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Quitting the day at +3R: expected profit drops from 0.75R to 0.62R, bad days unchanged

A common rule is to stop trading once you're up a set amount, say 3R, so the day can't give it back. Here is what that rule does with exact numbers.

Assume up to six setups a day, each winning 45% of the time for 1.5R and losing 1R, with independent outcomes. Each trade has an expectancy of 0.45 x 1.5 minus 0.55 = 0.125R, so six trades give 0.75R, which at $100 per R is $75 a day.

Now add the rule: after any trade, if the day total is 3R or more, stop. The expected day falls to 0.62R, which is $62. The average number of trades falls from 6.0 to 4.99. So the rule gives up 0.126R a day, about 17% of the expected profit, because on the days you quit, the trades you skip each carry the same 0.125R expectation.

What it doesn't change is the bad days. The chance of finishing a day at minus 3.5R or worse is 16.4% with the rule and 16.4% without it. Those days never reach plus 3R, so the rule never triggers on them. Days that end at plus 3R or more go from 25.5% to 36.5%, since the rule locks in days that would have given the gain back. The best day is capped at plus 4R instead of plus 9R.

So the rule trades some upside for steadiness on the good days only. If the goal is protecting the account, a limit on the loss side does the work.

Hi Fairman,

from my own experience i do not go out after i have good day. In bad day yeah, i have trashold in my mind, once i will have loss over 10 percent that day i end.

Because i found out, that for several days a year it works for me every single idea and im able to make really great outcome, so in good days i do not have any limit.
I will make as much as is possible.

Does the size of the cap matter? With the same odds, I ran exact numbers for quitting at three levels. Quit at +1.5R, which is as soon as the day total reaches 1.5R: expected day 0.42R, 3.36 trades on average, and the chance of a day at minus 3.5R or worse falls to 14.1%. Quit at +3R: 0.62R and 16.4%. Quit at +4.5R: 0.71R and 16.4%. With no cap it's 0.75R and 16.4%. A lower cap gives away more profit and shaves only a little off the bad days, because most of the bad days come from a run of early losses.

In monthly terms the gap is easy to see. Twenty trading days at 0.75R is 15R, which is 15% of the account at 1% risk. At 0.62R it's 12.5R, or 12.5%. So the +3R rule costs 2.5 percentage points a month on average in this model. If the rule keeps you from handing back profit on days when you tend to overtrade, it can earn that back, but that is a claim about your behaviour, and the math above assumes your later trades are just as good as the earlier ones.

You can test whether the rule suits you from your own journal. Take the days when you reached +3R or more early, and compare the R of the trades taken after that point with your average. If the post-target trades average clearly below your normal figure, say less than half of it over 40 or more trades, there is a case for the rule, since later trades really are weaker for you. If they average about the same, the rule is just giving up expected profit. Fewer than 40 trades in the second group can't tell you much, as the standard deviation is over 1R.

There's also a version aimed at prop firm targets. If the evaluation needs 8% and you risk 1%, the +3R rule means a 3% day ends the session. That ends a good session early, so reaching 8% takes more days, and it leaves the edge per trade unchanged. A profit cap can't raise the pass rate, since each trade still has the same odds. I'd treat it as a time management choice, and check the challenge's time limit and minimum trading days before using it. Many firms also set a profit target and a time window, so the cap and the calendar have to fit together.