🪙 Chance Lab
A question every beginner asks: can money management alone make you win? Doubling after a loss, raising after a win, following a progression… The lab puts it to the test with a coin (or a roulette wheel) and millions of tosses. The answer is no, and the interesting part is seeing why.
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The law that does not break
If you decide how much to bet before seeing the result, every bet has the same expectation as the game, whether you bet 1 or 1,000. With a fair coin, the mean of any system is the starting capital (in mathematics, the optional stopping theorem). What money management does change is the shape of the result.
No system moves the mean. Some win a little almost always and sometimes lose a lot; others, the opposite.
On average you lose the edge × everything you wager. Raising the bet after a loss only means betting more… and losing more.
Size decides everything: well sized (Kelly or a fraction of it) it multiplies the edge; betting too much ruins you even when you are right.
The game and the twelve betting systems
You choose the probability of winning and the payout (or a ready-made game: fair coin, European or American roulette, a coin with an edge, «trading-like» with 40 % winners and a 2:1 payout), the capital, the minimum bet, the table limit (what stops the martingale in a casino), the tosses, the series (up to one million) and, if you like, stopping when up or down a given %.
Flat, Martingale (with a cap on doublings), Double after loss, Double after win and Paroli (anti-martingale).
D'Alembert, Fibonacci, Labouchère and Oscar's Grind.
Fixed fraction, Kelly and half Kelly. With no edge, Kelly does not bet: the optimal bet is zero.
With your trades and your own rule
In «Where results come from» choose The trades of a strategy: one from the Portfolio (it is re-tested) or a CSV with the P&L of each trade. Each toss draws one of its trades at random. The unit is the average loss: a +1.8 trade wins 1.8 times what was risked. At the top you see your edge per unit risked and the strategy's Kelly. It is the real question: what does each betting system do with your edge?
Your own rule: what to do with the bet after a win and after a loss (same, back to 1, multiply or add units) and a cap in units beyond which it goes back to 1. «After a loss ×2, after a win back to 1, cap 16» is exactly the 4-doubling martingale.
What you see
In what % of series each system finishes first and last. The surprise: the one that wins most often is usually also the one that loses most often. It is not better: it is the one that swings most.
Mean (with its ± error), median, percentiles, % ending up, ruin, drawdowns, total wagered and the actual edge (result ÷ wagered), which always comes out as the game's. The mean is only coloured when it departs from the capital more than chance explains.
The central 90 % and 50 % bands, the median and the mean as a dashed line: with a fair coin it does not move, whatever the system does.
The histogram of final capital. With a 10-doubling martingale, about 6 in 10 series end up piled a little above… and almost 3 in 10 are ruined.
The first series, toss by toss: the curves of every system being drawn and the table with each one's result, bet and balance. When paused, the table holds every toss played: click it and step through with ↑ ↓, Page Up/Down and Home/End; the toss highlighted in orange is also marked on the chart with a vertical line. The header stays fixed as you scroll.
Each betting system is a point: to the right, a deeper average drawdown from the peak; higher up, a better median (the typical outcome); its size, how often it finishes first. The desirable spot would be top left, and with a fair coin nobody is there: the systems that «lift» the typical outcome (martingale, Fibonacci, Oscar's Grind) pay for it with much deeper drawdowns. With an edge, on the other hand, Kelly and half Kelly rise to the top.
The capital histogram, animated toss by toss. All series leave the starting capital together and, over time, each system takes its shape: flat betting slowly widens like a bell; the martingale splits in two, one pile moving to the right and another at zero that keeps growing. ▶ to play (1×, 2× or 4×), the slider to jump to any moment and the legend to choose which systems to show.
Repeat the experiment X times, each with other luck: for each betting system, the mean and the 90 % range of each figure (finishes first, ends up, ruin…). If two ranges overlap, you cannot say which is better. Vary the tosses (for example 10; 100; 1000; 10000): how each figure changes the longer you play. With a 10-doubling martingale, ruin goes from 0 % with 10 tosses to 29 % with 1,000 and 74 % with 10,000. Each «Run» uses a new seed; tick «fixed» to repeat exactly the same luck.
AniQuant can be tried free for 14 days, with every module and no card. If you have the book, 30.