Let's properly understand "Expected Value," the absolute basic of...
Yumi🌸@samuraipips358
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Jun 26, 2025
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Let's properly understand "Expected Value," the absolute basic of probabilistic thinking 🧵
Probabilistic thinking is extremely important for traders.
This time, I will explain "Expected Value" in detail.
🧵1/5
Probabilistic thinking is extremely important for traders.
This time, I will explain "Expected Value" in detail.
🧵1/5
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2/5
To succeed in trading, probabilistic thinking is essential.
While short-term results are strongly influenced by randomness, long-term results converge according to the law of large numbers.
In other words, in a coin toss with a 50% probability for each side, you might get tails 7 times out of just 10 tosses, but as the number of tosses increases to 100, 1000, and more, the outcome will converge to the true probability of 50%.
What's important here are edge and sample size.
If you have a strategy with a "positive expected value", then it is important to increase the "sample size" under the same conditions through consistent action.
I often use the expression "positive expected value", and this is something that is calculated mathematically.
By understanding the concept of "Expected Value", you will realize that you are always earning a reward as long as you follow your rules.
You are earning a profit not only when you win, but "even when you are losing".
To succeed in trading, probabilistic thinking is essential.
While short-term results are strongly influenced by randomness, long-term results converge according to the law of large numbers.
In other words, in a coin toss with a 50% probability for each side, you might get tails 7 times out of just 10 tosses, but as the number of tosses increases to 100, 1000, and more, the outcome will converge to the true probability of 50%.
What's important here are edge and sample size.
If you have a strategy with a "positive expected value", then it is important to increase the "sample size" under the same conditions through consistent action.
I often use the expression "positive expected value", and this is something that is calculated mathematically.
By understanding the concept of "Expected Value", you will realize that you are always earning a reward as long as you follow your rules.
You are earning a profit not only when you win, but "even when you are losing".
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To put it simply, expected value is the average amount of profit per trade when that trade is repeated over and over.
For example, let's say you know from a sample size of 1000 backtests that your system's performance per trade is a 60% win rate, 2% profit, and 1% risk.
In this case, the expected value is calculated as: (Win Rate × Profit) - (Loss Rate × Loss).
Expected Value (%) = (Win Rate × Profit) - (Loss Rate × Loss)
= (0.6 × 2%) - (0.4 × 1%)
= 1.2% - 0.4%
= 0.8%
The expected value per trade (win or lose) is +0.8%.
In other words, if your account is $10,000, using this system according to the rules means you have earned $80, win or lose. (10000 × 0.008 = 80)
If your account grows to $12,000, you multiply this amount by 0.8%, so it means you have earned $96 (12000 × 0.008 = 96).
Even if the immediate result is a loss, as long as you follow the system's rules, you are always earning 0.8% on your capital.
This is what it means to accumulate expected value.
To put it simply, expected value is the average amount of profit per trade when that trade is repeated over and over.
For example, let's say you know from a sample size of 1000 backtests that your system's performance per trade is a 60% win rate, 2% profit, and 1% risk.
In this case, the expected value is calculated as: (Win Rate × Profit) - (Loss Rate × Loss).
Expected Value (%) = (Win Rate × Profit) - (Loss Rate × Loss)
= (0.6 × 2%) - (0.4 × 1%)
= 1.2% - 0.4%
= 0.8%
The expected value per trade (win or lose) is +0.8%.
In other words, if your account is $10,000, using this system according to the rules means you have earned $80, win or lose. (10000 × 0.008 = 80)
If your account grows to $12,000, you multiply this amount by 0.8%, so it means you have earned $96 (12000 × 0.008 = 96).
Even if the immediate result is a loss, as long as you follow the system's rules, you are always earning 0.8% on your capital.
This is what it means to accumulate expected value.
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Many traders dislike losses, holding the perception that "a loss is something that moves you further from success," but this is incorrect.
If a system has a "positive expected value", you can logically understand from the concept of expected value that "every single trade you take by following the rules" brings you one step closer to success.
Since probability works according to the law of large numbers, you get closer to success and contribute to stability with each trade you take, in the sense that the sample size increases by one whether you win or lose; and, from this perspective of expected value, as long as you have followed the rules, you are always receiving the invisible reward of expected value.
In this way, the losses generated by a system with a "positive expected value" function as a cost, and there is absolutely no need for you to try to avoid them.
Many traders dislike losses, holding the perception that "a loss is something that moves you further from success," but this is incorrect.
If a system has a "positive expected value", you can logically understand from the concept of expected value that "every single trade you take by following the rules" brings you one step closer to success.
Since probability works according to the law of large numbers, you get closer to success and contribute to stability with each trade you take, in the sense that the sample size increases by one whether you win or lose; and, from this perspective of expected value, as long as you have followed the rules, you are always receiving the invisible reward of expected value.
In this way, the losses generated by a system with a "positive expected value" function as a cost, and there is absolutely no need for you to try to avoid them.
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The fundamental premise for your capital to increase by repeatedly following the rules is that "the system must have a positive expected value".
Conversely, and it should be obvious, if the system does not have a positive expected value, your capital will decrease as you continue to follow the rules.
In other words, as long as you continue to follow the rules, it means that "the system is always functioning".
People often say, "The system worked because I won," or "It didn't work this time because I lost," but this is a mistake.
As long as you are following the rules, the system is always functioning; a system with a positive expected value is earning a positive expected value regardless of the outcome, and a system with a negative expected value is earning a negative expected value regardless of the outcome.
It is true that these are conceptual and not reflected in your account balance as actual money, but it is important to leverage this understanding well in order to remain consistent without being swayed by short-term results.
Thanks for reading!
If you enjoyed this thread, check out my books on trading.
E-book (free preview available)
payhip.com/YumiSakura
Paperback
【THE PATH TO SUCCESS IN TRADING】
a.co/d/fXmRhIa
【Trading Psychology】
a.co/d/d0QJMxK
Hope these insights help your trading journey😊
The fundamental premise for your capital to increase by repeatedly following the rules is that "the system must have a positive expected value".
Conversely, and it should be obvious, if the system does not have a positive expected value, your capital will decrease as you continue to follow the rules.
In other words, as long as you continue to follow the rules, it means that "the system is always functioning".
People often say, "The system worked because I won," or "It didn't work this time because I lost," but this is a mistake.
As long as you are following the rules, the system is always functioning; a system with a positive expected value is earning a positive expected value regardless of the outcome, and a system with a negative expected value is earning a negative expected value regardless of the outcome.
It is true that these are conceptual and not reflected in your account balance as actual money, but it is important to leverage this understanding well in order to remain consistent without being swayed by short-term results.
Thanks for reading!
If you enjoyed this thread, check out my books on trading.
E-book (free preview available)
payhip.com/YumiSakura
Paperback
【THE PATH TO SUCCESS IN TRADING】
a.co/d/fXmRhIa
【Trading Psychology】
a.co/d/d0QJMxK
Hope these insights help your trading journey😊