Paroli: three wins, then reset

Paroli raises an even-money stake after wins. This guide uses the three-win convention: wager 1, 2, 4 units on successive wins, then return to one. Any loss ends the cycle and resets the next stake to one. Reverse Martingale and anti-Martingale can describe related rules, so the cap needs to be stated.

All four cycle endings

The second and third rows surrender earlier gains, producing the same one-unit cycle loss. The successful three-win cycle earns seven units. On a fair European wheel, its probability is (18/37)^3, about 11.51%. The remaining paths collectively account for about 88.49%. Those are probabilities for one new cycle under this exact cap.

Expected cycle net is 8×(18/37)^3−1, about−0.079 unit. The larger occasional gain and frequent small losses still carry a negative expectation. Changing the cap changes the distribution and amount wagered; the wheel probabilities remain fixed.

When a positive progression stops early

A required four-unit stake can be blocked by a table limit even after two wins. Record that as a stop under the chosen convention. Do not count it as a completed three-win cycle. A simulation should declare whether it stops after one cycle or restarts until a spin limit.

Match the version you use

The current native named Paroli plan defaults to a three-win cap and permits its configured cap to vary. The legacy Reverse progression template instead has capped multipliers 1, 2, 4, 8 and holds at its top stake. Those are different rules.

Compare 1-3-2-6 for another win-led sequence. Use the strategy simulator with matching limits, and read variance before choosing a result based on its best-looking path.