Relaxed Roulette Strategy

Complete analysed version

Start a line with [1]. Observe spins without betting: record the first non-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 → result’s dozenbetDozen1–12, 13–24 or 25–36, pays 2:1.Read full →, then continue until a result belongs to a different dozen, ignoring zero and further results from the first dozen. Select those two dozens and keep them fixed through every line reset in this analysed session. On a betting spin, stake each selected dozen by the sole entry when the line has one value, or by the sum of its two end values otherwise. After a loss, append that per-dozen stake to both ends of the line. After a win, remove both ends, or remove the sole entry when only one remains. An empty line resets to [1].

Why the convention matters

This is an explicitly analysed bilateral-cancellation version. It differs from descriptions that reset immediately after any win and from versions that select dozens from a streak. Those variants have different state changes and should not be treated as the same algorithm. Here, a win can merely peel a pair from the line rather than ending the entire sequence.

Two-dozen payoff

If the current per-dozen stake is s, two equal dozen bets cost 2s. One of the selected dozens wins on 24 pocketsequipmentPocketOne of the 37 numbered compartments on the rotor. Also: slot, cup.Read full →: its 2:1 payoutmoneyPayoutWhat a winning bet returns, quoted as “X to 1” on top of the returned stake.Read full → offsets both stakes and leaves +s. The unselected dozen and zero make 13 losing pockets, costing −2s.

Worked cancellation example

Beginning with [1], a loss stakes 1 per dozen and produces [1, 1, 1]. The next loss stakes 2 per dozen and produces [2, 1, 1, 1, 2]. The following stake is 4 per dozen; a win removes the outer 2 values and leaves [1, 1, 1]. A further win stakes 2 and removes the outer pair, leaving the original central [1]; the next win stakes 1 and clears the line, which then resets to [1]. The complete L, L, W, W, W path is shown below.

Risk and expectation

The per-spin expectation is (24 × s − 13 × 2s) / 37 = −2s/37. Selection based on recent dozens does not alter those probabilities. Repeated losses keep adding values at both ends, so the line and the per-dozen stakes are unbounded unless the player imposes a stop, a bankrollmoneyBankrollThe total amount set aside for play. Bankroll management is deciding how much of it to risk per bet and per session.Read full → limit, or a table limittableTable limitMinimum and maximum bet allowed. The maximum is what stops doubling progressions.Read full →. A cancellation line can complete, but completion does not erase the negative expectation of every amount wagered along the way.

Questions