Compound multiplier
For period returns r1 through rn:
Ending bankroll = starting bankroll * (1 + r1) * ... * (1 + rn)
A deterministic illustration of 1% growth for ten periods from GBP 1,000 is:
GBP 1,000 * 1.01^10 = GBP 1,104.62 after rounding
This assumes the return occurs in every period. It is not evidence that a betting method can produce 1% repeatedly.
Equal gain and loss do not cancel
A 2% gain followed by a 2% loss gives:
1.02 * 0.98 = 0.9996
The ending bankroll is 99.96% of the start, a 0.04% decline. After a 50% loss, a 100% gain is required to return to the starting amount because 0.50 * 2.00 = 1.00.
The unequal recovery requirement follows directly from multiplication. It is arithmetic, not a claim that one observed return path will continue.
Betting path versus investment projection
| Projection input | Required evidence |
|---|---|
| Constant period return | A justified reason the return is stable, not selected from a good period |
| Percentage stake | Exact bankroll snapshot and settlement sequence |
| Win probability | Later-sample calibration and current data validity |
| Payoff | Accepted price, costs, and settlement rules |
| Withdrawal | Date and amount removed from the compounding base |
Expected value and variance are separate; OpenStax provides the probability-weighted definitions. A mean return does not describe the order of outcomes.
Staking does not change the sign of the edge
Percentage or Kelly-style staking changes exposure as bankroll changes. It cannot make an adverse price favourable. Kelly's original framework maximizes expected log growth under known inputs; it does not validate a forecast or guarantee a smooth path.
Drawdown-constrained research makes the risk objective explicit (Busseti, Ryu and Boyd). A compound chart that contains no uncertainty, drawdown, or losing path is not a risk analysis.
Reproducible simulation
Publish the starting bankroll, stake rule, complete outcome distribution, dependence assumptions, horizon, withdrawals, limits, random seed, and every simulated percentile. Compare with no-bet and flat-stake baselines. Never show only the median or best path.
Show the distribution, not one curve
For a simulation, publish at least the 5th, 25th, 50th, 75th, and 95th percentile ending bankrolls, the probability of crossing declared drawdown levels, and the proportion of paths unable to place a minimum stake. Include the no-bet path and a fixed-stake baseline. One median line hides both left-tail failure and rare right-tail outcomes.
Stress the inputs by lowering win probabilities, worsening accepted prices, increasing commission, and adding correlated losses. Keep the random seed and code version. If projected growth disappears under a modest adverse input, the honest conclusion is model sensitivity. Do not convert the best simulated path or average of surviving paths into an annual return claim.
Next step
Use Percentage Staking for the next part of this topic.
Continue learning
- Next guide: Emotional Staking
- Related guide: Flat Staking Strategy
Assumptions and limitations
The 1% and 2% paths are deterministic arithmetic examples. Real betting returns are uncertain, irregular, and affected by price availability, stake limits, commission, and model drift. Compounding can magnify loss and does not make gambling an income plan.
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