Sector Analysis

Method

Divide the wheel into contiguous sectorswheelSectorA contiguous arc of pockets on the wheel, as distinct from a group on the layout.Read full →, usually six arcs of six or seven pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full →, following the wheel order rather than the layoutequipmentLayoutThe printed betting grid on the table. Also: table, felt, cloth.Read full →. For each sector of k pockets, expected hits are n·k/37 and the standard deviationmathStandard deviationSquare root of variance; the typical distance of a result from the expected value.Read full → is √(n·p·(1−p)) with p = k/37. Compute z = (observed − expected)/σ for each sector. A sector above +2 is worth a second look; above +3, in two independent samples, is interesting.

Roulette Wheel

Why sectors

Single-pocket tests have 37 chances to throw a false positive and a weak signal in each. Sector tests have six chances and a signal that adds across neighboring pockets. They also match the physics: a tilted rotorequipmentRotorThe spinning part of the wheel that carries the pockets.Read full → makes the ballequipmentBallThe small ball launched along the track against the rotor. Modern balls are ivorine or Teflon, 18–21 mm.Read full → drop preferentially on the low side, which favors an arc; a loose or bent fretequipmentFretThe metal divider between two pockets on the wheel.Read full → changes the bounce for the pockets beside it; a worn ball trackequipmentBall trackThe rim groove the ball runs along before it slows and falls. Also: upper track.Read full → creates a drop zone that favors whichever pockets are beneath it at the drop, which with a slowly varying rotor speed smears across a wide arc. None of these defects favors a single pocket in isolation.

Rotor SpeedRoulette Wheel Physics

Rolling sectors

Fixed boundaries can split a hot arc between two sectors and dilute it. A complementary approach slides a window of k pockets around the wheel, computing z at each of 37 positions, and looks for the maximum. The maximum of 37 correlated z-scores under fairness is typically around 2.2 to 2.5, so a rolling-window maximum under 2.5 is noise and the threshold for interest is correspondingly higher, around 3.5.

From sector to bet

If a sector is confirmed hot, the natural bet is neighborsbetNeighborsA number and the two pockets on either side of it on the wheel, five straight-up chips.Read full → on its center or a hand-placed set of straight upsbetStraight upA single number, pays 35:1.Read full → across it. The profitability test is the sector hit rate against the payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full →: a six-pocket sector must hit more than 6/36 = 16.7% of the time (observed, replicated) for six straight-up chipsmoneyChipA token representing a fixed amount, placed on the layout to make a bet. Also: check.Read full → to break even, against a fair 16.2%. The margin is half a percentage point, which is why confirming it takes tens of thousands of spins.

Sample Size

The analyzer

The Wheel Bias Analyzer on this site accepts a list of spins, computes the chi-square, and shows the wheel as a heat map with sector z-scores, with the partition above as default. It also shuffles your data to show what the same statistics look like under fairness, which is the quickest cure for seeing patterns.

Chi-Square Test

Formula

Questions