D’Alembert
Gradual changes can make escalation less obvious, not mathematically favourable.
What it describes
D’Alembert is usually grouped with gradual progression systems. Its story is often linked to the idea that opposing outcomes will eventually balance. Long-run proportions and short-run compensation are different concepts.
Formula & principle
Loss → previous stake + $10
Start at $10. After a win subtract $10, with a $10 minimum. On this loss-only path B(n) = $10 × n.
B(n) is one stake. On the left, the counter sums all losing stakes with a minus sign and freezes after round 25. On the right, all 25 results are watched without a stake. One $10 stake is then placed for round 26. Its payout follows the selected target: for an even-money bet, $20 returned means $10 stake plus $10 profit. Other targets use their own payout rules.
Same pattern. Different starting points.
A deliberately constructed series: 25 × No Odd, then a matching result at 26. The end is known in this demo only.
Two different snapshots: the left freezes accumulated losses after 25 stakes, before the break. The right skips all 25 rounds, places one $10 stake before round 26, and shows its winning payout, including the returned stake. Net profit is shown separately. This is a selected winning example with a predetermined break, not an equal-length profit comparison.
Without Winnary
Starts at round 1
Waiting for this track
With Winnary
Starts at round 26
Waiting for this track
Model: One additional unit after each loss. The left follows the strategy throughout the losing series. “With Winnary” shows only one initial $10 stake after 25 observed results; there is no earlier loss or stake progression in that column. It is not a measured product result. The Legendary label is illustrative, not a calculated rarity.
Fewer stakes mean less accumulated exposure in this selected sequence. A stake placed after round 25 has no better next-spin odds, and the pattern could continue beyond 26. This model assumes unlimited funds and no table limits. The break is observed after settlement; it cannot cancel a stake already placed. Winnary cannot enforce a loss limit at an external table. Every losing stake is added to the running loss. In the single-stake example, payout includes the returned stake; net profit subtracts that stake. Coverage payouts also account for losing parts of a split allocation. If the round-1 track continued through the same break at round 26, its net would be -$2,990; that final stake would be $260. The later start does not improve next-spin odds.
Demo ready. Both examples use the same predetermined results.
What the mathematics says
Suppose a fair single-zero wheel has produced an unusual imbalance between red and black. A later independent spin still has its original colour probabilities. The percentage imbalance may shrink as more observations accumulate without any mechanism forcing the missing colour to catch up.
How to read the evidence
The useful statistical question is how much variation an independent model would produce over a specified sample. Comparing observed variation with that model is legitimate. Turning the same variation into a promise of recovery is not.
D’Alembert: without and with Winnary
This compares the information available, not measured winnings or losses.
| Without Winnary | With Winnary |
|---|---|
| An imbalance may be interpreted as a debt that the wheel must repay. | Separate the reported imbalance from the claim that outcomes must now catch up. |
What does not change. Independent outcomes do not compensate for an earlier imbalance.
Roulette predictor claims: what evidence matters? ↗Where Winnary fits
Winnary is a roulette analyser that organises observations. Rarity labels and rankings are descriptive. They are not a prediction of the next spin, evidence of a profitable system or a recommendation to act.
Read about the analyser ↗