probability
Probability is very difficult to understand. It is easy to calculate wrong, and the mathematics for it are above most peoples understanding. I myself keep picking the wrong answers if I just rely on what I read and what would seem to be correct.
I like to verify things programmatically. It is usually easier to understand the logic in a test than in mathematical equations. It does not prove anything, but it gives us an easy way of seeing some numbers. And it is much easier to understand numbers than equations.
This repo will try to include a lot of typical probability questions an average person could think of.
Lotto
This includes different lotto probability checks
Two adjacent numbers
How often does a draw of lotto numbers include two adjacent numbers? It will change with the numbers you have to pick from, and how many numbers you must pick, but here is a list from doing 10 millions draw each time
Answer LottoAdjacentNumber
For 34 numbers where you pick 7 (standard norwegian lotto)
| run | percentage |
|---|---|
| 1 | 77 |
| 2 | 78 |
| 3 | 78 |
| 4 | 78 |
| 5 | 77 |
For 48 numbers where you pick 6 (standard norwegian viking lotto)
| run | percentage |
|---|---|
| 1 | 50 |
| 2 | 50 |
| 3 | 50 |
| 4 | 50 |
| 5 | 50 |
Picking same numbers vs picking different numbers
Is it smart to pick the same numbers each week, or should you pick different numbers? What is best?
Answer LottoSameNumbers
Each run tests 10000 rounds of first winner
| run | same | different |
|---|---|---|
| 1 | 5036 | 4964 |
| 2 | 4978 | 5022 |
I guess it does not really matter what you do, there is no real difference.
Picking same numbers with adjacent vs picking different numbers
Ok, we saw that it is very probable that you will find two numbers adjacent in a winning draw. So perhaps you then think it is smart to pick two numbers adjacent when you set up your numbers? Well, let us test
Answer LottoAdjacentSameNumbers
Each run test 1000 rounds of first winner, same as picking same numbers, but we're making sure we have at least two adjacent numbers in our same numbers. The different numbers are just random.
| run | same | different |
|---|---|---|
| 1 | 475 | 525 |
| 2 | 495 | 505 |
| 3 | 497 | 503 |
| 4 | 526 | 474 |