Step 5 · Cost
Expected cost to a passed account, break-even across the drawn series, and why multiple accounts do not raise the odds.
Expected cost
The calculation is the expected value across the required attempts. The number of attempts is the reciprocal of the pass probability; the cost per attempt is purchase price, subscription fees and resets, while activation is charged exactly once, on success.
Cost is not linear in p but in 1/p. For small p the range becomes strongly asymmetric, and a point estimate alone suggests a precision that 1,000 drawn paths do not support. That is why the range at plus/minus one standard error sits at the number.
The mean is correct; it is simply not the number that throws someone out of the plan. The number of attempts is geometrically distributed and therefore strongly right-skewed. What the path costs in the unfavourable case sits beside it.
When series stay open at the horizon
If series end neither passed nor breached and the model treats them as undecided, the attempt count is computed on the finished series. It thereby assumes the open ones would have split in the same ratio as the finished ones. That is an assumption, not a result, and the tile names its differing denominator in that case.
Price variants are products
A model can have several price variants. These are different products, not display options: the choice is made at purchase and cannot be changed afterwards. The analysis therefore does not promote any of them.
The refund is not deducted
At none of the firms examined is the advertised refund a contractual entitlement. It depends on a discretionary decision, sometimes additionally on an active request by the user, and several programmes do not offer it at all.
A display that quietly deducts it understates cost systematically. It is therefore shown separately.
Break-even
The calculation uses what arrives with the trader, i.e. after the profit split, against the full cost. Netting the withdrawal against cost puts break-even systematically too early.
The number applies to one funded account and not to a career. If it breaches, in reality a new evaluation and its cost follow, and the balance can drop below zero again. That cycle is not modelled. As long as it is missing, "permanently back in the money" is the same as "back in the money for the first time", because nothing is deducted after the account is passed.
Two scales meet here: cost is a mean across the required attempts, payouts are those of a single account. The spread is too small as a result.
Three numbers must not collapse into one and are kept apart: series without a funded account, funded accounts without break-even, and those with. Putting the first group into the denominator turns a rate over funded accounts into a rate over all series. Both are correct and answer different questions.
When it cannot succeed arithmetically
If the highest possible payout over the account's entire lifetime is below cost, no favourable path helps. That is something other than bad luck, and the view says so explicitly.
When the withdrawal ends the account
On some accounts the payout itself brings the balance to or below the threshold, without a single losing day. These cases are shown separately, because they would otherwise mix with the breached ones.
Multiple accounts at once
Running the same portfolio on several accounts at once gives you no additional attempts. The accounts move in lockstep and pass together or breach together. Cost multiplies, probability stays put.
The second line in the chart only applies if the accounts genuinely trade different things: different strategies, different entry times, different risk factors. The same portfolio on several accounts does not produce that.
Beside it sits how many accounts the firm permits at all. The number of evaluation accounts, of funded ones and the combined limit are shown separately, because the combined one is not the sum: one firm states 10 and 5 with a combined 10, i.e. stricter than 15.