Better Diagnostic Tactics with Math!
- If you want the cheapest path to a certain diagnosis, for your second color, diagnose the color unrelated to the two possible revealed layers.
- If you test the same color twice in a row and the result is twice inconclusive, there is a 86% chance the disease hides in the related second other color.
- Even if you only test a single color you can already correctly guess 63% of the times.
- Counterintuitive results at first due to relation to Monty Hall problem.
- Diagnosis+ potion inefficient for finding conclusive diagnosive.
Most of you know that a foolproof diagnosis needs 3 potions (or potion levels). But do we really need to spend 3? Can't we use the power of math to come up with better tactics? In this thread we do some math to analyse common strategies and summarize the variants. However, be aware I assume that all possible symptoms are equally likely, something I havn't had time to rigorously test yet. Please report your succes rates and sample size for any of the used tactics here!
But sometimes my diagnostic potion does nothing, in that case dont I need more than 3? No. Sometimes it indeed SEEMS like a diagnostic potion has no effect and is thus wasted. This can happen when 2 ambiguous slots are marked and you administer another diagnostic potion of either color. If that color was not the illness color, then the potion has no more eligible slots to reveal. However, this means the illness hides for sure in the color other than the ineffective potion you tried last. So always make an effort to remember the third color you administer.
Fastest Path to Certainty:
Diagnose any color, you'll most likely get an ambiguous two color side symptom result. Now diagnose the color that is NEITHER of those ambiguous colors just revealed and you'll have the biggest chance of a certain 2 potion diagnosis.
If you get the center symptom first, diagnose either of the other colors you didnt start the diagnosis with.
This tactic has a 42,6% chance of conclusive diagnosis within 2 potions!
Improved succes rate of 26,6% per potion. Uses 2,49 potions on average.
Best for those named kids you want to cure for sure.
Two of the Same Diagnostic Color (or a single color +):
If you get an ambiguous result, cure the disease of the other color
This tactic has a 86,1% chance of correctly curing. Improved success rate of 27,5% per potion. (But only 26,4% if you use color +)
But only has a conclusive diagnosis rate after 2 potions (or 1+) of 19,4%
Great for efficiently helping those plebs dying in the street.
Use a Single Color:
If you get a side ambiguous result, cure the disease of that other color, if you get ambiguous center result, guess either of the other 2 diseases.
This tactic has a 63,8% chance of correctly curing. Improved succes rate of 30,5% per potion.
Only tiny 8,3% conclusive diagnosis chance. Great return rate for when you're really desperate.
Single Color Complication:
The same as single color but additionally you add a second diagnostic potion if you get the ambiguous middle symptom. In that case, diagnose another color, if the result's ambiguous with the first color, cure the second. If it's ambiguous with the third, cure the third.
This tactic has a 75,9% chance of correctly curing. Improved succes rate per potion of 32,5% per potion. using 1,31 potions on average.