The Capybara Time Warp: Classic Betting Systems and Their Real Maths
Published June 04, 2026 • 5 min read • By Alex Rivera • Updated 2 October 2026
Betting systems are old. The Martingale is usually traced to 18th-century France, the d'Alembert carries the name of the French mathematician Jean le Rond d'Alembert, and the Labouchère is named after the 19th-century British politician Henry Labouchère. They keep coming back because they promise order in a random game. This article works through five classic systems with simple, labelled maths and explains the one thing none of them can do: change the house edge.
Assumptions used in every example below: European roulette, even-money bets (red/black). Probability of winning 18/37 = 48.65%, of losing 19/37 = 51.35%. House edge 2.70% (American roulette with a double zero: 5.26%). Base unit = 1, bankroll = 100 units, table maximum = 100 units. These are illustrative numbers, not data from any player or casino.
Martingale: double after every loss
Start with 1 unit; after a loss, double; after a win, go back to 1. Each completed cycle wins 1 unit. The bets grow fast: 1, 2, 4, 8, 16, 32, 64. Six losses in a row cost 1 + 2 + 4 + 8 + 16 + 32 = 63 units, and the seventh bet of 64 would need a total of 127 units - more than the 100-unit bankroll. The probability of six straight losses on an even-money bet is (19/37)^6, about 1.8%, or roughly once every 55 cycles. In other words, you win 1 unit about 54 times and then lose 63 units once. The table limit stops the system too: the eighth bet (128 units) would exceed the 100-unit maximum.
d'Alembert: add one after a loss, remove one after a win
Start at 1 unit; after a loss add 1 unit, after a win subtract 1 (never below 1). Example: lose 1, lose 2, win 3, lose 2, win 3 - staked 11, result +1 unit. The progression is slow, so it feels safe, but a long losing run still pushes stakes up step by step, and the expected loss is still 2.70% of everything you stake.
Labouchère: the cancellation line
Write a line, for example 1-2-3 (target profit 6 units). Bet the sum of the first and last numbers (1 + 3 = 4). A win crosses both off; a loss adds the lost amount to the end of the line. Example: bet 4, lose (line 1-2-3-4); bet 5, lose (1-2-3-4-5); bet 6, win (2-3-4); bet 6, win (3); bet 3, win - line cleared, profit 6 units after staking 24. Each loss lengthens the line, so a bad run creates a long list of large bets that may hit the bankroll or the table limit before the line clears.
Fibonacci: follow the sequence
Stakes follow 1, 1, 2, 3, 5, 8, 13, 21, 34, 55: one step forward after a loss, two steps back after a win. It grows more slowly than the Martingale, but after ten losses the next stake is 89 units and the total already lost is 143 units - beyond our 100-unit bankroll.
Paroli: double after a win
The Paroli is the reverse: double after a win, return to 1 after a loss, and bank the profit after three wins in a row (1, 2, 4 = +7 units). The chance of three straight wins is (18/37)^3, about 11.5%. Most cycles end with a loss of 1 unit. Risk is limited, but the edge is unchanged: the house still keeps 2.70% of every unit staked on average.
Summary
| System | Stake changes after | Main risk | Changes the house edge? |
|---|---|---|---|
| Martingale | Loss (double) | Rare but large loss; table limit | No |
| d'Alembert | Loss (+1) / win (-1) | Slow climb in long losing runs | No |
| Labouchère | Loss (line grows) | Line and stakes balloon | No |
| Fibonacci | Loss (next number) | Bankroll exhausted on long runs | No |
| Paroli | Win (double) | Frequent small losses | No |
The reason is simple: expected loss = house edge x total amount staked. A system only rearranges when you bet more or less; each individual bet still has the same negative expectation. Progressions that raise stakes after losses usually increase the total staked, and with it the expected loss in money terms.
Systems and CapibaraBet bonus terms
If you play with a casino bonus, the terms add another limit. According to clause 12 of CapibaraBet's terms (checked 2 October 2026), only bets up to 5 EUR count towards wagering progress. With a 1 EUR base unit, a Martingale reaches 8 EUR on its fourth step, so the larger bets in a progression would not count towards the x30 wagering of the casino welcome package, and the Slots Boost promotion caps bets at 5 USD. The daily cashback also excludes table games. The operator does not publish a full game-contribution table in its general terms, so check each promotion's page before playing roulette with bonus money. A summary is on our bonuses page.
What to do instead
- Choose the lowest edge available: single-zero roulette (2.70%) rather than double-zero (5.26%).
- Use flat stakes sized to your budget; see our bankroll management guide.
- Decide a session loss limit and time limit before you start.
- Treat any system as a way to organise entertainment, not as a way to win. For sports bettors, our article on disciplined betting habits covers record keeping and staking.
More definitions are in the glossary, and general advice is in our tips.
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Alex Rivera is the byline for capibarabet.net articles on odds, bankroll management and classic betting systems.
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