The best roulette system depends on your goal, not the system (simulation results)

I've been running roulette betting systems through a simulator, 10,000 simulated players per system and goal, single-zero wheel. Each player stops when they hit the goal or can't cover the next bet. One result surprised me more than any single system: the "best" system changes completely with the goal.

Small goal: win $50 and walk away

Martingale on red with $2,550 (8 doublings from $10): about 97–98% of players get there.

The mathematical ceiling for that bankroll and goal is about 97.7% (Bold Play, Dubins & Savage). So Martingale is almost perfect for this.

Most progression systems land 2–6 points below the ceiling.

Big goal: double the bankroll

Same Martingale, same $2,550: only about 1 player in 3 doubles it.

The ceiling for doubling is 48.6%, whatever the bankroll.

Putting everything on red, once, hits 48.6% exactly. The "dumbest" bet in the book is the best possible play.

Grinders like Oscar's Grind and D'Alembert, which look great at +$50, fall to roughly 25–30%.

Why

Every spin costs you 2.7% of what you bet. A small goal ends in a few spins, so a system that wins small and often is close to optimal. A big goal takes hundreds of spins with Martingale or Oscar's Grind, and the house edge grinds the bankroll down long before the target. The single bet gives the edge exactly one chance.

What it means

There is no "best roulette system", only the best one for the goal you set. And the bigger the goal, the more a plain bold bet beats every clever progression.

Full disclosure: I built the simulator myself. No link here, I'm only interested in the discussion.

Questions for you: What goal do you usually set when you sit down? And does anyone play a system that is meant for big goals? I'm happy to run it through the same test and post the numbers here.

Your results line up with the theory. On a single-zero wheel every even-money bet loses 2.7% of the amount staked on average, so what decides your chance of reaching a target is how much you have to put through the wheel to get there. A small target is reached in a few spins, so a progression that wins small and often barely gets taxed. Doubling a bankroll with Martingale or Oscar's Grind means hundreds of spins and a lot of total turnover, and the edge eats it. One bet on red puts the bankroll at risk exactly once, which is why it hits the 18/37 ceiling (48.6%) and nothing beats it. That is the Dubins and Savage result: in a game with a negative edge, bold play is optimal for hitting a fixed goal.

One thing worth adding to the sim if you have not already: real table limits. A Martingale with a table max stops long before the bankroll does, so the small-goal success rate drops once the cap is in. There is a write-up on how often a capped Martingale hits the limit on each wheel if you want to compare your numbers with it.

And the expected loss never changes with the goal: 2.7% of whatever you wager in total. The systems only move the shape of the results, not the average.

Thanks, that’s a great summary, and the turnover point is exactly it. I ran the table-limit idea straight away: Martingale, $10 on red, $2,550 bankroll, goal +$50, single-zero wheel, 200,000 players. When the next double would go over the table max, the player takes the loss and starts again at $10.

No table max: 97.6% reach +$50, average result −$11, average total wagered $436

$1,000 max: 97.1% reach +$50, average result −$20, average total wagered $764

$500 max: 96.4% reach +$50, average result −$38, average total wagered $1,407

So the cap barely moves the success rate, but it more than triples the average loss, because players who hit the max keep playing and put about three times as much money through the wheel. And your last point holds every time: the average loss is 2.5–2.7% of the total wagered, whatever the cap.

The real cost of a table limit isn’t fewer wins. It’s more turnover, and that’s where the 2.7% bites.

I’d be glad to compare this with the write-up you mentioned. Do the numbers there assume the player stops at the cap or starts over?