Risk-reward and win rate: the maths of passing a challenge

Win rate and risk-reward are two sides of one equation. Neither means much on its own. This guide shows the maths that links them, how it applies to a prop firm challenge, and why risk per trade matters as much as your edge. All numbers are illustrative unless a firm is named.

Measuring trades in R

Traders measure results in R, where 1R is the amount you risk on a trade. Risk $500 and make $1,000, and that trade made 2R. Lose the full $500, and it lost 1R.

Measuring in R lets you compare trades of different sizes. It also turns a challenge into a simple count of steps.

The breakeven win rate

For a reward-to-risk ratio of R, the win rate you need to break even, before costs, is:

Breakeven win rate = 1 ÷ (1 + R)

• 1:1 gives 1 ÷ 2 = 50%.
• 1.5:1 gives 1 ÷ 2.5 = 40%.
• 2:1 gives 1 ÷ 3 = 33.3%.
• 3:1 gives 1 ÷ 4 = 25%.

A bigger target lowers the win rate you need. But targets further away get hit less often. The ratio and the win rate always move together.

Our risk-reward calculator works these out for any ratio.

Expectancy: the number that matters

Expectancy is your average result per trade, in R:

Expectancy = (win rate × average win in R) − (loss rate × 1R)

• 45% win rate at 2R: (0.45 × 2) − 0.55 = +0.35R per trade.
• 35% win rate at 2R: (0.35 × 2) − 0.65 = +0.05R per trade.
• 40% win rate at 1.5R: (0.40 × 1.5) − 0.60 = 0R, which is breakeven.
• 55% win rate at 1R: 0.55 − 0.45 = +0.10R per trade.

A 35% win rate and a 55% win rate can both be profitable. What matters is the combination.

Turning the profit target into R

Divide the target by your risk per trade to see how many R you need.

Take a 100K account with a 10% target, as on phase 1 of FTMO's 2-Step Challenge in our database. The target is $10,000.

• Risking 0.5% ($500) per trade, you need +20R of net profit.
• Risking 1% ($1,000) per trade, you need +10R.

Now divide by expectancy. At +0.35R per trade:

• At 0.5% risk: 20 ÷ 0.35 ≈ 57 trades on average.
• At 1% risk: 10 ÷ 0.35 ≈ 29 trades on average.

These are averages. Real results vary widely around them. Our profit target calculator shows the target and the pace needed for any account.

Turning loss limits into R

Do the same with the loss limits. Our database lists a 10% maximum loss and a 5% daily loss for FTMO's 2-Step.

• At 0.5% risk, it takes 20 full losses to breach the max loss and 10 in one day to breach the daily limit.
• At 1% risk, it takes 10 and 5.
• At 2% risk, it takes 5. On the daily limit, two losses use 4%, so a third losing trade would breach it before its stop is reached.

A futures example: our database lists Topstep's 50K Combine with a $3,000 target and a $2,000 end-of-day trailing max loss. At $200 risk per trade, the target is 15R and the drawdown is 10R. Because the limit trails, profit you give back after a new end-of-day high also reduces your room.

Losing streaks are normal

Even a profitable strategy has long losing runs. Assume a 45% win rate, so a 55% loss rate. The chance of at least one losing streak of a given length within 100 trades is roughly:

• 5 or more losses in a row: about 92%.
• 6 or more: about 73%.
• 7 or more: about 50%.
• 8 or more: about 31%.
• 10 or more: about 10%.

At a 35% win rate, the chance of 8 or more losses in a row within 100 trades rises to about 69%. Low-win-rate, high-R strategies need room for long streaks.

These figures assume independent trades with a fixed win rate. Real trading is messier, but the lesson holds. Plan for streaks longer than you expect.

Why risk per trade changes your odds

We modelled a simple challenge: a 10% target, a 10% static maximum loss, fixed risk per trade, no daily limit and no time limit. The pass rates below are outputs of that model, not predictions.

Strong edge: 45% win rate at 2R (+0.35R)

• 0.5% risk: over 99% pass, averaging about 58 trades.
• 1% risk: about 97% pass, averaging about 28 trades.
• 2% risk: about 84% pass, averaging about 11 trades.

Thin edge: 35% win rate at 2R (+0.05R)

• 0.5% risk: about 73% pass, averaging about 187 trades.
• 1% risk: about 61% pass, averaging about 50 trades.
• 2% risk: about 55% pass, averaging about 13 trades.

No edge: 40% win rate at 1.5R (0R)

• About 50% pass at every risk level. Smaller risk only makes the result take longer.

Two lessons follow. With a real edge, smaller risk raises your pass odds, at the cost of more trades. Without an edge, no sizing choice helps. Daily limits, time limits and consistency rules all cut these odds further.

Be honest about your edge, too. A 45% win rate measured over 30 trades could easily be 35% in reality. Over 30 trades, the normal range of chance alone is about 9 percentage points either way.

Costs shift the maths

Spreads and commissions shrink every win and enlarge every loss. Take $500 of risk, a 2R target and $50 of round-trip costs:

• A win nets $1,000 − $50 = $950.
• A loss costs $500 + $50 = $550.
• Your real ratio is $950 ÷ $550 ≈ 1.73R, not 2R.
• Breakeven rises from 33.3% to $550 ÷ ($950 + $550) ≈ 36.7%.

Short-term strategies with tight stops feel this most, because costs are a bigger share of each trade.

Putting it together

1. Estimate your win rate and average R from at least 100 logged trades, not one good week.
2. Calculate expectancy after costs. If it is near zero, fix the strategy before you buy a challenge.
3. Pick a risk per trade that survives a likely losing streak with room to spare.
4. Convert the target and loss limits into R.
5. Divide the target in R by your expectancy to estimate trades needed. Check that against any time limit or minimum days.

For sizing details, see our position sizing guide and how to pass a prop firm challenge.

Key takeaways

• Breakeven win rate = 1 ÷ (1 + R).
• Expectancy, not win rate alone, decides whether you can pass.
• Convert targets and limits into R to see the real task.
• With an edge, smaller risk usually improves pass odds. Without one, nothing does.

The figures in this guide are illustrative models, not predictions of your results. Confirm current challenge rules on each firm's official site before you buy. This guide is educational and not financial advice. Trading involves risk.