## Clueless thinking is dangerous

General discussion about draughts and draughts community
clp
Posts: 199
Joined: Tue Jul 10, 2018 14:28
Real name: Kees Pippel
Location: IJmuiden

### Clueless thinking is dangerous

Laplace's Rule of succession

What do Job van Goudoever, Alexander Shwartsman, Lucia de Berk and Pierre-Simon Laplace have in common?
• Job lost 8 out of 8 games in the National League. His new rating is set at 810.
• Alexander won 7 out of 7 games in Baarn open,
According to the KNDB calculation rules, the performance rating becomes: 2812 (Ownrating + 1200).
(https://toernooibase.kndb.nl/opvraag/de ... attab=r117)
• Lucia de Berk was involved in 5 deaths (1 in 324 million chance of murder), and was sentenced to life in prison, and then acquitted.
• Pierre-Simon Laplace (1749 - 1827), the inventor of, among other things, the 'Laplace transform', thought about logic and reality.
If we repeat an experiment that we know may result in a success or failure n times independently, and we get s successes and n-s failures, then the probability that the next repetition will succeed is equal to:
• (s +1) / (n + 2).
Laplace and contemporaries pondered such questions as: Is a unanimous verdict of three judges (3 - 0) more reliable than the verdict of one judge? Or: is a jury verdict of 9 - 3 more or less reliable than 3 - 0? His book, Essai philosophique sur les probabilités translated into English, is still a good read for the enthusiast.

After explaining the probability that the sun will rise tomorrow, he notes in chapter The General Principles of the Calculus of Probabilities, Seventh Principle):
But this number (the probability of the sun rising) is incomparably greater for him who, recognises in the totality of phenomena the main regulator of days and seasons, sees that nothing at this moment can stop its course.
My interpretation is: not only within the mathematical model should the calculations be done correctly, but what we should not forget is the fit of the model to reality. In the Lucia de Berk's trial, things went wrong on these two fronts.

Applying the rule of succession to Alexander(1564) and Job (no rating) gives:

Code: Select all

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Alexander, P = (7+1) / (7+2) = 88,88%, DP = +311 , Average Opponent rating = 1175, Rp = 1524.
Job,       P = (0+1) / (9+2) = 09,09%, DP = -381 , Average Opponent Rating = 1422, Rp = 1041.

Or assuming a linear relationship between ±score and rating, 100% = 800 ratingpoints:
Alexander, P = (7+1) / (7+2) = 88,88%, DP = (P - 50%) / 800 = +311 , Average Opponent rating = 1175, Rp = 1524.
Job,       P = (0+1) / (9+2) = 09,09%, DP = (P - 50%) / 800 = -327 , Average Opponent Rating = 1422, Rp = 1095.

``````
Above results look more realistic.