A 60% win rate at 1:1 or 40% at 1:2: same expectancy, very different nights

[Fairman]

A 60% win rate at 1:1 or 40% at 1:2: same expectancy, very different nights

Both of these systems make 0.2R per trade before costs. 60% winners at 1R, or 40% winners at 2R. The expectancy sums are 0.6 minus 0.4 for the first and 0.8 minus 0.6 for the second. On paper it's a coin toss between them.

I ran each through 20,000 simulated runs of 200 independent trades to see what living with them looks like. The median final result is the same, around +40R. The path isn't.

Longest losing streak in 200 trades, median: 5 for the 60% system, 9 for the 40% one. At the 90th percentile it's 7 against 12.
Deepest drawdown from a peak, median: 7R against 12R.
Chance of a drawdown of 10R or more at some point: about 20% against about 80%.
Bottom 10% of final results: +22R against +13R.

At 1% risk per trade, 10R is a 10% drawdown. That's the entire limit on plenty of funded accounts, and more than four runs in five of the lower hit rate system would have a stretch that deep. Same edge, same average, completely different demands on the account rules and on the person running it.

The simulation is deliberately simple: fixed risk, no costs, independent trades. Treat the numbers as the shape of the thing, not a forecast.

[FXS Prop Desk]

Fairman, same expectancy and different nights is a nice way to put it. The 40 percent system will have longer losing streaks, and that changes how hard it is to follow. Simulating a thousand trades for each and looking at the longest losing streak and maximum drawdown makes the difference concrete before choosing which system suits the trader.

[Amanhasnoname]

I traded something close to the 40 percent version for about a year, a breakout system with targets around twice the stop. The numbers in your simulation match how it felt. I had a stretch of eleven losses in a row in my second month, and even though I knew that was possible, it took a lot of effort to keep taking signals.

What made me change was the prop account. A drawdown of nine or ten R was quite normal for that system, and at one percent risk that put me right against the limit on the evaluations I was attempting. I could cut risk to half a percent, but then the profit target took a very long time to reach.

In the end I moved the target closer, to around 1.3R, and the win rate rose to just over half. The expectancy dropped a little on paper, but the drawdowns became shallow enough that I could actually follow the rules, and real results improved because of that.

[Fairman]

Halve the risk on the 40% system and the picture improves a lot. At 0.5% per trade the median drawdown is about 6% and the one in ten bad case is about 10%, which is close to what the 60% system gives at a full 1% (about 7% and 11%). So a trader who finds a setup with 40% winners and 2R targets should probably size it at around half of what they'd use on a 60% one. The expectancy in R doesn't care about size, but the equity curve does. The cost is that the money made also halves: +40R at 0.5% is roughly +20%, against +40% for the 60% system at 1%. For the 60% system, risk of 0.5% would give a median drawdown of about 3.5%, a bad case of about 5.5% and roughly +20% over the 200 trades: a quiet ride, but a slow one.

[Fairman]

The streak numbers come from simple chaining. A 40% win rate means each trade loses 60% of the time, so five losses in a row starting from any given trade has a probability of 0.6 to the fifth power, 7.8%. For the 60% system it's 0.4 to the fifth, 1.0%. Over 200 trades you'll see several five loss runs on the 40% system, and it would be normal not to see even one on the 60% system. If you plan a break after a set number of losses in a row, that number should depend on which system you run. Stepping away after 5 losses is a sensible tripwire for one system and an ordinary Tuesday for the other.

[Fairman]

Costs hit the two systems the same per trade. With a 6 pip stop and 0.8 pip of spread and commission, each trade gives up 0.13R in both cases, so 0.2R before costs becomes about 0.07R after. The 1:1 system probably trades more often, though, since a 6 pip target arrives sooner than a 12 pip one. Twice as many trades at 0.07R isn't the same as the same number of trades. If trade counts differ, compare R per day or per hour rather than per trade. With only 0.07R left, a 0.2 pip rise in the average cost takes away 0.03R, which is nearly half of it.

[Fairman]

Which of the two is easier to believe? Against the random baseline, 1:1 targets get hit 50% of the time and 1:2 targets 33%. A 60% rate at 1:1 is 10 points above baseline. A 40% rate at 1:2 is nearly 7 points above it. In relative terms the first asks for a bigger edge in entry quality. Measuring your own entries against the baseline for each shape is a better test than comparing win rates across shapes. A trader at 52% on a 1:1 shape and one at 36% on a 1:2 shape are each only a couple of points above chance, even though 52% sounds like the better number.