Evening folks!
What is dependent and what is not is very interesting reading. Let me take you through a theory that you might not always be aware of this evening. Generally speaking , there are two ways we humans can make a mistake about independence; you may sometimes think that two outcomes are independent but they are not, or the other way around that you think two outcomes are not independent (dependent) when in fact they are. Believe me I have been there several times, making tons of mistakes in this area, annoying so to speak…
Let me give you an example; when people invest in stocks and funds on the assumption that they are completely independent, they are not. One of the lessons we learned from the recent economic crisis is that a vast range of assets – US stocks, real estate, funds/bonds etc. – are probabilistically dependent because of the highly international nature of modern finance and the complicated ways in which mortgages for instance are assembled and sold.
On the other hand, thinking that two outcomes are dependent when in fact they are not occurs – it happened to me (and probably you, sorry). I thought for once that I could predict the outcome of a roulette wheel based on its previous outcomes. What is truer is that this is not possible… these roulette wheels are set up in such a way as to make the outcomes completely independent. They have made it this way because it is a good and smart way for the casino host to make sure that people are not able to predict the outcomes. Nevertheless, many people, including me, believe we could predict the outcome of a roulette game. For instance, just make a quick search as I did on the internet for something like “roulette tips”. Then you will find a long list of webpages encouraging you to try different outcomes as probabilistically dependent, when in fact they are not (tip of the day).
For me, in the roulette example, the ball had fallen on black so many times in a row, it was more likely that the ball would fall on red sometime soon. So to derive this belief, I started to push money onto the table, betting on red. Oh, by the way, do you believe it fall on red? Yes, the ball fall on red. But not until the 17th spin. Until then each spin saw a greater number of people pushing their chips over to red. While the people who put money on the 17th spin won money, a lot more people lost their money due to the long streak of black. Personally I went out at the 10th spin. Imagine what he on 16th made of a loss? Its much… In my example I doubled the money on every spin so that if I lost on the first I would get it back on the second spin etc. The example below is based on doubling your money each spin.
Example in dollar terms:
1 = 10, 2 = 20, 3 = 40, 4 = 80, 5 = 160, 6 = 320, 7 = 640, 8 = 1280, 9 = 2560, 10 = 5120…
As you see the numbers become quite high already on the 10th try. To illustrate this I made a table that illustrate the gambler’s fallacy probability and the actual probability of the next spins on the roulette table, fascinating huh?
The above example is actually a theory, thinking that two outcomes are dependent when in fact they are not, is described as “The Gambler’s Fallacy”. More specifically it is thinking that a departure from the average behavior of some system will be corrected in the short term (Angner, E. 2016 - Behavioral Economics). People who think they will not have a dip in crypto since they have not experienced it yet are actually committing the gambler’s fallacy (It is possible that thinking you are always buying crypto at its peak makes it more likely you buy at the peak – that’s another story but you get it). Another example is when parents believe that on the fourth try, they will have a daughter because they already have three sons, they commit the gambler’s fallacy. The sex of the fourth child is causally unrelated to any preceding series of such events. Their chances of having a daughter on the fourth try are no better than 1 in 2 – that is, 50% chance.
I hope I made this theory somewhat clear to you and if you have any questions feel free to ask them. I bet that all of us at some points in life has been committing the gambler’s fallacy.
Comment below if you have committed a fallacy – I would love to hear them!
Cheers
-Olebulls