The best roulette strategy is provable.
It is also the opposite of everything sold to you. Every bet on the wheel carries the same edge, no system can change that, and the optimal play is to make as few bets as possible.
The short version, in dollars
At $5 a spin and about 50 spins an hour you are putting $250 of action across the layout every hour. What that costs depends on the wheel, and on nothing else you do.
- $3.38 an hour
- a single-zero wheel that gives you half your money back on zero. The cheapest bet in the building.
- $13.16 an hour
- the same $5 bet on a double-zero wheel. Four times the price for an identical-looking game.
- $31.58 an hour
- playing online, where the wheel spins twice as often. Speed is the bill.
- $0.00
- the difference every betting system made. Martingale, Fibonacci, all of them — identical cost, wildly different feelings.
Words we could not avoid
- house edge
- The share of every bet the casino keeps on average. A 2.7% edge means about $2.70 of every $100 you put on the table, however you spread it.
- a shoe
- The box a dealer draws cards from in games like baccarat and blackjack. It holds a fixed set of cards, so what has already come out changes what is left — which is why those games can be tracked and roulette cannot.
- bankroll
- The money you have set aside to play with — not the size of one bet, but everything you are prepared to put at risk.
- action
- The total amount you bet over a session, counting every bet separately. Bet $5 fifty times and you have put $250 of action through the table, even if you never had more than $5 at risk.
- la partage
- A rule on some wheels: if the ball lands on zero, you get half your even-money bet back instead of losing all of it. It halves the cost of playing.
- bold play
- Betting big and stopping early rather than grinding small bets. The opposite of what almost every system tells you.
- expected value
- What a bet is worth on average if you made it over and over. Negative for every bet in this piece.
What this was computed on
Roulette is a closed-form game, so most of this is arithmetic rather than simulation — the edges below are exact, not estimates.
The wheels
- Single zero — 37 pockets, the European wheel
- Double zero — 38 pockets, the American wheel
- Triple zero — 39 pockets, increasingly common
The rule that matters
- La partage: an even-money bet loses only half its stake on zero
- En prison is equivalent in expectation
- Neither applies to any bet other than the even-money ones
The systems
- Martingale · D’Alembert · Fibonacci
- Labouchère · Paroli · flat stakes
- Bankroll 100 units, goal 200, table maximum 100 units
Assumed
- 50 spins an hour at a live table, 120 online
- No wheel bias, no dealer signature, no physical prediction
- A fair wheel — every pocket equally likely
The only people who have ever beaten roulette did it physically — biased wheels, dealer signature, ballistic prediction. Those are exploits of a machine, not betting strategies, and none of them survive a modern maintained wheel or exist at all against a random number generator.
Everything here assumes the wheel is fair. That assumption is doing no work: a fair wheel is the best case for the player, and the house still wins.
Finding one
Every bet on the wheel has exactly the same edge.#
- single zero
- 2.703%
- double zero
- 5.263%
- triple zero
- 7.692%
- bet types priced
- 7, all identical
Straight up, split, street, corner, six line, column, dozen, red, black, odd, even — on a single-zero wheel every one of them returns 97.297 cents on the dollar. Not approximately: exactly. The payouts are constructed so that the shortfall is always the zero.
There is exactly one exception, and it is worse: the five-number bet on an American wheel pays 6:1 where the maths calls for 6.2:1, giving it a 7.895% edge against the 5.263% on everything else at the same table.
So the question "what is the best bet in roulette" has no answer, because it assumes a difference that does not exist. What differs between bets is not the cost, it is the ride — a straight-up bet carries roughly six times the volatility of an even-money bet for identical expected loss.
Finding two
Two decisions change your expected loss. Neither is a bet.#
- single zero + la partage
- 1.351%
- single zero
- 2.703%
- double zero
- 5.263%
- worst against best
- 5.7x
Which wheel you sit at, and whether la partage applies. That is the entire list.
La partage returns half your stake when the ball lands on zero, and it applies only to the even-money bets. It halves the house edge, from 2.703% to 1.351% — the best wager available in a casino outside of a few blackjack tables. En prison is the same idea and the same expectation.
The spread is larger than anything a system could pretend to deliver. A double-zero wheel costs 3.9 times as much per dollar as a single-zero wheel with la partage, and a triple-zero wheel 5.7 times. Walking to a different table is worth more than every betting system ever devised, combined, because those are worth exactly nothing.
Finding three
No system changes the edge. All six land on the same number.#
- systems tested
- 6
- that changed the edge
- 0
- measured range
- 2.669% to 2.823%
- theory
- 2.703%
Martingale, D’Alembert, Fibonacci, Labouchère, Paroli and flat stakes, each played from a 100-unit bankroll toward a 200-unit goal against a real table maximum. The column that matters is loss per unit wagered, and every system returns the house edge: 2.669%, 2.678%, 2.699%, 2.764%, 2.793%, 2.823%. Theory says 2.703%.
This is not a surprising empirical result, it is arithmetic. Expected value is linear: the sum of a series of negative-expectation bets is negative regardless of how the stakes are chosen, because no bet's outcome tells you anything about the next one. A staking rule is a function of past results, and past results carry no information about a wheel with no memory.
What the systems do change is the shape of the outcome, and dramatically. Chance of reaching the goal ran from 41.9% for the Martingale down to 0.40% for flat one-unit betting — a hundredfold spread on identical expected value. That gap is the entire reason systems feel like they work.
Finding four
The only quantity that matters is how much you put at risk in total.#
- flat betting, spins
- 3,675
- flat betting, wagered
- 3,675 units
- its average loss
- 99.19 units
- one bold bet, wagered
- 100 units
- its average loss
- 2.70 units
Expected loss is the house edge multiplied by everything you ever put at risk. Not your bankroll, not your session length — the running total of every stake you ever place.
Flat-betting one unit toward a 200-unit goal takes an average of 3,675 spins and wagers 3,675 units to chase a 100-unit profit. It loses 99.19 units on average, which is very nearly the entire bankroll. One bold 100-unit bet wagers 100 units and loses 2.70. Same edge, same game, 37 times the cost.
This is why every system that survives a losing streak is expensive. The Martingale, the Fibonacci and the Labouchère all work by increasing what is at risk after a loss. That is the mechanism by which they recover, and it is also precisely and unavoidably the mechanism by which they cost money.
Finding five
So the optimal strategy is to bet boldly, and it was proved in 1956.#
- P(double up), bold
- 48.65%
- P(double up), flat 1 unit
- 0.45%
- bold is better by
- 109x
- a fair game would give
- 50.00%
If you have a target — turn this into that, then leave — the strategy question becomes well-posed, and it has an exact answer. Dubins and Savage proved that in any game where the odds are against you, bold play is optimal: bet the smaller of your whole fortune and the amount that would reach your goal.
To double 100 units, bold play means one bet, and it succeeds 48.65% of the time. A fair game would give 50%. Grinding the same goal in single units succeeds 0.45% of the time — you keep less than one percent of what the same money is worth in a single wager.
It scales. Bold play reaches four times your bankroll 23.67% of the time against a fair game's 25%, and thirty-six times 2.39% against 2.78%. Five bold doublings and one straight-up number land in almost exactly the same place. You cannot out-manoeuvre the edge. Bold play only minimises how many times you pay it.
Which makes the honest advice the least marketable sentence in gambling: pick a single-zero wheel with la partage, decide what you came to win, bet it in as few wagers as the table allows, and leave. Every additional spin is a fee.
So, concretely
One flat chip, on an even-money box, on a French wheel.#
- the bet
- red / black / odd / even / high / low
- the wheel
- single zero, la partage
- what it costs
- 1.351%
- what everything else costs
- 2.703% or more
- staking
- flat
There is no clever answer here, and that is the finding. The cheapest wager available on a roulette table is an even-money bet on a single-zero wheel that runs la partage, staked flat. It costs 1.351%. Every other square on that felt — every number, split, corner, column and dozen — costs exactly 2.703%, twice as much, forever.
Which of the six you pick is arbitrary. Red, Black, Odd, Even, 1–18 and 19–36 are all eighteen pockets paying evens, and a wheel has no memory, so staying on one box for six hours and switching every spin are the same strategy. Nor is there a combination worth making: Red and Black together cover everything except zero, which simply doubles your exposure to the one pocket that costs you anything.
It is also the lowest-variance bet on the table: one unit of standard deviation per unit staked, against 5.84 for a straight-up number. For the same expected cost your bankroll lasts roughly six times longer, which is the only thing you are actually buying.
Flat, not progressive. Every progression — Martingale, D’Alembert, Fibonacci, Labouchère — works by putting more at risk after a loss, and total risk is the one input to expected loss. A progression cannot improve the price; it can only raise the bill.
One honest caveat, because it cuts against the rest of this page: a consistent bet is timid play, and finding five showed timid play is the worst way to reach a target. These are answers to different questions. If you want the best chance of turning $100 into $200, bet it once. If you want to sit at a table for an evening and pay as little as possible for the privilege, this is the bet — the cheapest way to stay, not the best way to win.
What it costs to sit there, per hour
House edge multiplied by spins per hour multiplied by average stake. Nothing about which bet you choose appears in that formula, because it does not matter.
| Single zero + la partage — $5 average bet | $3 |
| Single zero — $5 | $7 |
| Double zero — $5 | $13 |
| Single zero + la partage — $25 | $17 |
| Online double zero, 120 spins — $5 | $32 |
| Single zero — $25 | $34 |
| Double zero — $25 | $66 |
| Single zero + la partage — $100 | $68 |
| Single zero — $100 | $135 |
| Online double zero, 120 spins — $25 | $158 |
| Double zero — $100 | $263 |
| Online double zero, 120 spins — $100 | $632 |
What to do at the wheel
Priced at the study’s own pace: $5 a spin, about 50 spins an hour, which is $250 of action across the layout every hour.
scripts/make-playbooks.mjs · derived from this study’s own measured edges
Before you sit down
Neither of these is a bet, and together they are worth more than every betting system ever published.
Things that feel like decisions
Both of these are real choices. Neither one changes what the hour costs.
What you are actually there for
The edge is fixed, so the only question left is what you want out of the session.
A straight-up number and an even-money bet cost you exactly the same. They differ only in volatility — roughly six to one.
La partage halves the house edge. One rule, on the same wheel, worth more than every betting system ever published.
Playing online typically doubles your spins per hour, and therefore doubles your hourly cost at the same stake.
The reason this study has a clean answer and our baccarat one did not is worth stating: a shoe of cards depletes, so the odds move and there is something to track. A roulette wheel has no memory. Every spin is drawn from the same pockets, the probabilities never change, and there is nothing for a system to attach to. That is not a gap in the search — it is why the search is finished.