If you can do something where there is an expected return of more than zero in a very short amount of time, should you do it?
Say you wager $100 and we flip a coin; Heads you get $50 (50%), Tails you lose only $40 (40%).
The Expected Return is 50%*0,5 - 40%*0,5 = 5%
You could argue that someone who doesn't take this bet isn't being rational. You might say that people who don't take this bet suffer from a bias (stupidity) called Loss Aversion: https://en.wikipedia.org/wiki/Loss_aversion
On the other hand, if you are investing, that is trying to compound your wealth, you shouldn't take the bet. Recall: Warren Buffett's Rule Nr. 1 "Never Lose Money (Value)" (Rule Nr. 2 "Don't forget rule Nr. 1) https://www.fool.co.uk/investing/2015/12/17/what-does-warren-buffett-really-mean-by-never-lose-money/
If you lose money, then you have fewer resources with which to make money in the future. It has to do with time and probabilities. Charlie Munger said, "If you don't get this elementary, but mildly unnatural, mathematics of elementary probability into your repertoire, then you go through a long life like a one-legged man in an ass-kicking contest. You're giving a huge advantage to everybody else. One of the advantages of a fellow like Buffett, whom I've worked with all these years, is that he automatically thinks in terms of decision trees and the elementary math of permutations and combinations...."
Let's go back to wager: $100 and we flip a coin; Heads you get $50 (50%), Tails you lose only $40 (40%).
If you are trying to grow your wealth investing in a series of this wager would make you lose money!
Say you get Heads, Tails, Heads, Tails, Heads, Tails, Heads, Tails, Heads. You win 5 times and lose only 4 times. When you win you earn more than what you would have lost on that throw, but you lose money in the long run:
Your assets would be $100, $150, $90, $135, $81, $122, $73, $109, $66, $98
So it isn't that strange or wrong that people and investors, don't always want to take this bet! Researchers who say people are mistaken and acting illogically in cases like this might themselves be mistaken (The Bias Bias https://www.nowpublishers.com/article/Details/RBE-0092 )
On the other hand, if you can take this bet without your past result affecting how much you can wager now, then it makes sense to take the bet.
If you can bet $100 every-time and you get Heads, Tails, Heads, Tails, Heads, Tails, Heads, Tails, Heads like above, your cumulative winnings will be: $50x5 = $250 - $40x4 = $90 you're winning but not compounding your wealth.
Note:
Rule Number 1: Don't lose money (Value). To compound, you need to limit your loss of intrinsic Value. As an investor, you own things (companies, real estate, loans) that have the capacity to create cash flow. The important thing is to have that Value increase exponentially, short term decreases in the (stock) Price (aka quoted value) is not the same as losing Value. Buffett: “Unless you can watch your stock holdings decline by 50% (in Price) without becoming panic-stricken, you should not be in the stock market”.
"Any series of numbers multiplied by zero at the end is zero." Buffett
"You can't compound zero." Joel Greenblatt
Further reading: Ergodicity https://www.nature.com/articles/s41567-019-0732-0 , Kelly Formula
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