Statistics

Rules

Dice don't remember!

Statistical relevance: You need a certain number of occurrences before there is the possibility of a relation between events.

Even if there is a statistical relevance, it is not a proof. It just allows you to now try to find the reasons for the relation.

Misc

Physical objects we use for statistics

Whenever we talk about physical objects here, we mean perfect physical objects. A dice is a perfect dice with the exact same chance for each side. A coin is perfect, with exactly 50% chance for each side, there will be no corner cases like a coin standing or such things. If the coin is standing I'll shoot you, so you will never know. The coin is perfect!

Multiple times the same choice

If you throw a coin then you have 50% chance for each side each time. If you throw a coin two times there are four cases:

• heads / heads
• heads / tails
• tails / tails
• tails / heads

Nothing special here. Because the chances for each event are the same it is very easy. Each of the four cases has a 1/4 (25%) chance of happening.

What you have to keep in mind is that "Dice don't remember!". And coins don't remember too. So if you had 99 times "heads", the chance for the 100th throw to be heads is still 50%.

Monty Hall problem

The "Monty Hall problem" shows how pseudo science can influence people. Currently - 2023-08-29 - there is an entry in the Wikipedia which uses over 50000 (yes, that are 50 thousand) letters to tell us that the chance of a win between two equal choices is 1/3 instead of 1/2.

You find a lot of articles who tell you the same. You find books and web novels where the protagonist is the only one smart enough to understand that the solution is 1/3.

The problem is, this is wrong.

Remember the first rule? "Dice don't remember!" Gates don't remember too.

So, it is of NO relevance how many doors there were before or what the moderator thinks or says.

You have a situation with two equal chances which makes the chance to for a win 50% and the chance for a loss 50%.

Why? Because gates don't remember!

All that smart ass talk which goes around and around and seems so incredible smart, it is just wrong and common sense gives the right answer.