Worked solutionOne step at a time
Write the average profit of one trade
Call the win rate p. Each trade wins $100 with probability p or loses $1,200 with probability 1 − p. The average profit per trade is the probability-weighted sum.
Break even means that average is zero
Over many trades, total profit is close to the number of trades times this average. Zero average is the line between slowly winning and slowly losing.
Solve for p
Collect the p terms: 100 p + 1,200 p = 1,200. Another way to see it: one loss costs as much as twelve wins, so the strategy needs twelve wins for every loss, which is 12 trades out of every 13.
Answer: B, about 92.3%
The strategy in the reel wins 90.0% of its trades, 2.3 points short. Each point of win rate is worth $13 a trade, so it loses about $30 a trade: 0.9 · 100 − 0.1 · 1,200 = −$30. Over 500 trades that is about −$15,000, exactly what the typical trader ended with. A 90% win rate sounds high, but with a loss twelve times the win it is not high enough.
What the simulation showedThousands of small wins, a few cliffs
The reel runs 1,000 traders through 500 trades each (seed 4): +$100 with probability 0.9, −$1,200 otherwise.
- The measured win rate over all 500,000 trades was 90.0%, and the average profit was −$29.95 a trade, next to the expected −$30.
- The median trader ended at −$15,000, and 96% of traders ended below where they started.
- The best winning streak was 123 wins in a row, about +$12,300 that looks like skill. One loss wipes out 12 wins.
- The trader highlighted in amber was up $8,300 at the peak, then ended at −$15,000. That is not unusual: across all 1,000 traders, 92% were ahead at some point and still ended behind. A running P&L that climbs most days says nothing about its average.
Wrong answersWhy each one is tempting
| Pick | What went wrong |
|---|---|
| A · 91% | Assumed one more point of win rate closes a $30 gap. A point is worth $13 a trade (one more $100 win, one fewer $1,200 loss, per hundred trades), so it still loses $17 a trade. |
| C · 95% | Rounded up to a safe-looking number. At 95% it already makes +$35 a trade. |
| D · 99% | Felt that a loss twelve times the win needs near-perfection. It only needs 12 wins per loss. |
Follow-ups an interviewer asks nextTry these before opening them
Keep the 90% win rate. What is the biggest average loss that still breaks even?
0.9 · $100 = 0.1 · L, so L = $900. The real loss of $1,200 is $300 past that, which is the −$30 a trade: 0.1 · $300.
Why did the typical trader land so close to 500 × −$30?
Each trade's profit has a standard deviation of about $390, so over 500 trades the total has a spread of about $8,700 around −$15,000. The average drifts down by $30 a trade while the noise only grows with the square root of the number of trades.
Why do 92% of traders look good at some point?
With a 90% win rate the first loss arrives after about 10 trades on average, and long runs of wins are common: in 500 trades the longest run is typically about 40. Being briefly ahead is the normal path, not a sign of edge.
Where does this shape show up?
Any payoff with frequent small gains and rare large losses: selling insurance against rare events, or a sorting heuristic that is fast on 90% of inputs and very slow on the rest. Always weigh how often by how much.
