That doesn't even make sense.

Are any solutions more likely than any others?

How are you getting an "optimal play algorithm" when the entire game is about using what you know to filter the solutions that are still possible?

You're framing it like an information extraction game, but it is also frameable as a zero-sum minimax game. And its an easy, and common solution to games like this. Read up.

https://en.wikipedia.org/wiki/Mastermind_(board_game)#Algori... https://en.wikipedia.org/wiki/Minimax#In_zero-sum_games

One of the early solutions to mastermind was by Donald Knuth. paper: https://www.cs.uni.edu/~wallingf/teaching/cs3530/resources/k... an implementation: https://github.com/johnathanlouie/mastermind

further development: https://arxiv.org/abs/1908.06183

It just says the "minimax" solution for the person who chooses the pattern is to pick randomly from patterns with more than one color.

Well the game is trivial for the person picking the pattern. So I dont expect the optimal play for them to be interesting.

If the game is trivial for the person picking, what is the strategy for the player after the filtering I described?