Prop-firm rule math

Two traders take the same evaluation: reach +$3,000 before losing $2,000. Both have the same modest edge — 52% winners at 1:1 reward-to-risk. One risks $100 a trade, the other $200 so they can “pass faster.” Under a static drawdown limit, the first passes about 81% of the time and the second about 64%. Under a trailing drawdown, those numbers fall to roughly 56% and 40%. Same edge, same rules — the outcome is set by arithmetic most traders never do.

A proprietary trading evaluation (bài đánh giá quỹ prop) is a rule set: hit a profit target before you break a loss limit, while obeying side rules. Rules vary between firms and change often. Everything below uses generic, illustrative numbers to teach the mechanics. It does not describe any particular firm. Always read the current rulebook of the firm you are actually trading with.

Chart first: static vs trailing drawdown

 Equity
   +3,000 ┤·····························  PROFIT TARGET
          │                 /\
          │        /\      /  \
          │       /  \    /    \__        ← trailing floor follows the peak up
        0 ┼──/\──/────\──/───────\─────
          │ /  \/      \/
   −2,000 ┤━━━━━━━━━━━━━━━━━━━━━━━━━━━━━  STATIC floor: never moves
          │
          └──────────────────────────── time
   Trailing floor = (highest equity so far) − 2,000
   → after a +1,500 run-up, the floor is at −500, not −2,000

• Static drawdown (sụt giảm cố định): the floor stays at a fixed level below the starting balance.
• Trailing drawdown (sụt giảm trượt theo đỉnh): the floor follows your highest equity upward, so every profit you give back counts against you. Firms differ on the details: some trail on closed-trade balance and others on intraday unrealised equity (much stricter), and some stop trailing once the floor reaches the starting balance.
• Daily loss limit (giới hạn lỗ trong ngày): a smaller cap per session. Breaking it ends the day, or sometimes the account.
• Consistency rule (quy tắc ổn định): a cap on how much of your total profit may come from your single best day, for example “no day may exceed X% of total profit.” The effect is that one lucky outsized day cannot pass the evaluation alone, and you need more trading days.

The math: gambler’s ruin

Model each trade as a step: win +1 unit with probability p, lose −1 unit with probability q = 1 − p. One unit = your risk per trade (1R) in dollars. You start a units above the floor and b units below the target. The classic gambler’s ruin (bài toán phá sản của con bạc) result gives the probability of hitting the target first:

             1 − (q/p)^a
P(pass) = ─────────────────        (for p ≠ 0.5)
           1 − (q/p)^(a + b)

P(pass) = a / (a + b)              (for p = 0.5, no edge)

With a $2,000 limit, a $3,000 target and $100 risk per trade: a = 20, b = 30.

This is a simplification. Real trades are not exactly ±1R, win rates drift and trades are not independent. But it captures the structure, and it is easy to check with a simulation.

Worked example: same edge, different rules and sizes

Static limit, exact formula. Trailing limit (closed-trade peak, never stops trailing), estimated by Monte Carlo simulation with 40,000 paths, so trailing figures are accurate to about ±1 percentage point:

Read the rows one at a time.

No edge (p = 0.5). Under a static limit the pass probability is a/(a+b) = 2,000/5,000 = 40%, whatever your size. Risking more or less does not help a trader with no edge; it only changes how fast the coin flip resolves. The trailing limit drops it to about 23%, because every give-back after a run-up counts toward the floor.

Small edge, small size (p = 0.52, $100). 81% static. The edge gets 50+ trades to show up, and the law of large numbers works for you.

Same edge, double size ($200). a and b are halved, so there are fewer trades for the edge to beat variance: 64% static, about 40% trailing. “Sizing up to pass faster” is the single most expensive decision in this table.

Larger edge (p = 0.55). 98% static, about 91% trailing. A genuine edge absorbs even the trailing rule, which is why the real work is M10.01–M10.07: knowing whether your edge is real before you pay for evaluations.

Two more effects the table leaves out:

• Costs (M10.02) lower the effective win rate. A 52% gross scalper can be a 48% net trader, and then every size fails more often than it passes.
• Daily loss limits truncate bad days. That can help a disciplined trader (it forces a stop) but it also cuts off the recovery path inside a day. A consistency rule forces the profit to be spread over several days, which adds trades and so helps a real edge and hurts a lucky one.

Common mistake: Treating an evaluation fee as a lottery ticket and buying repeated attempts at high size. With no edge, each attempt passes at best a/(a+b) of the time under a static limit, and much less under a trailing one. Repeated attempts don’t change the odds of each attempt. They only add up the fees. If your measured net edge is near zero, the fix is research, not size.

Recap:

• Static floors stay put. Trailing floors follow equity peaks, so the same edge passes noticeably less often under a trailing rule.
• Gambler’s ruin: P(pass) = (1 − (q/p)^a) / (1 − (q/p)^(a+b)), with a and b measured in units of risk per trade. With no edge it is a/(a+b), whatever the size.
• With a real edge, smaller risk per trade means more trades before a barrier and a higher pass probability. Doubling size can cut it sharply.
• Rules differ between firms and change. Use generic math to understand the structure, then read the current rulebook.

Quiz: An evaluation has a $2,500 static drawdown limit and a $2,500 profit target. You win 50% of trades at 1:1 risking $125 per trade. What is your pass probability? Would risking $250 per trade change it? Answer: a = b = 20 units, p = 0.5, so P(pass) = a/(a+b) = 50%. At $250 per trade, a = b = 10 and P(pass) is still 50%. Explanation: with no edge, a static-limit evaluation is a fair coin weighted only by the distances to the two barriers. Size changes how fast it resolves, not who wins. Only a real edge (p > 0.5 after costs) makes smaller size better.

Further reading:

• Any standard probability textbook’s chapter on random walks / gambler’s ruin. The formula above is the classic two-barrier result.
• M10.02 (costs in ticks): convert your gross win rate into a net win rate before using the formula.
• The current rulebook of any evaluation you consider. Read the exact definitions of drawdown (closed vs intraday equity, whether it stops trailing), daily limits and consistency.

Prerequisite: M10.02 Costs & slippage in ticks, M6.09 (position sizing) · Next: back to M7.11 (weekly review) with a validated method · Connects to: M7.12 (the psychology of size), M10.06 (lockbox discipline)

Educational content only — not financial advice. Futures trading involves substantial risk of loss. Prop-firm rules shown are generic illustrations, not any firm’s actual terms.