Betting systems, and what they really change

A "betting system" (a rule that fixes the next stake from the results of the previous ones) is one of the most durable promises around the casino, and it comes in at least twenty versions. The names sound like methods, from the "martingale" and the "Fibonacci" to the "Paroli" and the "Labouchère", and the table below lists each of them with its obstacle.

We have read the arithmetic of all twenty, which is the only reading they need, and we consider that a single proof a few lines long settles the question for every system at once. What changes from one system to another is the shape of a session (how often it ends in profit, how badly otherwise), and the shape is worth knowing for readers who arrive here after a run of losses, with someone offering them a system that "recovers" everything.

The proof that covers every system at once

Every bet at a casino game has an expected loss equal to the "house edge" (the share of each stake the game keeps on average) times the stake. The expected loss of a sum of bets is the sum of their expected losses, in whatever order and at whatever size the bets are placed.

From these two facts, which are not a matter of opinion, the whole subject follows. The expected loss of a session is the house edge multiplied by everything that crosses the table (the "turnover"), and a system changes the order and the size of the bets, in other words the distribution of the result, without touching the edge or the sum.

A player who stakes $10 on red for 100 spins of a European wheel (where every bet carries an edge of 2.70 per cent, as the house edge page explains game by game) puts $1,000 across the table and should expect to lose $27.

With a martingale over the same spins, at a table whose limits run from $10 to $500, the same player stakes about $31 a spin on average (each loss doubles the next stake), and by our computation the expected loss becomes about $85 on some $3,130 of bets. The martingale has not found a cheaper wheel; it has bought three times as much of the same one!

Two consequences follow, and we would put them at the top of any page on the subject. The first is that a player loses less only by betting less in total (not more slowly, not in smaller pieces cleverly arranged, but less), which is why a system that makes a session last longer costs more rather than less.

The second is that, per dollar wagered, no system is worse than another in expectation, and none is better. They differ in "variance" (how widely the results spread around the same average), and each family offers its own exchange between frequent small results and rare large ones; the choice between them is a matter of taste, while the price is the same for all.

What a system can change, and what it cannot

A system can change how often a session ends in profit, and the change can be large. The martingale player on the table we have just described wins $10 in about 54 "sequences" out of 55 (a sequence being the run of stakes that ends with a win) and loses $630 in the remaining one, so most evenings end with a small gain and the memory of a method that works.

It can also change the size of the rare bad result (by moving the ceiling or the first stake) and the pace, since bets per hour multiply the cost. It cannot change the price.

The same holds for the "coverage" systems, which spread the money over several bets at once instead of staking in sequence. A player who covers twenty-five numbers with the "James Bond" ($140 on 19 to 36, $50 on the "six-line" from 13 to 18, $10 on zero) pays the house its 2.70 per cent on the whole $200, like a player backing one number, as the page on roulette bets shows bet by bet.

The systems that pick numbers from past results meet a wheel without memory. On a fair wheel the number you saw most often in the last thirty spins is neither more nor less likely than any other on the next spin, and the "hot number" is a story about the past, not information about the future.

Seven families and twenty names

The names are many and the families few, and we have grouped all twenty below by the rule each follows, with one sentence per system and its obstacle. The four families with an arithmetic of their own (negative and positive progressions, flat betting, Kelly) have a page each, while the minor systems keep their row, which in our view is what they are worth.

Twenty systems in seven families, with one price per dollar wagered

System	Family	How it stakes	What stops it
Martingale	Negative progression	Twice the previous stake after every lost bet, back to the opening stake after a win, so that each sequence aims at one unit.	The table maximum, after six stakes from $10 under a $500 limit.
Grand martingale	Negative progression	Doubles the stake and adds a unit whenever a bet loses, so that a win on the fifth bet leaves the sequence five units ahead.	The same maximum, one stake sooner: 10, 30, 70, 150, 310, and 630 is refused.
Fibonacci	Negative progression	Each stake is the sum of the two before it; a loss moves one place up the sequence, a win two places down.	A slower climb to the same ceiling, where the loss is fixed in advance.
D'Alembert	Negative progression	One unit more after a loss, one unit less after a win.	A stretch in which losses outnumber wins, costing about half the square of the gap, in units.
Labouchère	Negative progression	Bets the first and last numbers of a written line together, strikes them off on a win and appends the lost amount on a loss.	The maximum, reached by about one line in twelve in our computation ($10 units, line 1-2-3-4, $500 cap).
Tiers et Tout	Negative progression	A third of the session money, and after a loss the remaining two thirds.	Two losses in a row, about one attempt in four, which take everything.
Pyramid	Negative progression	A staircase that climbs a step after a loss and comes down a step after a win, in the manner of the D'Alembert.	The same stretch of losses as the D'Alembert.
Reverse martingale	Positive progression	Twice the stake after every winning bet, one unit again after a loss.	Nothing stops it, so it keeps nothing unless the player stops it.
Paroli	Positive progression	Leaves stake and winnings riding through three straight wins, then banks the eight units on the table, seven of them profit.	The three straight wins, about one attempt in nine.
Anti-D'Alembert	Positive progression	One unit more after a win, one unit less after a loss: not the reverse martingale under another name.	A balanced run, which costs one unit per loss.
1-3-2-6	Positive progression	One, three, two and six units on four consecutive bets, starting over as soon as one of them loses.	The four wins, about once in eighteen cycles.
Oscar's Grind	Positive progression	Raises one unit after a win, never beyond what closes the series one unit up.	The rare series that sinks, about one in two hundred in our computation ($10 units, $500 cap).
Flat betting	Flat	One stake, unchanged from the first bet to the last.	Nothing, and nothing is promised.
All-in	Single bet	The whole session money on one bet.	Nothing: the smallest turnover and the widest swing.
James Bond	Coverage	$140 on 19 to 36, $50 on the six-line 13 to 18 and $10 on zero, 25 numbers for $200.	The price, 2.70% of the $200 like any other bet.
Two columns	Coverage	Two columns at once, 24 numbers out of 37.	The price, 2.70% of both stakes.
Six-lines	Coverage	Several six-number lines at once, five of them covering 30 numbers.	The price, paid as five units lost on one of the seven numbers left out.
Hedging	Coverage	Bets that partly cancel each other, such as red with the second column (eight black numbers of twelve).	The price of every chip, whether it offsets another or not.
Andrucci	Number picking	Records some thirty spins, then backs the most frequent number straight-up for a similar run.	A wheel without memory: the gambler's fallacy in its purest form.
Kelly	Sizing	Computes the share of the bankroll to stake from the odds and the probability.	Nothing, which is the point: with a negative edge it advises no stake at all.

The table reads in one direction only. Every row ends with the same price per dollar wagered, and what differs is the road: the negative progressions climb after a loss until a ceiling stops them, the positive progressions climb after a win and give their gains back in small pieces, flat betting does not climb at all, and the Kelly criterion is a formula that decides whether to bet.

The wall each family meets

For the progressions that raise after a loss the wall is physical, and it can be counted. On the $10 to $500 table of the example above, the sixth loss in a row costs the martingale player $630 in all, and the seventh stake, $640, is beyond the "table maximum"; on a European wheel, where red loses on nineteen of the thirty-seven numbers, such a run comes about once in 55 sequences.

Under a $1,000 maximum the stakes become seven, the "exposure" (the total lost when the run arrives) $1,270, and the run comes about once in 106 sequences. Raising the ceiling makes the disaster rarer and larger, which is the same trade at a different rate.

For the progressions that raise after a win there is no wall, since the larger stakes come out of winnings already collected, and for exactly that reason they recover nothing. A run of losses costs them one "unit" (the base stake) at a time, and only a winning streak, which ends when it ends, makes up for it.

Flat betting (the same stake every time) meets no wall and makes no promise, which in our view makes it the honest benchmark. The single "all-in" bet, at the other extreme, puts the whole budget at risk with the least money crossing the table, and so with the smallest expected loss, at the price of the widest swing!

The Kelly criterion, finally, is in our reading the only entry in the table that answers the question it is asked. For an even-money bet at a single-zero wheel it returns minus one thirty-seventh (minus 2.70 per cent): the formula's own way of advising a stake of zero.

When a system becomes a scam

A betting system described for what it is (a way of arranging bets at a known price) is not a scam, and a player who enjoys the rhythm of a Paroli is buying entertainment at the declared price. The line is crossed when a system is sold as a "winning method": a course, software, a channel of "signals" or a book that promises an income from the wheel, often with a link to a particular casino and a deposit to make first.

The test we apply is simple. A method that really won at a game with a negative expectation would be worth far more to its owner played than sold, so the seller who needs buyers earns from the sale (or from the deposit made through the link), not from the method; the page on technical promises goes through its forms, from the "bug" in the casino software to the prediction tool.

The choices that do move the result

Three decisions change what your evening costs, and none of them is a system: the game (the edge differs between games and between versions of a game), the total wagered and the moment to stop. We would advise making them in that order and treating the money for the evening as the price of a ticket rather than as capital to defend.

If you have just lost more than you intended, the plainest line here is the most useful one: in every version we have read, the system promising to "win it back" is the one that puts more money across the table, and so costs more on average. When the losses have stopped feeling like a choice, the responsible gambling page lists the tools that licensed operators offer and the services that help free of charge.

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By the Rand Casinos editorial team · Last updated October 2026 · Online since 2007