American vs European Roulette Simulator

Compare the rules before comparing a session

American and European roulette share many familiar wagers, but their standard wheels contain different numbers of pockets. American roulette includes 0 and 00 for 38 total outcomes. European roulette includes one zero for 37. When payouts and other rules are held constant, the extra American pocket lowers the chance that a standard numbered wager wins.

That comparison is about the mathematical model, not a guarantee about two short sessions. An American practice run can finish above a European run because the realized outcomes differ. To understand the formats, separate the known rule difference from the random path a particular virtual balance takes.

Junko Bodie offers both modes through its membership experience. The American and European pages explain each format individually. This article focuses on comparing them without changing several variables at once.

Count the pockets explicitly

Both standard wheels contain the numbers 1 through 36, with eighteen red and eighteen black numbered pockets. European roulette adds one green zero. American roulette adds two green pockets. Zero labels are separate outcomes; double zero is not just another spelling of zero.

For a specified straight number, European winning probability is 1/37, approximately 2.70%. American probability is 1/38, approximately 2.63%. The difference may look small for one wager, but the payout remains the same, so it changes the expected result.

For red, the comparison is 18/37, approximately 48.65%, versus 18/38, approximately 47.37%. Neither is 50% under standard full-loss green treatment. Start with these counts rather than with a slogan that one wheel is "fair" or that the other is impossible to win.

The payout can stay the same while the probability changes

A standard straight wager pays 35 to 1 in profit on both formats. A ten-chip win earns 350 and returns 360 including the original stake. That payment does not increase to compensate for the additional American pocket.

A standard split pays 17 to 1, a street 11 to 1, a corner 8 to 1, and a six-line 5 to 1. Dozens and columns pay 2 to 1; standard even-money outside wagers pay 1 to 1. These common ratios are documented in published roulette rules.

Because the usual payment is unchanged, the comparison cannot be made by payout alone. A page showing only the payout table may conceal the most important difference between the formats: how many possible outcomes fail to receive that payout.

Derive the standard house edges

For a one-chip European straight wager, expected value is (1/37 × 35) - (36/37 × 1), or -1/37. Dividing expected loss by stake gives a house edge of approximately 2.70%.

For an American straight wager, expected value is (1/38 × 35) - (37/38 × 1), or -2/38. The corresponding edge is approximately 5.26%. The same standard edges apply to most ordinary wagers in their respective formats under these assumptions.

These are averages per amount wagered. They are not taxes applied after the session or mandatory deductions from each result. A straight wager still settles as a win or a loss. The odds guide explains the expected-value interpretation in more depth.

Compare equal turnover, not just equal starting balances

Suppose two hypothetical exercises each commit a total of 1,000 chips to standard wagers. Expected loss is approximately 27.03 chips on the European model and 52.63 on the American model. The difference is approximately 25.60 chips of expectation.

These figures are calculated, not observed experimental results. They also require equal turnover. Two sessions starting with 200 chips can produce very different total wagering if one lasts longer or uses increasing stakes. Equal opening balances do not ensure a controlled comparison.

Record the sum of every stake. Returned chips can be wagered repeatedly, so turnover can exceed the opening balance. Without that measure, a larger loss may be incorrectly attributed to the wheel when the exercise simply involved more wagering.

Treat the American basket as an exception

The five-number basket covers 0, 00, 1, 2, and 3. Its standard 6-to-1 profit payout produces a house edge of 3/38, approximately 7.89%. It is not part of the ordinary 5.26% group.

There is no identical standard European five-number basket in the calculator's model. Comparing it with a European corner changes both the wheel and the wager. That can still be an interesting comparison, but it is not a clean test of the extra zero alone.

When the goal is isolating the wheel difference, choose the same standard wager available in both modes. When the goal is studying special wagers, describe the changed coverage and payout explicitly.

Do not assume special rules from a wheel label

European roulette is sometimes discussed alongside la partage and en prison. Those terms concern additional settlement treatment for certain wagers. A wheel having one zero does not establish that either rule is offered.

The examples here and the public calculator use full loss on uncovered pockets. They do not model an imprisoned stake or a half-stake return. A different special-rule result therefore needs a different calculation.

Similarly, a game with multipliers, unusual payouts, or side bets should not inherit the standard figures without inspection. Read the rule model rather than assuming that the familiar wheel graphics settle the question.

Layout differences and learning transfer

Many numbered-grid placements are familiar across the two modes. A straight wager still targets a pocket; a split selects a valid adjacent pair; a corner selects four cells meeting at an intersection. This makes basic placement knowledge transferable.

However, the zero region differs, and the American basket requires its own attention. The circular wheel order also differs from the rectangular table order. Do not use the location of a wheel neighbor to infer a valid table split.

A good practice comparison first checks that the accepted wager is the intended one. Only then compare probabilities. The inside and outside bets guide helps resolve placement ambiguity before it becomes a false format comparison.

A controlled paper exercise

Choose a five-chip corner available in both formats. It covers four pockets and pays 8 to 1 in profit. A winning wager therefore earns 40 and returns 45 on either wheel. An uncovered result loses five.

Calculate its expected value separately. European probability is 4/37; American probability is 4/38. Weight the +40 and -5 outcomes by the appropriate probabilities. You should obtain an expected loss of 5/37 chips for European and 10/38 for American.

This exercise shows that you can compare rules without waiting to observe rare outcomes. It is also a useful check on calculator settings: change only the wheel, keeping the wager and amount fixed. Label the result as a calculation, not as evidence from a played trial.

Why a short comparison can look reversed

A lower expected loss does not require the European exercise to finish higher every time. With a high-payout wager, one additional hit can outweigh the expected difference over a short block. Random variation can therefore dominate the small average effect.

For example, a straight win at a five-chip stake produces 175 chips of profit. Whether that one event appears in a short sample can have a much larger effect on final balance than the expected difference between wheel formats over the same limited turnover.

This does not make the house edge meaningless. It means the house edge answers an average-value question rather than predicting the ordering of two individual samples. Avoid using one screenshot as proof that the known mathematics has changed.

Independence is shared by the standard models

Under the independent uniform assumptions, neither wheel remembers the previous outcomes. A long absence of a number does not increase its next-spin probability. The same applies to a sequence of red or black results.

For a specified European number, no hits in n spins has probability (36/37)^n. For a specified American number, it is (37/38)^n. Both expressions describe fixed blocks of trials. Neither means that a missed block makes the next spin compensatory.

The general count model is described in OpenStax's binomial chapter. These expressions are applications of that model and are not a certification of a particular implementation.

Decide what the comparison is for

If you want to learn the layout used by a specific game, practice that format. If you want to understand the mathematical effect of zero pockets, use identical standard wagers and equal turnover. If you want to test a staking rule, keep the format fixed during the initial comparison.

Those are different learning objectives. Mixing them can produce a long session without a clear conclusion. A useful note at the end might be "I can explain why the same corner payout has a different probability," rather than "this wheel was lucky."

The practice lesson offers a sequence for learning one variable at a time. The strategy guide covers the additional assumptions needed for a conditional staking rule.

Keep product access separate from the mathematical choice

Choosing American or European mode does not turn virtual chips into cash. Junko Bodie is a membership-based educational and entertainment simulator. Review the current access terms rather than interpreting play-money language as a promise of unrestricted free use.

This article uses hypothetical stakes and transparent calculations. It does not claim to report a controlled platform experiment, an independent RNG audit, or a method that predicts roulette outcomes. The practical benefit is understanding exactly which rule changes and what that change does to the numbers.

A comparison sheet with two separate columns

Write one column for European and one for American. In each, record total pockets, selected wager, winning pockets, profit payout, and zero treatment. Do not fill a blank from memory if the actual game has not established it.

For a six-line, the ordinary winning set has six pockets and the profit ratio is five. At a two-chip stake, a win profits ten and returns twelve in either standard format. The European expected result is (6 × 10 - 31 × 2)/37, or -2/37. The American result is (6 × 10 - 32 × 2)/38, or -4/38.

The extra losing pocket appears explicitly in the second numerator. This is a useful way to see the mechanism without relying on rounded percentages. It also makes clear why a change in payout would require a fresh comparison rather than merely swapping the denominator.

What to include in a future simulation comparison

A credible comparison report would state the number of attempted sessions, exact wager rules, stake, stopping conditions, and method used to generate outcomes. It would retain losing runs and explain whether the two formats were sampled independently.

Its charts should show a distribution or a range of outcomes, not only the most favorable example. The report should distinguish the expected difference from the observed difference and avoid claiming that one sample proves the result of every future session.

This article has not run such an experiment. The numerical examples are calculated directly from the stated pocket counts and payouts. That is sufficient to explain expected value, but it should not be relabeled as measured product performance.

Three common comparison mistakes

One mistake is comparing different stakes and calling the larger balance swing a wheel effect. Another is comparing a standard wager with a special wager, such as the American basket, without acknowledging the changed payout. A third is treating a short run's ranking as a reversal of the mathematical expectation.

Correct each mistake by identifying which variables changed. A controlled question holds other settings constant, while a broader product comparison explicitly lists differences. Neither requires pretending that every available format is identical except for zero.

For practical learning, you can separate the work into two sessions: first understand each format on its own, then compare one shared wager on paper. This reduces the chance that unfamiliar placement or an access setting becomes confused with a probability difference.

A final interpretation check

If an American exercise finishes higher, record that observed outcome without calling it a better probability model. If a European exercise loses, do not conclude that its smaller house edge failed to operate. In each case, separate the finite result from the rule-based average. That distinction is the main lesson of a careful comparison and applies equally to screenshots, manual sessions, and larger future experiments.