The Expectation – Your Holy Grail For Success
Anyone who knows me knows that I only dogmatically follow very few rules.
To pay attention to the expected value is definitely necessary.
Because why should I play when the numbers speak against me?
I would like to sharpen the reader’s eye for this really simple ratio, because I believe in success and also for financial freedom , an eye for it is indispensable.
- How can you calculate the expected value? A simple explanation
- There is also a non-monetary expectation
- We do not have to know everything very well
- A disadvantage of the expected value
- Why am I still dogmatic about the expected value?
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How can you calculate the expected value? A simple explanation
For those of you who do not know exactly what an expectation value is and how to calculate it, here’s a simple example:
Imagine we both throw a coin.
With 50% probability head comes and with 50% probability number appears.
But we do not just throw it, we bet for cold hard money. We agree that if you win I pay you 10 €. But if I win, I get 10 € from you.
We know that in 50% of the cases you win and in 50% of the cases I win. Therefore, we can calculate the average profit per game :
0,50 * (+ 10 €) + 0,50 * (- 10 €) = 0 €
That is, if we repeat our game, the coin toss, very often, neither you nor I will go home in the long run with profit but also not with loss.
The expected value is therefore € 0 for both of us.
Of course it can happen in between times that one of us wins a couple of times in a row. It may even be that one wins more often than the other.
But the more often we throw our coin, the sooner we will approach the expected value on average. This follows from the law of large numbers and can be graphically represented as follows:
Of course, the curve can have virtually any shape, but they all have one thing in common: sooner or later, they will strive against their expected value:
Here comes the first two of the four most important insights in the whole article:
- That the above curves are against their expectation value is like a law of nature. Nobody can shake it.
- Every game is mathematically worth the same. The 1st just as much as the 10,000.
Now let’s change the rules a bit:
Every time you win, I pay you 10 € but every time I win I only get 9 € from you.
Your expected value: 0.50 * (+ 10 €) + 0.50 * (- 9 €) = 0.50 €
My expected value: 0.50 * (+ 9 €) + 0.50 * (- 10 €) = -0.50 €
That means, on average, you win 50 cents every game. Great for you, bad for me. Because I lose on average every time 50 cents.
From your point of view, this can be interpreted graphically like this:
That means you have a systematic advantage here.
You may also be in the loss zone, but in the long run it is inevitable that you will make a profit. It may as well be that I have more money in between than before in this game. But in the long run the numbers work against me.
It is, as I said, like a law of nature.
This is followed by the second two most important findings in this article:
3. If we have a negative expectation, then we should avoid it at all costs.
4. If we have a positive expectation, then we should take it under all circumstances.
There is also a non-monetary expectation
An expected value does not always have to be related to money. There is also an emotional expectancy.
For example, before the first kiss of a newly in love couple. One of the two makes a start and risks something. What if it is too early? What if you are rejected? That would be emotionally a disappointment.
But what if it is the right time? It could be phenomenal. The beginning of something very big!
After more or less reasoning, he dares and lo and behold, it was fully worth it.
Here nothing else happened, as the unconscious attempt to form an expectation value. You look at the possibilities and try to figure out how likely they are.
If the result fits halfway, then we just do it.
The nice thing about emotional expectancy is that when we’re solidified in ourselves, it’s almost always positive.
Imagine, the above first kiss would not have been so good. Would the loss really have been that dramatic?
Sure, at first it’s probably uncomfortable, embarrassing and you think the shame will stay forever. But honestly, the earth keeps spinning, that’s life, and two days later that’s ticked off.
The loss is limited, so we should be more emotionally confident without much thought.
We do not have to know everything very well
Now, of course, one can argue that one does not always know the amount of profit or loss from the outset. Much more likely (attention Wortwitz) it is even that one does not know the probabilities of the individual events exactly.
I ask you:
Do we have to do that anyway?
In my opinion no. Often in life, we encounter situations in which it is crystal clear whether we face a positive or negative expectation.
Prime example study or further education:
We can not gauge exactly how much more salary we will receive from our investment in ourselves and not what the likelihood is.
But we suspect that it is well worth it, because the average salary has been proven to be higher in many studies. This can not be translated into anything other than a positive expectation.
This approach may not be completely clean from a scientific point of view, but it is incredibly efficient.
There are many such situations in life and I even claim that each one translates into a monetary or emotional expectation. Really everyone.
Tip: A help for expectations in everyday life is to ask “What can I lose?”. If the answer is nothing or almost nothing, then the expected value is very likely to be positive. Then just do it and do not hesitate.
A disadvantage of the expected value
Now I’ve been raving about the concept in very high tones all the time. Time so, even a point of criticism a little closer.
Take a look at the two following decision trees. Let’s pretend that it’s two stocks. Both are worth 100 € today and in one year there are two ways they can have developed.
Again, for the sake of simplicity, both options are equally probable, 50/50.
Expected value: 0.50 * (110-100) + 0.50 * (110-100) = 10 €
Expected value: 0.50 * (150-100) + 0.50 * (70-100) = 10 €
Both stocks have the same expected value and are equivalent in their view.
Nevertheless, every reasonable person would choose the first game. Because what the expected value ignores is the variance or volatility of the possibilities.
With stock A we certainly get the expected value, with stock B it may be that we get a lot more but also that we make a loss.
The expected value does not matter. He just tells you, “That’s okay, just do it. And immediately. “
Why am I still dogmatic about the expected value?
Even if one can practice criticism from an academic point of view, from a practical point of view, the expected value is nevertheless unbeatable.
He is simple, he can often be touched at least over the thumb and he is simply incredibly efficient.
Look at it like this:
The answer of meaningfulness of things of life and money concentrates in a single number.
If you succeed in ranking as many games with positive expectation in your life as one after the other, then success is, in any case, a mathematical certainty.
With the concept of Expectation, we have an incredibly powerful tool to rank and evaluate our decisions. Be it financially or emotionally.
It allows us to gauge what we do and, more importantly, what we should do better.
Because no one escapes this law and I do not know how you see it, but I do not want to mess with the power of numbers.
What do you think about the expected value? Do you like the philosophy behind it? Let me know now!