate, share finishing ahead, median session, catastrophic loss, and the histogram shape) is this site's own Martingale Simulator: simulateMartingale and the closed-form deepestLoss, both from src/tools/martingale-simulator/math.ts, at that tool's own shipped defaults ($1 base, $250 table limit, $500 bankroll, 48.6% win probability per bet, i.e. the same single-zero even-money return above, 50 rounds, no profit target), its own default seed (777) and its own 5,000-session sweep size. The guide's interactive embed immediately above the figure calls the identical function with the identical parameters, so a reader who presses 'Run simulation' is re-running the same model the settled figure already printed, not a different one. The bust rate (about 9.0%) and share finishing ahead (about 87.8%) are sampled from that sweep; the catastrophic-loss figure ($255) is not sampled, it is the closed form deepestLoss computes from the table limit and base bet alone, which martingale-simulator/math.test.ts already pins as exactly equal to this sweep's own sampled worst session at these params and this seed. That same $255 floor is what 'What each system actually does' and the FAQ's Martingale answer both restate in words, as about 11 times the $23 median session, and, in the FAQ, as about 51% of the $500 bankroll, rather than a separate claim: neither sentence says 'loses everything' or 'loses your whole bankroll', because at these params the bankroll never binds first (see below), and neither understates the loss as merely capped well short of the bankroll, because it is not: it is about half of it in one sitting. The 'eight losses in a row' table-limit claim earlier in that section is limitBreakLosses(1, 250), the same function's own closed form: it returns 8, so the sequence of bets $1, 2, 4, 8, 16, 32, 64, 128 (eight losses) puts the ninth bet at $256, over the $250 limit. The prose previously read 'six or seven losses' before this pass corrected it to the exact figure; the bankroll ($500) does not bind first at these params, since cumulative staking after seven losses is only $127.

Verification

Checked against this site's own /tools/roulette-payouts (math.ts) and /tools/house-edge (edges.ts) single-zero wheel rows, which roulette-payouts' own sourceVerification independently cross-checks against Pragmatic Play's and Play'n GO's published 97.3% RTP figures for European Roulette titles (both retrieved 2026-09-14); and martingale-simulator's own math.ts (simulateMartingale, deepestLoss, limitBreakLosses) and math.test.ts, which independently enumerates the same Markov chain and checks the Monte Carlo sweep against it: agrees on the 97.3% single-zero return, equal to roulette-payouts' 2.70% edge and house-edge's roulette-eu row; the settled figure's bust rate (~9.0%), share finishing ahead (~87.8%), median session, and the $255 catastrophic-loss ceiling, which math.test.ts pins as exactly equal to this sweep's own sampled worst session at these params and seed (verified by roulette-payouts' math.test.ts and house-edge's edges.test.ts; martingale-simulator's math.test.ts plus src/guides/figures/martingale-settled-data.test.ts (this guide's own settled figure, re-derived independently and cross-checked against the tool's pinned identity), 2026-09-29).

Know the risk

• A system that wins most sessions is not a system that is working. Martingale wins small on roughly nine sessions out of ten and the tenth erases all nine, so a personal run of wins on the system is exactly what a losing strategy looks like most of the time, not evidence it has an edge.
• Believing an unlimited table or bankroll would fix Martingale. It would not: even with infinite resources the expected value stays negative, because the rare losing run still costs an unbounded amount, a real table limit or bankroll just happens to cap the loss sooner rather than causing it.
• Reading D'Alembert or Paroli as safer because they raise stakes more gently, or on wins instead of losses. That changes the shape of the risk, a narrower spread of outcomes instead of a fat losing tail, not the fact that every one of these systems carries the same negative expectation as flat betting.

Gambling can cause serious harm. The National Problem Gambling Helpline is free, confidential and open 24/7, call or text 1-800-MY-RESET (1-800-697-3738), or chat at ncpgambling.org/chat.