Start with the wheel, not the bet
A roulette simulator in Excel is a model of a physical process. Before you write a single formula, decide which wheel you are modelling. A European wheel has 37 pockets, numbered 0 through 36. An American wheel has 38: the same numbers plus a double zero. The extra pocket changes the arithmetic on every bet, so the simulator must know which wheel it is pretending to be.
The core of the model is one cell that generates a random pocket. Excel's RANDBETWEEN function does this cleanly. In an empty cell, enter =RANDBETWEEN(0,36) for a European wheel or =RANDBETWEEN(0,37) for an American layout, where 37 represents the double zero. Every time the worksheet recalculates, that cell produces a new spin. That single cell is the entire random engine; everything else in the simulator is bookkeeping around it.
RANDBETWEEN is not a true random number generator. It is a pseudo-random function that draws from a deterministic algorithm. For a teaching model, that distinction rarely matters. For anything you would use to make decisions about real money, it matters a great deal, and a spreadsheet is the wrong tool entirely.
Map the number to a bet outcome
A spin produces a number. A bet produces a win or a loss. The simulator needs a rule that connects the two. The cleanest way is to build a small lookup table on a second sheet or to the side of the main model. List the pockets in one column and the outcome for your chosen bet in the next.
Suppose the modelled bet is a straight-up wager on a single number. The lookup returns a win when the spin equals that number and a loss for every other pocket. If the bet is on red, the lookup returns a win for the eighteen red numbers and a loss for the black numbers and the zero pockets. If the bet is on a column, the lookup returns a win for the twelve numbers in that column.
The lookup table is where the house edge enters the model. On a European wheel, a straight-up bet wins on one pocket and loses on thirty-six. The payout for a win is set by the table rules, not by the wheel. When you set the win amount in the simulator, use the payout the table pays, and the model will show the edge automatically. You do not need to type an edge percentage anywhere; it falls out of the mismatch between the chance of winning and the payout when you do win.
| Bet type | Pockets that win on a European wheel | Pockets that lose | What the simulator must encode |
|---|---|---|---|
| Straight-up | 1 | 36 | Win only on the chosen number |
| Red or black | 18 | 19 | Zero pockets lose on both colours |
| Column | 12 | 25 | Win on the twelve numbers in the column |
| Dozen | 12 | 25 | Win on the twelve numbers in the range |
Track the bankroll across spins
One spin is a curiosity. A simulator becomes useful when it runs hundreds or thousands of spins and records what happens to a starting bankroll. Set up three columns: spin number, spin result, and bankroll after the bet. The first row starts with a bankroll you choose. Each subsequent row takes the previous bankroll, adds the win amount if the lookup says the bet won, and subtracts the stake if it lost.
The formula is simple. If the stake is in one cell and the net result of the spin is in another, the bankroll column just adds the net result to the previous bankroll. Use absolute references for the stake and the payout so you can change one cell and recalculate the whole history.
What you will see, if you build the model and press F9 a few times, is that the bankroll line wanders. It does not glide downward at a steady rate. It spikes up after wins, sags after losses, and sometimes spends a long stretch above where it started. That wandering is variance. The house edge is a long-run average, and a few hundred spins are not the long run. The simulator shows both things at once: the edge is built into every spin, and the path of any particular session is noisy.
Decisions per hour change total exposure
A roulette table does not spin once per day. It spins continuously, and the speed of play changes how much money passes through the model. The simulator can show this by adding a column that counts cumulative stake. If each spin costs one unit, then after a hundred spins the player has wagered a hundred units, regardless of whether the bankroll is up or down.
Total exposure is stake multiplied by number of spins. The edge applies to the total wagered, not to the starting bankroll. A player who brings a fixed bankroll and bets small amounts for a long session will put far more money through the table than a player who bets larger amounts for ten minutes. The simulator makes this visible because the cumulative stake column climbs even while the bankroll column bounces.
This is also where bet selection matters. Different bets on the same table carry different edges. A straight-up bet and a red bet are not equivalent wagers, even though they sit on the same layout. The simulator can compare them by running two models side by side with the same spin sequence and different lookup tables. The difference in the bankroll paths is not luck; it is the arithmetic of the two bets.
Why progression systems do not change the edge
Once the simulator is running, it is tempting to add a progression system: double the stake after a loss, or raise it after a win, or follow some other pattern. The model can do this easily. Add a column that sets the stake for each spin based on the previous result. The bankroll formula still works; it just reads a changing stake instead of a fixed one.
What the simulator will show, over enough spins, is that the progression changes the shape of the bankroll line but not its direction. A martingale produces many small wins and occasional large losses. The large losses arrive when a losing streak forces the stake to grow beyond the bankroll or the table limit. The edge is still applied to the total amount wagered, and the total amount wagered has grown.
This is the clearest lesson the spreadsheet can teach. A progression system redistributes outcomes. It moves the losses around in time, concentrating them into fewer, larger events. It does not remove the built-in edge from any individual bet. The simulator shows this without argument, because the arithmetic is right there in the cells.
Build a summary row that separates luck from edge
The raw bankroll column is mostly luck. The summary row is where the edge becomes visible. Add cells that calculate total spins, total amount wagered, net result, and net result as a share of total wagered. That last figure is the empirical return of the session. Over a few hundred spins it will swing wildly. Over tens of thousands of spins it will settle toward the theoretical figure for the wheel and bet you modelled.
The theoretical figure is the complement of the house edge. Return to Player and house edge sum to 100% for the same bet under the same rule set. If the simulator models a European wheel with a straight-up bet, the long-run return approaches the figure implied by the wheel's thirty-seven pockets and the table's payout. You do not need to type that figure into the model. Run enough spins and the summary row will find it on its own.
The gap between the short-run empirical return and the long-run theoretical return is the entire point of the exercise. A simulator does not predict the next spin. It shows what happens to a bankroll when a random process with a built-in edge runs for a long time. That is a different question from whether the next spin will be red, and it is the question a spreadsheet can answer.
FAQ
Can I use the simulator to test a betting system before playing for real money?
You can use it to see what a betting system does to a bankroll over many simulated spins. What it will show is that no staking pattern changes the edge on each bet. The simulator is a tool for understanding variance and exposure, not for finding a way to overcome the house advantage.
How many spins should I simulate to see the house edge clearly?
More than you expect. A few hundred spins are dominated by variance. The empirical return only settles near the theoretical figure over tens of thousands of spins. The simulator can run that many rows easily, but the point is not to reach a precise number; it is to see how slowly the average converges.
Does the simulator work the same way for American and European wheels?
The model is the same; the lookup table changes. An American wheel has an extra losing pocket for most bets, which changes the long-run return. Build the simulator with a cell that switches between thirty-seven and thirty-eight pockets, and the summary row will show the difference over enough spins.
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