A "positive progression" increases the stake after a win and goes back to the "base stake" (the first, smallest bet) after a loss. The larger bets are therefore paid with money that the table has just paid out, not with the player's own, which is the whole of its appeal.
The family includes the "Paroli", the "reverse martingale", the "anti-D'Alembert", the 1-3-2-6 and Oscar's Grind; in our reading the usual sources treat it as the cautious half of the subject. The price per dollar does not move (a European wheel keeps 2.70 per cent of each stake, as the house edge page shows), while the shape of a session becomes the "mirror" of the negative progressions, with many small losses against a rare large win.
The Paroli in figures
The Paroli leaves the stake and its winnings on the table after a win, a "let it ride" repeated up to three wins in a row, then banks the profit and starts again. Any loss sends it back to the first stake. With a $5 unit the three bets are $5, $10 and $20, and if all three win the $5 becomes $40 (a profit of $35, or seven units).
On a European wheel the probability of three wins in a row at even money is eighteen thirty-sevenths to the third power, about 11.5 per cent. The Paroli therefore completes about once in nine attempts (8.7, to be exact), and in the other eight it loses its $5. Over a hundred attempts the arithmetic we have redone gives about 11.5 completed runs worth some $403 and about 88.5 failures costing some $442, a net loss of about $39!
That loss is once again the price of the wheel, 2.70 per cent of the roughly $1,460 that the hundred attempts put across the table (each attempt stakes $5, then $10 if the first bet wins, then $20 if the second wins too). The Paroli made the wheel neither cheaper nor dearer; what it changed, in our view, is how the evening feels, with frequent small disappointments and an occasional run paying seven times the stake.
Why nothing stops them, and why they recover nothing
A positive progression meets no "wall", because the stake grows only when the table has paid, and the money at risk from the player's own pocket is never more than the first unit. The martingale player of the page on betting systems risks $630 to win $10 (with a $10 first stake and a $500 limit). The Paroli player at $5 risks $5 to win $35, and the comparison is often offered as proof that this family is the "safe" one.
It is safe in one sense only. Each attempt costs at most one unit, but nothing in the progression recovers the units lost along the way (ten failed attempts cost ten units), and only a completed run, which comes when it comes, pays them back.
The negative family hides its cost in a rare large loss, and the positive family spreads it over many small ones (one unit at a time), so that if you remember only the losses of the first and the wins of the second you will judge them very differently. For the same money wagered the sum is the same, which is why we would not let the comfort of small losses pass for an advantage.
A licensed casino with a single-zero wheel
An operator with a European wheel and a published licence, for a player who would like to try a short progression where the price is 2.70 per cent.
888 Casino
Gibraltar and MaltaGibraltar remote gambling licence RGL No. 112, Virtual Global Digital Services Limited; MGA licence for EU players
18+ · Sponsored link · Terms on the operator's site
The reverse martingale and the anti-D'Alembert are two systems
The "reverse martingale" (also sold as the "anti-martingale") doubles its stake after every win and goes back to one unit after a loss, which makes the Paroli its version with a stop after three wins, while the "anti-D'Alembert" adds one unit after a win and removes one after a loss. The two are often presented as the same system, which they are not, and the confusion matters because their curves have little in common.
The difference shows when both start from one unit and win five times in a row. The reverse martingale, letting everything ride, has 32 units on the table and a profit of 31, while the anti-D'Alembert has won 1, 2, 3, 4 and 5 units (a profit of 15) and is about to stake 6, so one curve "doubles" and the other "climbs a step at a time".
The anti-D'Alembert has a weakness of its own, the mirror of the D'Alembert's promise: ten wins followed by ten losses leave it ten units down, one for each loss. Over a hundred spins at even money, by our exact computation, it ends ahead in fewer than one session in four (about 24 per cent), while the D'Alembert ends ahead in about 59, which is the whole mirror in two numbers.
The 1-3-2-6 ladder
The 1-3-2-6 stakes one unit, then three after a win, then two, then six, and starts again when the fourth bet wins or when any bet loses. Its selling point is genuine, and we would grant it: after two wins the "cycle" can no longer end in a loss, since losing the third bet leaves two units of profit and losing the fourth leaves the player "level" (neither up nor down).
| How the cycle ends | Probability | Result |
|---|---|---|
| Loss on the first bet | 51.4% | 1 unit lost |
| Win, then loss on the second bet | 25.0% | 2 units lost |
| Two wins, then loss on the third bet | 12.2% | 2 units won |
| Three wins, then loss on the fourth bet | 5.9% | level |
| Four wins in a row | 5.6% | 12 units won |
The table shows where the price hides. Three cycles in four end with a loss of one or two units, while the twelve units of the full "ladder" arrive about once in eighteen cycles (5.6 per cent of the time). On average a cycle loses about a tenth of a unit, which is 2.70 per cent of the 3.6 units it stakes on average; the ladder is a pleasant shape for an evening, and no more than a shape.
Oscar's Grind, a positive progression with a negative profile
Oscar's Grind raises the stake by one unit after a win and keeps it unchanged after a loss, but never stakes more than what would close the "series" (the run of bets that lasts until the player is one unit up) with exactly one unit of profit.
By its mechanics it belongs to this family, since it raises only after a win; by its profile it belongs to the other, because a series stays open until its unit is won, however long the bad stretch lasts.
At $10 a unit and with a $500 table limit, by our computation about 199 series in 200 end with their $10. The remaining one sinks until the stake it would need is above the maximum, and its hole is about $4,000 on average (roughly four hundred times the unit it was chasing). That is the martingale family's trade, frequent small gains paid for by one rare and heavy loss, reached by a system often described as a "cautious" one!
What the family really buys
Every positive progression buys the "inverse" of what the negative family sells, frequent small losses against a rare large win, at an unchanged price per dollar wagered (Oscar's Grind is the exception in shape, not in price), and the bill depends on the total wagered, not on the order of the stakes. We consider it a more comfortable shape for a player who wants a few peaks in an evening without the risk of one large hole.
A player who wants that bill fixed in advance will find the plainest instrument on the page on flat betting, where the stake never changes and an evening's cost is known before it starts. If you play a Paroli, our advice is to treat the three-win run as the entertainment you are paying for, never as a "method", and to stop at the amount you set aside (a budget fixed before the first spin), whatever the last spin did.
Three more casinos we list
Three operators, each with what we could read of its licence, for a reader who wants to compare before choosing.
Cabaret Club
Licence not confirmedThe site states a Malta Gaming Authority licence without naming the licensee or the number
18+ · Sponsored link
Cazimbo
Licence not confirmedNo readable page of the site names a licence or an operator (16 October 2026)
18+ · Sponsored link
Dachbet
Licence not confirmedAn Anjouan licence of Next Global Era Limited is reported by a third-party listing, not confirmed at source
18+ · Sponsored link
Questions
What is the Paroli system?
A positive progression that lets a winning stake ride up to three times in a row and then banks seven units; on a European wheel the three wins arrive about once in nine attempts, and the other attempts each lose one unit.
Is the reverse martingale the same as the anti-D'Alembert?
No: the reverse martingale doubles after each win, while the anti-D'Alembert adds one unit after a win and removes one after a loss, so after five wins in a row the first shows 31 units of profit and the second 15.
Are positive progressions safer than negative ones?
Each attempt risks less, but every dollar wagered still pays the wheel its 2.70 per cent, and the losses arrive as many small ones instead of one large one.
How does the 1-3-2-6 system work?
It stakes 1, 3, 2 and 6 units on four bets in a row and restarts after any loss; three cycles in four end with a small loss, and the full ladder of twelve units arrives about once in eighteen cycles.
Is Oscar's Grind a low-risk system?
It raises only after wins, but because each series stays open until one unit is won, about one series in two hundred (at $10 a unit, under a $500 limit) sinks into a hole of around $4,000.
