| Single-attempt assumption | Five shared outcomes | Five independent outcomes |
|---|---|---|
| 10% | 10.0% | 41.0% |
| 15% | 15.0% | 55.6% |
| 20% | 20.0% | 67.2% |
Mathematical sensitivity only. Neither column estimates your strategy.
The multiplication people usually use
If one attempt has probability p and every attempt is independent, the probability of at least one pass across n attempts is 1 - (1 - p)^n.
That equation is valid for the independence assumption. The mistake is treating separate account IDs, entries, or random seeds as proof that the outcomes are independent.
Independent case: P(any pass) = 1 - (1 - p)^nWhat the shared-outcome case shows
At the other boundary, all accounts effectively succeed or fail together. In that shared-outcome case, adding accounts does not change the pass probability: it remains p.
Real outcomes can sit between, outside, or change over time depending on position overlap and execution. The two cases are sensitivity checks, not a guaranteed range.
Shared-outcome case: P(any pass) = pA better account decision
Start with the single-attempt assumption you can defend. Show both dependence cases. Then inspect whether the same strategy, instrument, session and risk logic make simultaneous failure likely.
- Do not call account count diversification.
- Do not present the independence result as a forecast.
- Use actual trade-history replay before replacing an assumption with a QK estimate.