The Chernyshov system waits for three consecutive results of one color, then bets on the opposite color and triples the stake after a loss. It is a betting progression, not a way to predict an independent spin. Waiting for a streak does not give the player an advantage.
Theory
For a fair coin with independent tosses, the probability of heads on the next toss is always 1/2, even after several heads in a row. A rare sequence does not make the opposite outcome due. Assuming otherwise is the gambler's fallacy.
The same independence applies to a fair European roulette wheel with 18 red pockets, 18 black pockets and one zero. On every spin, red has probability 18/37 ≈ 48.65%, black has probability 18/37 ≈ 48.65%, and zero has probability 1/37 ≈ 2.70%. After three reds, the probability of black on the next spin is still 18/37. Zero is neither color and loses a standard color bet.
Before a specified block of three spins begins, the probability of three reds is (18/37)3 ≈ 11.51%. The probability of three results of the same color, either all red or all black, is 2 × (18/37)3 ≈ 23.03%. These are probabilities of complete future sequences, not probabilities of the next result once a streak has already happened.
Likewise, the probability of at least one black in n future spins is 1 − (19/37)n. It increases with the number of future opportunities, while the chance on each individual spin stays the same. At least one winning bet does not necessarily mean an overall profit after all losses and stakes are counted.
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Practice
In the version described here, the player waits until the last three spins have all been red or all been black, then bets one base unit on the opposite color. Zero breaks a color streak. This waiting rule selects when to bet; it does not improve the 18/37 chance of winning.
After a losing bet, the next stake is three times the previous stake. After a win, the player returns to the base unit. Each bet is placed only when the last three results have the same color. Spins observed without a bet do not change the stake progression.
With a $1 base unit, consecutive losing bets lead to stakes of $1, $3, $9, $27 and $81. Even if the chosen color changes between bets, every placed bet still loses with probability 19/37 under the stated assumptions.
Stake Growth and Risk
Waiting can reduce the number of bets placed over a given number of spins, but tripling stakes increases the amount at risk quickly. After four losing bets of $1, $3, $9 and $27, the total loss is $40 and the next required stake is $81. Funding that fifth bet requires $121 from the start of the sequence. If it also loses, the total loss becomes $121 and the next required stake is $243.
After k consecutive losing bets, the cumulative loss is (3k − 1)/2 base units and the next stake is 3k base units. A bankroll or table limit can prevent the next bet. A larger stake does not make a win more likely, and recovery is never guaranteed.
For standard 1:1 color bets where zero loses the full stake, the expected net result per $1 wagered is (18/37 × $1) + (19/37 × −$1) = −$1/37. The house edge is about 2.70% of the amount wagered. This calculation excludes special rules such as la partage or en prison. Tripling a stake triples its expected dollar loss as well as its possible gain or loss.
The system is straightforward to follow where spins can be observed without betting, but it does not offer a higher probability of winning an individual bet or a reliable income. Set a spending limit before playing and account for the entire possible loss of the progression.
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