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Roulette is a game of chance with a built-in house edge. No staking pattern, system or timing changes the odds in the player’s favor over time, and most players lose money in the long run. Nobody should gamble money they cannot afford to lose. This article describes how some well-known patterns work so that you can see why they do not do what their reputations suggest.
What a progression is
A progression is a rule for changing the size of your next bet based on what just happened. The usual setting is an even-money bet such as red or black, and the rule says how many units to stake after a win or a loss. Most are sold, by implication, as a way to “manage” results. In practice, they only change how wagers are distributed over time. The simplest and most widely known, doubling after each loss, is the martingale system. Here are several others.
Fibonacci
The staking sequence follows the Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21 and so on, where each term is the sum of the previous two. The common rule is to move one step forward after a loss and two steps back after a win.
A hypothetical example with a $1 unit: six losses in a row would mean bets of 1, 1, 2, 3, 5 and 8 units, totaling 20 units lost. The seventh bet would be 13 units. A win at that point returns 13 units of profit, and the player steps back two places, to the 5-unit bet. Because a win recovers only part of the earlier losses, the sequence grows more slowly than doubling, but a long losing run still leads to large stakes, which table limits may cap.
Labouchere
Also called cancellation, this method starts with a written list of numbers, for example 1-2-3. Each bet equals the first number plus the last, so the first bet here is 4 units.
- After a win, cross off the two numbers used. With 1-2-3, a win leaves 2, and the next bet is 2 units.
- After a loss, add the amount just lost to the end of the list. A first-bet loss of 4 turns 1-2-3 into 1-2-3-4, and the next bet is 1 + 4 = 5 units.
If the list is ever fully crossed off, the total profit equals the sum of the starting list, which is 6 units here. That tidy result is the appeal. The catch is that a run of losses makes the list longer and the bets bigger, and the process stops being tidy exactly when the bankroll is under pressure.
D’Alembert
This pattern adds one unit after a loss and subtracts one after a win. It grows slowly, which makes it sound gentle. Equal numbers of wins and losses would leave the player at about break-even, but losses are slightly more frequent than wins. On a single-zero wheel, an even-money bet wins with probability 18/37 and loses with 19/37.
Paroli
The reverse of the martingale: raise the bet after each win, often to a target such as three wins in a row, then return to the starting bet. This limits the size of losses to the base unit during a cold streak, but it reaches a goal only if several wins happen consecutively, and the chance of that on an even-money bet is below one in two each time. Three wins in a row on a single-zero wheel has a probability of (18/37)^3, which is about 11.5%.
Why none of them change the expected loss
Every spin is a separate event. The ball and wheel do not know your previous bets, so the chance of each outcome is the same every time, a point that connects to independent events. On every spin, the expected result of a bet is minus the house edge multiplied by the amount staked. A progression chooses the amounts staked, but it cannot choose the odds.
Add this up across a session and the expected total loss equals the house edge times the total amount wagered. For a single-zero wheel with even-money bets that figure is about 2.70% of the amount wagered. What a progression changes is how much gets wagered and how results are spread out:
- It can make small wins more frequent.
- It makes occasional large losses larger.
- It may lead to more total money being wagered, which raises the expected total loss, not lowers it.
The same reasoning applies to betting systems generally, whatever the cleverness of the pattern.
Why they feel as if they work
A pattern that wins a small amount most of the time and loses heavily now and then will look successful in a short sample, since small samples rarely include the rare large loss. Memory also favors the wins. That is part of the broader set of cognitive biases that make streak-based thinking appealing. The long-run picture, which the law of large numbers describes, does not depend on any of this.
Practical points
- Table limits stop open-ended escalation.
- A bigger bet size means bigger swings, which raise the risk of ruin for a fixed bankroll.
- If a pattern ever feels like a way to recover losses, that is a signal to stop, not to bet more. Chasing losses tends to make things worse, and a local support service can help anyone who is struggling.