1-3-2-6: a positive progression riding a winning wave.
Most systems chase losses. 1-3-2-6 does the opposite: it raises the bet only after a win — in the order 1, 3, 2 and 6 units — and returns to the start after every loss. Four wins in a row mean +12 units; a loss at the end of the cycle leaves you at zero. Here you can take the system apart step by step and test it on simulated spins.
Test 1-3-2-6 on your own bankroll
Set the bankroll, the value of a unit and the number of spins. The simulator shows how the bankroll develops, the rhythm of the 1-3-2-6 bets and — above all — which step the cycles most often die on.
Bankroll and unit
Bet and wheel
All the even chances share the same mathematics — the choice only changes the flavour of the experience. The zero (and on an American wheel the double zero too) always loses.
A win advances you along the 1-3-2-6 sequence; a loss — and a completed cycle — returns you to 1 unit. Every run uses a fresh random sequence of spins.
Where the cycles died
Bankroll over time
A slow, calm decline with the occasional +12 step upward — no drama, but the direction is set by the house edge.
What happened in the simulation: Click "Run the simulation" and you will get a short, plain-language explanation of the result here.
Four steps — and what each one risks
The order 1-3-2-6 is not accidental. The 2-unit step tucks profit away, so the second half of the cycle is played largely with money already won.
The balance of every possible ending
The only two scenarios where you lose your own money are defeats at the first two steps. But those are by far the most common — which is why the average of the whole cycle comes out negative.
How deep into the cycle you get
Every further step requires a win on an even chance (48.65%). The odds fall geometrically — only one cycle in eighteen reaches the big +12.
Why 1-3-2-6 rather than, say, 1-2-4-8?
The sequence is designed so that after two wins the cycle can no longer end at a loss: steps 1 and 3 leave you +4, of which you stake only 2 — the rest is “locked”. Let the bet grow geometrically instead (1-2-4-8) and a loss at the last step would cost you −1 rather than ±0, and the system would lose its main psychological advantage: the sense of playing the second half of the cycle with the casino’s money. It does not change the maths, though — the average stays at −2.70% of every unit staked.
What does 1-3-2-6 really cost you per hour?
This calculator turns the sequence into money: the average cost of one cycle, the number of cycles an hour at your pace of play — and from that an honest hourly rate.
Enter a unit value and a pace of play. The result shows the average cost of an hour, the cost of one cycle and the chance of completing the whole sequence.
Is 1-3-2-6 a good roulette system?
The calmest progression you will meet in roulette — and yet it ends the same way as all the others. Here is the whole picture, maths and practice, in one place.
What is the 1-3-2-6 system?
1-3-2-6 is a betting strategy for even-money bets — red/black, odd/even, 1–18/19–36. It belongs to the so-called positive progressions: the size of the bet changes only after a win, never after a loss. It began as a modification of the older 1-3-2-4 system and spread mainly in baccarat and roulette, where bets paying 1:1 are common.
The cycle has four steps. You start with one unit; after each win you move to the next number in the sequence — 3, then 2, then 6 units. Whenever you lose, you return to the start. A completed cycle of four wins yields +12 units and begins again from one.
How 1-3-2-6 works exactly
The heart of it is the balance of each ending. Lose at the very first step and it costs you a single unit. A loss at the second step means −2 (you won 1, lost 3). At the third step it is different: after wins of +1 and +3 you stake only 2 units, so even a loss leaves you at +2. And a loss at the last, six-unit step ends exactly at zero — everything you had won up to that point you have staked back.
That is precisely the design trick of the sequence: from the third step on you can no longer lose your own money. Most players read that as “playing with the casino’s money” — and it is a pleasant feeling. But the mathematics knows no “casino money”: units once won are yours, and losing them is a loss like any other.
The charm (and the trap) of a positive progression
Negative progressions like Martingale raise the bet while you are losing — which is why they can go bust during a single long streak. 1-3-2-6 is the exact opposite: after a loss you bet the minimum, so a run of losses costs you only a unit per spin. No explosion, no dramatic ruin. That is a real and measurable advantage — in the simulator above you will see the risk of exhausting your bankroll is a fraction of Martingale’s.
The trap lies elsewhere: the system depends on four wins in a row, and on an even chance those arrive in only 5.6% of attempts. The other 94% of cycles end sooner — most often at the very first step — and each one carves a little off the bankroll on average. So 1-3-2-6 does not lose dramatically but persistently: about a tenth of a unit every cycle.
What exactly does the house edge mean for 1-3-2-6?
Every bet on an even chance has an expected value of −2.70% — the zero loses, which is why you win 18 numbers out of 37, not out of 36. The 1-3-2-6 system assembles four such bets into a cycle, and because the average of a sum is the sum of the averages, the whole cycle also comes to exactly −2.70% of the money staked. On an American wheel with its double zero it is −5.26%.
So the sequence does not change, by even a tenth of a percent, how much of every dollar staked you hand the casino over time. It changes only the distribution: instead of an even drip you get frequent small minuses and the occasional +12 jump. For the experience that is a difference; for your wallet after a thousand spins it is not.
Variants: 1-3-2-4 and friends
The older sibling 1-3-2-4 ends the cycle with four units instead of six. Completing it yields only +10, but a loss at the last step leaves you at +2 rather than ±0 — after two wins the cycle can never end worse than in profit. It is a more defensive compromise: a lower peak, a softer floor, the same negative average.
You will occasionally meet a two-step paroli (1-3) or a more aggressive 1-3-2-6-12. The rule is always the same: the longer the sequence, the rarer the completion and the more the result depends on one long streak. The length of the sequence is merely a slider between “often a little” and “rarely a lot” — it does not move the average.
The biggest risks and limits
The main risk of 1-3-2-6 is paradoxically its safety: the system feels so harmless that players stay with it for a long time. But “slowly” does not mean “a little” — at 60 spins an hour you get through about 33 cycles, and each one costs something on average. Over an evening those inconspicuous tenths of a unit add up to the same percentage you would have carried away from any other bet.
The second risk is psychological: the sense of playing “with the casino’s money” from the third step on tempts you to raise your unit after a good evening. So you scale up at exactly the moment chance happened to be kind — and the average collects it back from the larger bets. Table limits, by contrast, are no problem: the sequence peaks at 6 units, which you will only reach with an extremely large unit.
How to read the bankroll chart
The 1-3-2-6 chart is a jagged, gently falling line with occasional larger steps upward — those are completed +12 cycles. No steep plunges: the worst spin costs 6 units and the most common loss is a single unit. Switch the simulator to “Bet size” and you will see the characteristic rhythm: a long band of ones broken by short 3-2-6 staircases that rarely arrive complete.
The “Where the cycles died” panel below the statistics is the quickest reality check: over half the cycles die at the very first step and only a handful reach the closing six. These numbers — not the final bankroll of one run — are what tell you how the system really behaves.
How to use 1-3-2-6 sensibly in the tester
One run is one random history. In the Roulette system tester 1-3-2-6 comes preloaded — run it over 100 or 500 independent runs and compare it with Martingale on exactly the same sequence of spins. You will see a textbook contrast: Martingale carries a high risk of ruin and occasional explosions, while 1-3-2-6 almost never busts but its median falls just as relentlessly.
Watch three figures above all: the share of runs in profit, the median result and the maximum bet. With 1-3-2-6 the maximum bet will always be 6 units — that is its honesty. The other two numbers will tell you that calm and profit are two different things.
The verdict: is 1-3-2-6 usable?
If you are going to play roulette with a system at all, 1-3-2-6 is among the most sensible choices: a firm structure, a natural stop after every loss, no escalation of bets, and a maximum cycle loss of just two units of your own money. As a way of giving your play order and making it last longer for the same money, it works well.
As a route to profit it does not work — and unlike the sellers of “guaranteed systems”, its authors never claimed it did. The expected value is −2.70% of every unit staked and no ordering of bets changes it. The greatest value of 1-3-2-6 is that it demonstrates this truth gracefully: no drama, no ruin — just quiet, persistent mathematics.
The biggest misconceptions about the 1-3-2-6 system
A positive progression invites the feeling that you have outwitted risk. Here are the most common myths, explained so a beginner can follow them.
The moment the croupier pays you, it is your property — losing it is a loss like any other. “Casino money” is an accounting trick inside your head, not in the mathematics.
The sum of four bets with a negative average has a negative average. 1-3-2-6 only rearranges when you bet more — the long-term loss stays at −2.70% of the money staked.
On an even chance the odds of four consecutive wins are 5.6%. Over half the cycles end at the very first step — and those are what pay the bill for the occasional +12.
1-3-2-6 really does almost never cause ruin — the bets do not escalate. But the bankroll drips away steadily: a tenth of a unit per cycle on average, hour after hour.
1-3-2-6 vs. other roulette systems
Positive and negative progressions are mirror-image approaches to the same problem — and neither solves it. The only difference is how you lose.
| System | Risk | Principle | Best for |
|---|---|---|---|
| 1-3-2-6 | Low | The positive 1-3-2-6 progression after wins | A calmer game riding a winning wave |
| Parlay | Medium | The win stays in play (let it ride) | Short runs after a win |
| Reverse Labouchere | High | The line grows on a win and is crossed off on a loss | Hunting streaks with a capped loss |
| Martingale | Very high | Doubling the bet after a loss | Understanding the risk of a progression |
| Fibonacci | High | A progression following the Fibonacci sequence | A slower progression after a loss |
| d'Alembert | Medium | +1 unit after a loss, −1 after a win | The gentlest progression |
| Labouchere | High | A cancellation line; the bet is first + last | More advanced players and experiments |
| James Bond | Low to medium | A flat 20-unit ticket on 25 numbers | Broad coverage with no progression |
| Holy Grail | High | 18 distinct numbers with a progression | Covering half the wheel |
| Bally | Very high | 24 numbers with a 12–36–108–324 progression | Blanket bets with a harsh progression |
The name of a system takes you to its page with an interactive test — the current system is highlighted. Want to compare several systems on the exact same sequence of spins? Use the Roulette system tester.
Common questions about the 1-3-2-6 system
Is the 1-3-2-6 system profitable?
Not in the long run. Every bet in the cycle has an expected value of −2.70%, and so does their sum. But the system is among the safest — the bets do not grow after a loss, so you lose slowly and in a controlled way.
How exactly is 1-3-2-6 played?
You bet 1 unit on an even chance. After a win you continue with 3, then 2, then 6 units. After any loss — and also after completing a whole cycle — you return to 1 unit.
What does a completed cycle yield?
+12 units (wins of 1 + 3 + 2 + 6). At a $50 unit that is $600. But the chance of completing it is only about 5.6% — one cycle in eighteen.
How much can I lose in one cycle?
At most 2 units of your own money (a loss at the second step: +1 −3). A loss at the third step ends at +2, at the fourth at ±0. That is exactly why the system feels so safe.
Why does the two come after the three in the sequence?
So that you tuck the profit away after two wins. After +1 and +3 you stake only 2 units — even if you lose, you walk away with +2. The sequence is designed so the second half of the cycle can no longer go into the red.
Is 1-3-2-6 better than Martingale?
Safer, definitely: the maximum bet is 6 units, there is no escalation and the risk of ruin is minimal. More profitable, no — both have the same long-term return of −2.70%. Only the shape of the risk differs.
What bankroll do I need for 1-3-2-6?
Surprisingly little: 100 units will cover even a long run of bad luck, because the worst cycle costs 2 units of your own money. So a sensible bankroll is 100–200× the unit value.
Does 1-3-2-6 work on American roulette?
It works the same, just more expensively: the double zero cuts the chance of winning to 18/38 and the average loss doubles to −5.26% of the stake. If at all, play a European or French wheel.
What is the 1-3-2-4 system?
A more defensive variant: the last step is 4 units instead of 6. A completed cycle yields +10, but a loss at the last step ends at +2 rather than ±0 — after two wins you can never finish at a loss.
Does 1-3-2-6 change roulette’s house edge?
No. European roulette has a house edge of 2.70% and American 5.26% — and no ordering of bets changes that. The system changes only the distribution of results over time, not their average.
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First understand the principle, then work out the risk — and test longer scenarios over thousands of spins.