Hold the stake.
Loss
1Loss
Loss
Loss
The stake stays constant after wins and losses.
The Strategy Laboratory
Roulette
Strategies
Martingale doubles after losses. Fibonacci follows a sequence. Paroli raises stakes after wins. Each changes how much is put at risk, without changing the chance of winning a spin.
Compare the same spinsFlat Hold the stakeAfter losses Increase exposureAfter wins Press, then reset
The staking rule changes. The wheel’s probabilities do not.
01 / Decisions and outcomes
The stake changes.
The chance stays.
A staking system determines the size of the next bet. On a fair single-zero wheel, Red wins on 18 of 37 outcomes. No progression improves that probability or guarantees a profit.
A unit is the chosen base amount. An eight-unit stake is eight times that amount. A winning even-money wager returns the stake plus an equal amount of profit. Net result is total returned minus total wagered.
18 Red18 Black0
18/3748.65% chance of Red
19/37 chance of a loss, including zero
After three losses, the next stake is
8 unitsMartingale doubles three times: 1, 2, 4, then 8.
Respond to losses.
Loss
Loss
Loss
Next wager
Martingale doubles after a loss. Other negative progressions use different rules.
Respond to wins.
Win
Win
Win
Reset
A three-win Paroli cycle raises the stake after each win, then resets.
02 / Martingale
A one-unit recovery.
A growing commitment.
Start at one. Double after a loss, reset after a win. A successful recovery earns one unit only when the required wager is both affordable and permitted.
The winning wager
8 units on Red- Spin 11Loss
- Spin 22Loss
- Spin 34Loss
- Spin 48Win
Sixteen returned.
One unit ahead.
8stake returned
7earlier losses recovered
1net profit
The return covers the eight-unit winning stake and the seven units lost on the first three spins. Only one unit is profit.
Total wagered15
Total returned16
+1 net. Eight units had to be put at risk to complete this recovery.
Default limits: 127 demo units available; maximum stake 64. A required 128-unit bet is not placed when either limit blocks it.
03 / Alternative progressions
Different rules.
Different exposure.
Fibonacci and D’Alembert increase stakes differently from Martingale after losses. Neither improves the chance of winning the next spin.
Fibonacci
After a loss, move one position forward. After a win, move two back, stopping at the first 1. The sequence begins 1, 1, 2, 3, 5, 8. Moving back does not necessarily recover earlier losses.
01102103204305506807130821
Required wager · not yet placed
1 unit
Position 1 · the first one-unit wager.
Three losses lead to a three-unit Fibonacci wager. Martingale would require eight units after the same losses.
D’Alembert
Add one.
Remove one.
Each loss adds one base unit to the next wager. A win removes one, down to a minimum of one.
One unit to begin.
1unit required
From a one-unit stake, both D’Alembert and Martingale require two units after one loss. Further losses increase their stakes at different rates.
127 units available · no bets placed.
04 / Labouchère
Add the first
and last numbers.
Begin with 1, 2, 3, 4. Bet the first plus the last. A win cancels both ends; a loss adds the amount wagered to the list.
1234
1 + 4
=5next wagerFirst and last entries determine the five-unit wager.
127 units available · net 0
The initial list sums to 10, the target profit if the cycle clears. A single remaining entry is wagered once. A growing list can reach bankroll or table limits before it clears.
05 / Paroli · Reverse Martingale
Press a win.
Then reset.
In a capped three-win cycle, double after each win: 1, 2, 4. Reset after any loss or after the third consecutive win.
Three wins produce seven units of net profit. A loss before the third win ends that cycle at −1 unit net, including any earlier winnings. A streak never predicts the next spin.
+7 net from three wins
Win 1+1
Win 2+2
Win 3+4
Cycle completeBack to 1
06 / The Strategy Laboratory
One sequence.
Different exposure.
Keep the outcomes. Change the staking rule. Follow the wager that has just settled, the amount it returned and the next stake it requires.
European single zero · Red · base stake 1 · bankroll 127 · table maximum 64 · all amounts in demo units
Same spins for every strategy
Spins 1–4 of 4
0 spins completed · 0 bets placed
MartingaleDouble after a loss; reset after a win.
One-unit chips at the same depth scale.Ready to wager
1unit on Red
Next result
?
Awaiting the first spin
No wager settled.
Next decision
1unit · not placed
Ready for the first spin.
Earlier stakes · amounts in units
No completed wagersTotal wagered0
Bankroll left127
Session net result0
Total returned0
Flat Betting on the same spins: no wagers yet.
A stopped strategy places no more bets. Later outcomes remain in the shared history. All totals include every wager placed, including those outside the visible history.
07 / Exposure and its price
Seven losses.
Two very different bills.
Under the same seven non-red results, Flat Betting loses seven units. Martingale loses 127 and cannot fund its next wager. A different sequence can favour a different system; neither changes the house edge.
Start with 127 units.
Each position below represents one unit of the initial bankroll.120 left
7 lost
Next stake: 1
0 left
127 lost
Next stake: 128
128required next
not wagered
128 > 0 available bankroll
128 > 64 table maximum
Either boundary prevents the next bet. The seven completed losses remain 127; an unavailable wager adds no further loss.
Per unit wagered
18/37 × 1
− 19/37 × 1
= −1/37
Every unit wagered carries the same house edge.
Each standard European Red wager has an expected net loss of approximately 2.70% of its stake. Earlier results do not change the probabilities of the next independent spin.
Across many sessions with a fixed spin limit, expected loss is 1/37 of the expected total amount wagered. Systems that lead to more betting can therefore have larger expected losses in units. An individual session can finish above or below that average.
Understand roulette odds and RTPLimiting stakes or setting a stopping point limits exposure, but does not improve the return per unit wagered. Wheel and settlement rules can change the edge.
2.70%European · standard5.26%American · ordinary bets1.35%La Partage · eligible even-money bets
Compare roulette types and zero rules08 / The rulebook
The rules behind
each wager.
A reset rule determines when a progression starts again. A bankroll or table limit determines whether the next required wager can be placed.
Constant stakes
Flat BettingAfter a lossSame base stakeAfter a winSame base stake+
- Reset or stop
- Keep the base stake until the session ends or the next bet is unaffordable.
- Exposure
- Exposure grows with the number of wagers. A fixed stake does not recover previous losses automatically.
Four ways to respond to a loss
MartingaleAfter a lossDouble the stakeAfter a winReset to one unit+
- Reset or stop
- Stop before a required bet exceeds funds or the table maximum.
- Exposure
- A long losing run creates rapidly increasing stakes. Recovery depends on being able to place the next wager.
FibonacciAfter a lossForward one positionAfter a winBack two positions+
- Loss / win rules
- Move forward one position in 1, 1, 2, 3, 5, 8… Move back two positions, without passing the first 1.
- Reset or stop
- Remain at the start when a win would move farther back.
- Exposure
- Growth is slower than doubling but can still reach the financial limits. Other versions use different reset conventions.
D’AlembertAfter a lossAdd one unitAfter a winRemove one unit+
- Loss / win rules
- Add one base unit. Subtract one base unit, never below the base.
- Reset or stop
- Continue at the base after a win at one unit.
- Exposure
- Smaller increases can still exhaust the bankroll or reach the table limit. Red remains less likely to win than to lose, including zero.
LabouchèreAfter a lossAppend the lost stakeAfter a winCancel both ends+
- Loss / win rules
- Append the wager just lost to the list. Cancel the first and last entries; cancel a sole entry once.
- Reset or stop
- The cycle ends when the list is empty. Financial limits can stop it earlier.
- Exposure
- The initial entries add up to the cycle’s target profit. Clearing the list would achieve that target, but bankroll or table limits can stop the cycle first.
A capped winning run
Paroli / Reverse MartingaleAfter a lossReset to one unitAfter a winDouble, then cap at three wins+
- Reset or stop
- Reset after the third consecutive win.
- Exposure
- A loss can give back earlier gains in the cycle. A winning run does not make another win more likely.
What a progression cannot promise
“Red is due.”
Six Black outcomes leave the next independent spin’s chance of Red at 18/37. Hot and cold counts describe the past; they do not predict a fair wheel’s next result.
“Doubling guarantees recovery.”
The required winning wager must fit the available bankroll and table limit. An unplaced bet cannot recover anything.
“More winning sessions means a better system.”
Frequent small profits can coexist with occasional substantial losses. Session-win frequency alone ignores the size of each gain, loss and stake.
The next spin is independent.
The wheel doesn’t
follow a strategy.
The player does.
A staking rule determines the next amount put at risk. It cannot change which pockets win or the probabilities of a fair, independent spin.