How many prop accounts must you burn to get paid?

1. Objective

The question this study answers:

Three secondary constraints shape the answer. The payout should arrive as soon as possible, the campaign must not stretch across an entire year, and risk per trade is a free variable to be chosen rather than a given. That last point matters more than it appears: risk sizing turns out to be the dominant lever in the entire model.

"Maximum payout" is defined here as the $2,000 first-payout cap on a funded 50K account. Reaching it once ends the campaign for accounting purposes, though the funded account survives and can continue producing income — so every ROI figure below is a floor, not a ceiling.

2. Simulation approach

Every number in this report comes from a trade-by-trade Monte Carlo, not a closed-form formula. Path-dependent rules — trailing drawdown, profitable-day counts, consistency limits — cannot be captured analytically, so each account is simulated tick by decision, and 250,000–400,000 accounts are run per configuration.

2.1 What one simulated account does

1. Buy a $50,000 evaluation. Balance starts at $50,000; the drawdown floor sits $2,000 below.
2. Trade 1–2 times per day. Each trade independently wins with probability 0.38 (+2.5R) or loses (−1R), where R is the chosen dollar risk.
3. Check the floor after every trade. If account equity touches the drawdown limit, the account is dead and a replacement is purchased.
4. Trail the floor at the end of each day. The floor rises to (closing balance − $2,000) and stops trailing permanently once it reaches the $50,000 starting balance. Intraday highs never move it — only end-of-day closes do.
5. Pass at +$3,000. The account converts to funded, balance resets, drawdown resets.
6. In the funded phase, reach +$2,000 and accumulate 5 profitable days of $200 or more, while satisfying the consistency rule, then withdraw $2,000. Campaign over.

2.2 Rules that turned out to matter

Touching the limit is a breach. An early version of the model treated the drawdown as violated only when equity fell strictly below the limit. At $500 risk against a $2,000 drawdown, four consecutive losses land exactly on the line and survived. Correcting this dropped challenge pass rates from 62% to 54% at that size — a material change, and a reminder that boundary conditions in prop-firm rules are not cosmetic.

The consistency rule sets your funded risk, and the arithmetic is exact. Most firms require your best single day to be no more than ~40% of total profit at payout. A single winner is +2.5R and a two-win day is +5R, so clearing the rule at a $2,000 payout balance requires balance ≥ 12.5R, i.e. R ≤ $160. This is precisely why $150 funded risk works (P = 0.917) and $175 does not (P = 0.874) — at $175 one good day locks you out until you grind to $2,187.

The monthly fee stops once funded. Funded-phase calendar time is therefore free under every fee model, which is why optimal funded risk is low across the board: sprint the metered phase, crawl the free one.

2.3 Validation

The engine was checked against results that can be derived independently before any conclusions were drawn:

• Per-trade edge and variance match theory to 4 decimal places (+0.3300R, σ = 1.6989R).
• With trailing disabled, simulated pass rates track the closed-form barrier-crossing formula for a drifting random walk. The residual gap is the expected discretisation effect and narrows correctly as risk per trade falls.
• A trailing floor is strictly harder than a fixed floor, and the consistency rule never increases a pass rate — both verified with common random numbers.

2.4 Three fee models

Prop firms bill in structurally different ways, and this is not a detail — it inverts the optimal strategy. All three are modelled at $87.50 per unit for a like-for-like comparison:

• Recurring — $87.50 every month an account remains in the challenge.
• One-time — $87.50 once per account, however long it lives.
• Hybrid — $87.50 once, plus a $130 activation fee charged each time you pass.

3. Headline findings

4. Risk sizing: the core trade-off

Risk per trade is the only real dial, and it trades accounts against time. Risking small means you almost never blow up but grind for months; risking large resolves accounts in weeks but kills many of them.

The two-account configuration is strictly dominated. It is slower (4.4 months versus 2.8) and more expensive ($257 versus $163) than the four-account configuration. Under recurring fees, calendar time is the real cost, not account count: a burned account dies in about two weeks for a single month's fee, while a timid account accrues three months of fees before resolving either way. Buying more cheap accounts and resolving them quickly is the cheaper path.

The other structural result is that challenge risk and funded risk should not be equal. The challenge is a sprint with no consistency rule — size up. The funded phase is a metered-free grind with a consistency rule — size down. The optimal ratio is roughly 3:1.

5. Fee structure inverts the answer

This is the single largest driver in the study, larger than risk sizing itself.

5.1 One-time fee — $87.50 per account

Here every account costs the same regardless of lifespan, so time is free and only account count matters. E[fees] = avg # accounts × $87.50, exactly.

Note the tail: worst-case spend is $175, so even the unluckiest 1% of runs return over 1,000%. One-time pricing is dramatically tighter in the tail, because a bad run costs you time rather than money.

5.2 Recurring fee — $87.50 per month

Here the multiplier is months billed, not accounts. In the top row you buy about 1.44 accounts but are billed for 1.65 months, because some accounts survive into a second billing cycle. That gap is the recurring-fee penalty, and it is what pays for sizing up.

5.3 Hybrid — one-time fee plus activation

An activation fee is charged every time you pass, making it an unavoidable toll on success. A $130 activation costs more than every evaluation fee combined and roughly halves ROI without changing optimal sizing at all. The "activations paid" figure creeps above 1.0 on aggressive rows — that is passing the challenge, paying $130, blowing the funded account, and paying again.

5.4 The break-even price

The best recurring configuration costs $147 expected. A one-time firm therefore wins if its per-account price sits below:

In short: a one-time-fee firm under roughly $115–130 for a 50K evaluation beats an $87.50/month firm. Above that, monthly wins, because you will usually pass or die inside one or two billing cycles anyway.

6. The real risk is the win rate

Everything above assumes the 38% win rate is genuine and stable. Break-even for a 1:2.5 strategy is 28.57% — less cushion than it appears.

6.1 How confident can you be in 38%?

A measured win rate is an estimate with error bars that depend entirely on sample size:

7. Stress test

The base model is deliberately not the most pessimistic one. A stress variant adds tick-by-tick equity checking (a winning trade that first moves half a unit against you can still breach the floor), $8 per trade in commissions and slippage, and a $600 buffer required above the payout threshold.

ROI degrades from roughly 1,100% to roughly 930%, and the account budget rises by two. The edge is robust to execution friction — it is not robust to the win rate being wrong. That asymmetry is the practical takeaway: spend your effort validating the strategy, not optimising the sizing.

8. Recommendation

9. Limitations

• Trades are assumed independent and identically distributed. Real strategies cluster — losing streaks in unfavourable regimes are longer than a coin model predicts, so true tail risk is worse than shown.
• Execution is assumed identical across every account. The 99% figure is model confidence, not life confidence. It presumes no tilt after a burn, no rule drift, no fatigue across a months-long campaign.
• Firm rules vary. The 40% consistency rule, the 5 profitable days, the $200 daily minimum and the drawdown lock point are modelled on common terms but should be checked against your firm's actual contract.
• Promotional pricing is ignored. Monthly firms discount heavily and often; an effective rate of $40–50 materially strengthens the recurring case and lowers the break-even price toward $70–80.
• Resets are not modelled. If a failed account can be reset more cheaply than replaced, a recurring firm starts to behave economically like a one-time firm.
• The $2,000 is not terminal. The funded account survives its first payout, so realised returns should exceed every figure here.

10. Glossary