Roulette Heatmap Analyzer

The Roulette Heatmap Analyzer compares how often one number hit in a sample of spins against the uniform expectation for a European or American wheel. Three inputs: Spins Sampled (default 100), Number Hits (default 5), and Wheel Type (European 37 pockets by default, or American 38). Expected Hits = spins / pockets. Deviation = (hits − expected) / expected × 100%. On the defaults, expected = 100/37 ≈ 2.7027, displayed as 2.7, and deviation = (5 − 100/37) / (100/37) × 100% = 85.00%. Five hits in 100 spins is 85% above a fair European single-zero expectation of about 2.70.

Switch the wheel to American. Expected becomes 100/38 ≈ 2.6316, displayed as 2.6, and deviation = 90.00%. The same five hits look slightly “hotter” on a 38-pocket wheel because the fair baseline is lower. That is arithmetic, not physics. The double-zero pocket does not make number 17 more likely; it makes every number’s fair share slightly smaller.

Scale the sample. 370 European spins (ten full wheels) with 10 hits on a number: expected = 370/37 = 10.0, deviation = 0.00%. That is the regression test in the suite. 380 American spins with 10 hits: expected = 10.0 again. A “hot number” board in a casino is usually 100–500 spins, which is one to two orders of magnitude too small for the law of large numbers to flatten Poisson noise. Five versus 2.7 looks dramatic; it is one extra hit or two in a tiny sample.

The tool does not draw a wheel heatmap. It scores one cell. To build a mental heatmap, run it per number, but remember that 37 tests at a 5% significance idea will light up about two numbers by chance even on a fair wheel. Pearson’s chi-square for the full 37-vector is the joint test; this page is the single-cell relative error.

Do not bet the 85% deviation. House edge on a straight-up European number is 2.70% regardless of the last 100 spins. The analyzer exists to put a denominator under the LED board, not to pick a colour.

Roulette heatmaps — “hot and cold numbers” displayed above the wheel — are a marketing layer on a uniform distribution. Each spin on a fair European wheel has 37 pockets; each number has probability 1/37. The count of hits on a fixed number in n independent spins is Binomial(n, 1/37), or approximately Poisson(n/37). The mean is n/37. Fluctuations of tens of percent in a 100-spin window are the default behaviour of that Poisson, not evidence of a biased rotor.

The mathematics of a possibly biased wheel is older than the LED board. In the late nineteenth century, Joseph Jagger famously exploited a biased wheel at Monte Carlo by recording frequencies — a genuine parameter shift, n large, one pocket over-represented. Pearson’s chi-square (1900) is the systematic test of whether a whole vector of 37 frequencies matches n/37. SorteCalc’s analyzer is the one-number relative deviation, a much weaker statistic, because that is what the heatmap UI shows players: this number is +85% versus expectation.

European versus American matters for the denominator. Single-zero: 37 pockets, house edge 1/37 ≈ 2.70% on even-money and on straight-ups (payout 35:1 against fair 36:1). Double-zero: 38 pockets, house edge 2/38 ≈ 5.26% on even money (except the 2:1 “even-money” bets that still lose on 0 and 00 in American rules). Expected hits in 100 spins drop from 2.70 to 2.63. The heatmap does not display house edge; it displays frequency noise.

Limits: no chi-square p-value, no multiple-testing correction, no rotor-speed physics, no dealer-signature model. A physically biased wheel is a different hypothesis (p_i ≠ 1/37 for some i) and needs thousands of spins, not 100. Poincaré wrote on the mixing of the roulette map; modern casinos use inspectable wheels and frequent rotor swaps precisely so that Jagger’s project fails. If a heatmap is your only data, you are looking at noise. If you have 10,000 spins and a chi-square of 80 on 36 degrees of freedom, you have a conversation with a physicist, not with this form.

Educational use: convert “5 hits” into “expected 2.7, +85%,” then remember that Poisson(2.7) easily produces 5. The law of large numbers is a statement about n → ∞, not about the last hour.

A lecture on how to score a “hot number” begins with the uniform mean, not with the light-emitting board above the wheel. One hundred spins, five hits on a chosen pocket, European wheel of 37 pockets. Expected hits equal 100/37 ≈ 2.7027, shown as 2.70. Relative deviation is (5 − 100/37) / (100/37) × 100 percent = 85 percent exactly. Five hits in a hundred spins sit 85 percent above a fair single-zero expectation of about 2.70. Switch to 38 pockets and the same five hits become 90 percent “hot,” because the fair baseline dropped to 100/38 ≈ 2.63. That is arithmetic, not physics; the double zero does not make number 17 more likely.

Distribution of hits on a fixed number follows a binomial count with success chance 1/37, or approximately a Poisson law with mean 2.70. Fluctuations of tens of percent in a 100-spin window are the default behaviour of that Poisson, not evidence of a biased rotor. The single-cell Pearson residual is (5 − 2.70) / √2.70 ≈ 1.40, well inside ordinary scatter. A proper test of the whole wheel is Pearson’s chi-square on the 37-vector with 36 degrees of freedom; that statistic is named here as the right instrument and is not computed on this page. Testing 37 numbers at a 5 percent idea will light about two pockets by chance on a fair wheel.

Joseph Jagger exploited a genuinely biased wheel at Monte Carlo in the late nineteenth century by recording long frequencies — a parameter shift, n large, one pocket over-represented. An LED heatmap of the last hundred spins is the opposite project: short-run noise sold as a map. Poincaré wrote on the mixing of the roulette map; modern casinos inspect rotors and swap them so that Jagger’s project fails. House edge on a European straight-up is 1/37 ≈ 2.70 percent regardless of the last hundred spins, the same 2.70 that appears as expected hits per 100. Coincidence of units, not a betting signal. Straight-up pays 35 to 1 against fair 36 to 1; that leak does not move when the board flashes plus 85 percent.

Assumptions: independent uniform spins, one number, no sector dependence. A dealer who launches from a similar point with similar force can create short-run sector clustering; that is a hidden story on the rotor, not this relative error. Pearson in 1900 and Neyman’s later work on tests of fit are the intellectual frame: frequency boards without a test are decoration. Three hundred seventy European spins with ten hits would show expected 10.0 and deviation 0.00 percent, the tautology of a round multiple of 37. One hundred spins with five hits remain plus 85 percent of noise. Do not bet the deviation.