Chernyshov Roulette Strategy

The analysed convention

Every wager in this analysis requires the previous three results to be the same colour; the wager is one unitmoneyUnitThe base stake a system or a player works in. Progressions are described in units so they apply at any table.Read full →, or the current progressionstrategyProgressionAny rule that changes the stake based on previous results. Negative progressions raise it after losses, positive after wins.Read full → stake, on the opposite colour. A zerowheelZeroThe single green pocket that no even-money, dozen or column bet covers; the source of the house edge. Also: single zero, 0.Read full → breaks a colour trigger. If a colour wager has already been placed and zero lands, that wager loses. After a losing wager, triple the next stake; after a winning wager, reset the progression to 1. Spins on which no wager is placed do not advance the stake. Different reset variants exist, so this is an analysed convention rather than a claim of one canonical rule.

Trigger frequency is not a prediction

For a specified three-spin block, the probabilitymathProbabilityChance of an outcome, from 0 to 1 or 0% to 100%. One number: 1/37 = 2.70%.Read full → that it is all redbetRedEven-money bet on the 18 red numbers. French: rouge.Read full → or all blackbetBlackEven-money bet on the 18 black numbers. French: noir.Read full → is 2(18/37)^3 = 23.0273%. That calculation describes how often a qualifying block occurs. Once it has occurred, the next chosen opposite colour still wins with probability 18/37; the wheel has not become more likely to balance the observed run.

Stake progression table

Only losing wagers move the progression. Observing spins while waiting for another three-colour trigger leaves the current stake unchanged.

Worked example

After red, red, red, bet 1 unit on black. If red lands, the wager loses and the next qualifying opposite-colour wager is 3 units. If that 3-unit bet loses, the following qualifying wager is 9. After four losses at 1, 3, 9 and 27, the cumulative loss is 40 units and the next required stake is 81. A zero on any placed colour bet is a loss; it does not pay as either colour.

Risk and expectation

Each placed colour bet of s units has expected result −s/37 on a European wheel. Waiting may reduce the number of wagers per hour, but it cannot change the expectation per unit staked. The main risk is the gap between the frequent small stakes and the rapidly growing stakes needed after losses, including table limitstableTable limitMinimum and maximum bet allowed. The maximum is what stops doubling progressions.Read full → and a finite bankrollmoneyBankrollThe total amount set aside for play. Bankroll management is deciding how much of it to risk per bet and per session.Read full →. A long red or black streak is evidence only of prior results, not a reason to expect reversal on demand.

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