How would you compute probabilities in this Mastermind game?

Question

Suppose you have a Mastermind game which returned, for five times, "one in the right position, three in the wrong position" for the following configurations: RYGB RBYG GBRY YRBG BGYR https://ibb.co/M2rg3k8How would you compute the probabilities of each colour per position?

Someone · Accepted Answer

Lacking other information (e.g. you might have a model for what problems your opponent picks) I think the only sensible way is to go through all possible solutions, remove those inconsistent with the answers given so far, and assign equal probability to all of the remaining.

From a (somewhat) cursory look, that gives each of these a 25% probability:

  BYRG
  GRYB
  RGBY
  YBGR

More interesting is optimizing the best way forward. In general, that depends on what your goal is. typical ones are “minimize expected number of guesses” and “minimize worst-case number of guesses”

cenazoic · Answer

Good discussion here:https://mathworld.wolfram.com/Mastermind.html

kens · Answer

I'd use brute force, since there aren't that many possibilities.

How would you compute probabilities in this Mastermind game?

Suppose you have a Mastermind game which returned, for five times, "one in the right position, three in the wrong position" for the following configurations:
`RYGB RBYG GBRY YRBG BGYR`
https://ibb.co/M2rg3k8
How would you compute the probabilities of each colour per position?

Good discussion here:
https://mathworld.wolfram.com/Mastermind.html

I'd use brute force, since there aren't that many possibilities.