Games
Betting systems, and the one sum that decides every one of them
A betting system is a rule that sets the next stake after a win or a loss, and every one of them, from the martingale to the Kelly criterion, changes the shape of an evening without changing its cost. The arithmetic that proves it fits in a few lines, and it applies to every system in the table below, whatever name it is sold under.
The one sum that settles them all
Every bet against the house has a negative "expected value" (the average result over many repetitions), which equals the house edge times the amount staked, and the expected value of a series is the sum of the values of each bet, whether the bets rise, fall or stay level. The average loss of an evening is the house edge times everything staked (the "turnover"), and a system only rearranges the bets that make up that sum.
What a system does change, in our reading, is the "distribution" of results, which is how the same average loss is spread across evenings. A system that raises the stake after a loss trades many small wins for a rare large loss, and one that raises it after a win does the opposite; the only way to lose less on average is to stake less in total. Not more slowly, and not in smaller steps, but less.
The martingale on a real table
The "martingale" doubles the stake after every loss, so that the first win recovers everything that was lost in the sequence plus one unit. The European Roulette Pro demo we played has table limits of 1 to 100, which allows seven bets (1, 2, 4, 8, 16, 32 and 64) before the eighth, at 128, is refused because it exceeds the maximum.
Seven losses in a row on an even-money bet come up about one time in 106 sequences on a single-zero wheel, and they cost 127 units against the one unit that each successful sequence wins. Over many sequences the 105 small wins do not cover the one large loss, and the shortfall (about 22 units every 106 sequences) is the 2.70 per cent of everything that crossed the table.
A table from 10 to 500 allows you only six bets (10 to 320, an "exposure" of 630), and six losses in a row arrive one time in 55. The ratio between maximum and minimum decides the length of the ladder, and we know of no table that is wide enough to make the arithmetic change sign!
Slower ladders
Fibonacci, D'Alembert and Labouchère raise the stake more gently after a loss (along the Fibonacci numbers, by one unit at a time, or along a written line of numbers that grows with each loss), so they reach the table limit later and need several wins, rather than one, to recover a losing run. D'Alembert rests on the belief that wins and losses must "balance", which is the "gambler's fallacy" in disguise (a wheel after five reds owes nobody a black).
Raising after a win
The "Paroli" (also called the reverse martingale) doubles after a win, usually for three wins in a row, and then returns to the base stake, so that a good run is pressed and a bad one costs only single units. The anti-D'Alembert, which adds one unit after a win and removes one after a loss, is often confused with it in the common guides, but the two follow different curves; the 1-3-2-6 and Oscar's Grind are fixed or slower versions of the same idea.
Nothing stops a positive progression (no table limit gets in its way), and nothing in it recovers a loss either; the good run ends when it ends, and the cost per unit staked stays where the game put it. We would treat these systems as a way of choosing the shape of an evening, which is a legitimate taste, and never as a way of changing its price.
Covering the table
Covering many numbers is the same mistake, seen from the other side. The "James Bond" bet that many system guides recommend (140 on 19 to 36, 50 on the six line from 13 to 18 and 10 on zero) covers twenty-five numbers out of thirty-seven and wins on most spins, yet it loses 2.70 per cent of the 200 staked on average, like every other bet on the table.
| Family | How it stakes | Systems | What stops it |
|---|---|---|---|
| Negative progression | raises the stake after a loss | martingale, grand martingale, Fibonacci, D'Alembert (also called the pyramid), Labouchère, Tier et Tout | the table maximum and the bankroll, which grow more slowly than the stake |
| Positive progression | raises the stake after a win | Paroli (reverse martingale), anti-D'Alembert, 1-3-2-6, Oscar's Grind | nothing stops it, and nothing in it recovers a loss |
| Flat betting | the same stake every time | flat betting | no wall and no promise: the benchmark |
| Single bet | everything at once | all-in | the least turnover, so the smallest average loss, with the widest swing |
| Covering | several outcomes together | James Bond, columns, six lines, hedging | twenty-five numbers out of thirty-seven cost the same 2.70% as one |
| Number picking | follows past results | Andrucci | the wheel has no memory |
| Sizing | computes a fraction to stake | Kelly criterion | with a negative edge it says not to bet |
Kelly, the formula that says no
The "Kelly criterion" computes the share of a bankroll to stake when a bet has a known edge, and common guides present it as a casino strategy. Applied honestly to an even-money bet on a single-zero wheel, where the payout is one to one, the formula reduces to the chance of winning minus the chance of losing (18/37 minus 19/37), which is minus 1/37, the house edge with its sign showing.
A negative fraction means the right stake is nothing, so on a casino game Kelly answers "don't bet" (the examples in circulation use a sports bet where the bettor assumes an edge, which is a different problem). We consider it the strongest argument on this page, since it takes two lines to check.
Flat betting, and the honest benchmark
Some guides call "flat betting" (the same stake on every bet) flawed because it never recovers losses quickly, which faults it for not being a martingale. It is the only approach that promises nothing, and for a given turnover it produces the smallest swings, which makes it the benchmark for judging all the others.
At the other extreme, an "all-in" bet keeps turnover (and with it the average loss) as low as it can go, although it brings the widest swing. Between the two, every system is, as we read it, a choice of shape, and if you want an evening to cost less, the one lever that works is a smaller total stake, set as a "loss limit" before the first bet (the page on responsible gambling lists the tools every registered site in Alberta must offer).
Picking numbers, and selling systems
The Andrucci system picks the numbers that came up most often in recent spins, which is the "hot numbers" panel turned into a method, and the wheel's lack of memory disposes of it (our European Roulette Pro page shows the panel after a single spin). Anyone selling you a system that "beats the casino" is selling the same house edge in a new order, and our page on winning systems describes those offers.
By the Alberta Casinos Online editorial team · Last updated: November 13, 2026 · Online since 2026
