The Best Roulette Strategy Simulator: Martingale vs the House Edge

Run it yourself

Change the settings and re-run. Watch the shaded band widen while the line it surrounds keeps the same slope. Variance grows with the square root of the rounds played, the edge grows linearly with them, and the gap between those two rates is the whole illusion that staking systems trade on.

What a roulette strategy actually changes

A roulette strategy, in the sense the word is normally used online, is a rule for choosing your next stake from the result of the last one. Before testing any of them it is worth being precise about what they are up against. A wheel with 37 pockets pays 35 to 1 on a number whose true odds are 36 to 1, and even money on a colour that arrives 48.65% of the time. That shortfall is the house edge: 2.70% of everything staked, charged per pound rather than per round.

Nothing about the ORDER in which you stake your money touches that figure. Doubling after a loss, raising a unit after a loss, following a sequence discovered in the thirteenth century: all of it rearranges which rounds carry which stake, and none of it alters what a pound is worth when it goes onto the felt. This is not a claim about these particular systems; it is a property of any bet with a fixed negative expectation.

What a staking plan genuinely does change is the shape of your results. Some plans make small wins frequent and large losses rare but severe. Others spread outcomes evenly. Both trades are real, and one of them might suit how you want your evening to feel. Neither is an edge. The chart below is designed to make that distinction impossible to miss.

How the simulator works, and what it refuses to do

Each run plays 20,000 independent sessions of 200 rounds, betting an even-money proposition on a European wheel at a £5 base stake, against a table maximum of 100 times the base. It reports the average net outcome after every round, plus the band containing the middle 80% of sessions.

One decision matters more than all the others. The simulation does not stop a session when a bankroll would have been exhausted. Ending losing sessions early removes their worst outcomes from the sample, so the remainder average out better than the true expectation, which is precisely how a chart can be made to show a system beating the wheel. Here the net is allowed to run wherever the coin-flips take it.

What the simulation does enforce is the table maximum, because that limit is real, printed on every table, and the exact point at which a doubling progression stops functioning. When the next required stake exceeds it, the progression resets and books the loss instead of chasing it. It runs as a free roulette strategy simulator in your browser, with no account, and no data leaves your device.

Read the fourth column first, and then read it sceptically. In theory it is the same number in every row: the stake for any round is decided before that round is played, so its expected return is minus one thirty-seventh of whatever it happens to be, and summing over a session gives an expected loss of exactly 2.70% of turnover for every system in the table. No staking rule can touch that, and the table maximum does not either.

The measured column agrees, and the size of the sample it took to agree is the most instructive thing on this page. All four rows sit within about a tenth of a percentage point of 2.70%, but only across 20,000 sessions. At two thousand sessions, Martingale and Fibonacci still read a full percentage point away from it, because both earn most of their losses in rare, enormous sessions and a sample that size has not reliably seen enough of them.

Sit with that for a moment, because it is the whole trick. Over any number of sessions a person could actually play in a lifetime, a doubling system's running average is still wandering, and it wanders upward about as often as downward. That is not evidence the system works. It is precisely what makes it sellable, and why a testimonial with a few hundred sessions behind it is worth nothing at all.

Then read the last two columns together, because that is where the systems genuinely differ. More sessions finishing ahead, bought with a worse worst case, is a real and permanent trade, just not a profitable one.

Martingale, and why doubling feels like it should work

Martingale is the doubling system: after every loss you double, so the first win recovers everything lost in the run plus one base unit. Its appeal is that the logic appears airtight. A win must eventually arrive, and when it does you are ahead.

Both halves of that sentence are true and the conclusion is still wrong, for a reason with nothing to do with luck. The stake required grows exponentially while the recovery stays fixed at one unit. From a £5 base, a seventh consecutive loss demands £320, and the eighth demands £640, all to recover £5. Runs of seven losses on an even-money bet arrive roughly once every hundred and fifty rounds, which is well inside a single evening.

That is what the table maximum does to the method. The progression is a promise to keep doubling, and the table has already told you the promise is void above a certain number. In the run above, Martingale finished ahead in 39.1% of sessions against flat betting's 32.3%, and produced a worst session of -£3,420.00 against flat betting's -£300.00. Frequent small wins funded by rare enormous losses is not an edge; it is the same expected loss served in a different order.

D'Alembert and Fibonacci: gentler slope, same destination

D'Alembert raises the stake by one unit after a loss and lowers it by one after a win, on the reasoning that wins and losses roughly balance and the stake therefore drifts back down. It is much gentler than doubling and its worst sessions are correspondingly milder.

Fibonacci walks up the sequence 1, 1, 2, 3, 5, 8 after losses and back two places after wins. The growth sits between the other two: steeper than D'Alembert, slower than Martingale, and it reaches a table ceiling later.

Both land on the same fourth column. This is the most useful thing on the page: three structurally different progressions, three different risk profiles, one identical cost per pound staked. Once you have seen it in your own numbers, the marketing for the next roulette strategy becomes quite easy to read.

The wider family, and why the folklore outlived the maths

Martingale, D'Alembert and Fibonacci are not the whole picture. A fourth staking rule, Labouchère, is common enough in strategy write-ups to deserve a look, even though it is not one of the four systems this simulator runs. All four carry a name that promises pedigree: an etymology nobody quite agrees on, a mathematician, a sequence Leonardo of Pisa described in his 1202 Liber Abaci to model a growing population of rabbits rather than a roulette table, and a politician. That pedigree, and the specific history behind each name, explains something the fourth column in the results table above cannot: why a losing method keeps finding new believers a century after the losing part was settled.

Labouchère: recovery spread across many wins instead of one

Where Martingale tries to recover an entire losing run with a single win, Labouchère spreads the recovery across several smaller ones. A player first decides how much they want to end the session ahead, say £30, and writes that target as a line of numbers that sum to it, such as 5, 10, 5, 10. The next stake is the sum of the first and last numbers still on the line, 15 in that example. A win crosses off both of those numbers. A loss does the opposite: it adds the amount just lost to the end of the line, lengthening the road back rather than shortening it. Play continues until the line is empty, which recovers the target exactly, or until a stake the table refuses, or a bankroll that will not stretch, ends the run early.

The method is also called the cancellation system, or the split martingale, and it is usually credited to Henry Labouchère, an English politician, journalist and theatre owner who died in 1912. His grandson's 1914 biography tells a more specific story than the marketing does: Labouchère did not work out the numbers himself. He came across the method in a letter written generations earlier by the French mathematician Condorcet, and the name that survived was the man who popularised the system rather than the one who solved it. A staking rule wearing a real name reads as tested. Labouchère's own biography shows how cleanly credit and mathematics can travel apart.

A mathematician who never saw a wheel, and a win that proved nothing

D'Alembert has a stranger relationship with the game carrying his name. Jean le Rond d'Alembert, the mathematician and physicist who co-edited the Encyclopédie with Diderot, died in 1783. Roulette itself is usually dated to Paris in the 1790s, so the wheel did not exist yet when he died. What he actually argued, in a 1754 essay on coin tosses called Croix ou Pile, was that a run of tails makes heads more likely on the next toss, because results should balance out over time. That is false: a coin toss has no memory of the last one, and a wheel does not either, whatever run of colours just landed. D'Alembert's staking system inherited the mistake wholesale. Raising the stake after a loss only pays off if losses really do get less likely the longer the run goes on. They do not.

Martingale's own name is less settled than either of those two. One popular account credits a London casino owner called Martindale, whose surname gamblers supposedly corrupted into "martingale" after copying his doubling method. It is a good story, and it is probably the wrong one: French dictionaries were already defining jouer la martingale, to always stake everything just lost, by around 1750, decades before any London casino owner could have coined it. A rival, more scholarly trail leads to an old Provençal phrase, jouga a la martegalo, roughly "to play in a way that is absurd and hard to follow." If that derivation holds, the method now sold as a disciplined route to beating the house is named, in its own language, for the opposite quality.

The clearest example of how one result can outrun the maths belongs to Charles Deville Wells, an English confidence trickster who arrived in Monte Carlo in July 1891 with about £4,000 he had raised from investors on the promise of a musical skipping rope that never existed. He won 100,000 francs quickly enough that the casino draped the wheel and closed the table to fetch more cash, then came back later that year and won roughly a million francs more over three days. A music-hall song about him, "The Man Who Broke the Bank at Monte Carlo," is still known today. What actually happened at the table is disputed. Some accounts credit a genuine eye for a wheel running slightly out of true, in the tradition of Joseph Jagger, who won over two million francs at the same casino in 1873 by spotting a real mechanical bias. Others say Wells simply had an extraordinary run of luck on a fair wheel, and that his long career as a fraudster is doing the work of turning luck into legend. Either way, nothing about the win involved a staking system. Within a few years Wells had lost every franc, gone back to fraud, served eight years in prison for it, and died with nothing.

That is the whole mechanism by which these systems keep recruiting believers. A method attached to a mathematician's name, a politician's biography or a headline win reads as tested, when what has actually been tested is the story's staying power rather than the arithmetic behind it. The "double until you win" argument is not even wrong on its own narrow terms. Given an unlimited bankroll, an unlimited table maximum and unlimited time, a player really would win eventually with certainty, and that single win really would clear every loss racked up along the way. The argument only fails where every casino session fails it: on the size of the word "unlimited." Cap any one of those three resources, which every table, every wallet and every closing time does without exception, and the guarantee dissolves before the house edge is ever needed to explain the loss.

The best roulette betting strategy, assessed honestly

If the question means "which staking pattern returns the most", the answer is that they are all equal per pound staked and the cheapest is therefore the one that stakes least: flat betting, because it generates the least turnover for a given number of rounds.

If the question means "how do I lose least while enjoying it most", there are real answers, and none of them is a staking pattern. Choose a French table and the edge on even-money bets falls from 2.70% to 1.35% under La Partage, which halves your expected cost outright and is a larger improvement than any system claims. Refuse the American wheel and you avoid doubling the edge to 5.26%. Play fewer, slower rounds and less money crosses the edge. Those three decisions are worth more than every progression in this simulator combined, and all three are made before the first spin.

So the best roulette betting strategy is table selection plus a stake you have decided in advance and a session length you keep to. It is less exciting than a system. It is also the only version that survives contact with a wheel. The wheel comparison covers the table-selection arithmetic, and the odds and payouts guide sets out what each bet actually returns.

Playing within limits

A simulator is a safe place to be wrong, which is exactly why it is here: you can watch a thousand sessions cost nothing. Real play is different, and the useful habits are unglamorous. Decide the amount before you start and treat it as the price of the evening. Set a deposit limit while you are calm. Leave when you reach your number, in either direction.

If it stops being entertainment, the tools are free and immediate. GAMSTOP excludes you from every Gambling Commission licensed operator at once. GamCare runs the National Gambling Helpline on 0808 8020 133, at any hour and at no cost, and BeGambleAware publishes self-assessment tools and advice for family. Our responsible gambling page collects all of it in one place.