Expectancy is only half the story
Know the odds.
Survive the streaks.
A strategy can make money on paper and still put you out of the game. The question is whether your account, your loss limits, and your discipline can survive the path to that return.
Two profitable ideas. Two very different rides.
Win 25% of your trades at a 1:4 risk-to-reward ratio, or win 60% at 1:1. The first has slightly higher expectancy. The second has a higher profit factor and less than half the volatility per trade. In this model, the 60% system is the smoother one.
1R is the amount risked on a trade. A 1:4 trade risks 1R to make 4R.
The numbers behind the edge| Metric | 25% WR1:4 | 60% WR1:1 |
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| Win / loss | +4R / −1R | +1R / −1R |
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| Break-even win rate | 20% | 50% |
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| Expectancy per trade | +0.25R | +0.20R |
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| Profit factor | 1.33 | 1.50 |
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| Standard deviation per trade | 2.17R | 0.98R |
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| Profitable after 100 trades | 85.1% | 97.3% |
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Chance of a losing streak in 100 trades| At least | 25% WR1:4 | 60% WR1:1 |
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| 4 losses | >99.99% | 80.1% |
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| 5 losses | >99.99% | 45.9% |
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| 6 losses | 99.9% | 21.2% |
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| 7 losses | 99.0% | 8.9% |
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| 8 losses | 95.7% | 3.6% |
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| 10 losses | 79.0% | 0.58% |
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WR means win rate. Streak odds mean at least one run of that many consecutive losses anywhere in 100 trades, not just the next few trades.
10 straight losses−9.56%at 1% of current equity per trade
That same streak hurts both accounts equally at the same sizing. What changes is how often it shows up: about 79% versus 0.58% over 100 trades. Risk a fixed 1% of starting equity instead, and ten losses cost exactly 10%, before fees and slippage.
Where risk of ruin comes in.
Ruin means hitting the point where you can no longer continue. That might be an account loss limit, a margin requirement, or your own capital floor. Its probability depends on that boundary, position sizing, and the sequence of all trades. A mix of wins and losses can also breach a limit. The streak table alone cannot tell you your chance of ruin.
If both systems hold up equally well on unseen data, the 60% system offers a smoother path in this comparison. That extra 0.05R of expectancy comes with a lot more volatility. Size for the losses you may have to sit through, not just the return you hope to collect.
Model assumptions: 100 independent trades, unchanged win probabilities, exact stated payoffs, and no costs. Profitability uses a fixed cash value of 1R and means finishing above zero, not breaking even. These are calculated examples, not observed trading results. Real losses can cluster and edges can change. A smoother model does not prove a more robust strategy.
Method: binomial probabilities for final profit; exact run probabilities for losing streaks. References: NIST on the binomial distribution and CME on position sizing.