hmm. Minimax provides an optimal strategy for mastermind. But minimax doesnt work for hidden state games. Therefore, I can only assume mastermind doesnt really satisfy the hidden state property due to the fact that the opponent cannot changed the state between your turns.

Why are you assuming anything, just learn how the game works. This game can be solved on the command line with grep. There is no opponent. What are you talking about here?

About two months ago i learned how mastermind worked, put a good hour into reading about it and the solutions. played a few games too. Having spent a very long time implementing algorithms for chess and tictactoe a number of years ago I immediatly understood it. My friend also gave presentations on some solutions in rust, that I attended twice. I admit i am responding with old knowledge but I believe it is still correct. I dont find the game or its solution that interesting. However, the concept of hidden state games that have no possibility for state changing between turns did seem interesting to me. As somebody well versed in reinforcement learning, it surprised me that its a distinction I never came across previously. Usually algorithms for games like this are divided into non hidden state (minimax solveable if branching factor is small) and hidden state games (a whole other thing). In masterminds case the "opponents move"( a relevant framing if you know how minimax works) is just presented to you after your turn. The "opponent" always plays optimally in that the response is fixed. So its not really hidden state, despite the player not knowing the initial conditions. I knew that there were optimal tabular and minimax solutions to mastermind, but those techniques only work if the game is truly a no hidden state game. However, the person above posted that mastermind actually is a hidden state game because the player does not a-priori know the state of the hidden rule. It occured to me that must be irrelevant for some reason, and so I tried to deduce why.

I hope I have explained my motivation, and why I responded about the particular aspect of the game in the way that I did. My apologies for coming off retarded and shit.

You don't need to be well versed in reinforcement learning "a-priori" knowledge or worry about opponents moves or "optimal tabular and minimax solutions" or branching factors or anything else.

Start with a text file of every combination separated by lines.

RRRRR RRRRG RRRGG

Then use cat to output it to grep and use grep for all the constraints.

One for colors that aren't there. One for colors you know are in the right place. Then after that one grep for every color you know is there somewhere and one for each color you know isn't in a certain spot.

cat combinations.txt | grep -v [colors that aren't there] | grep ..R.G | grep B | grep -v .Y...

That's it. All you need is a command line. Generate guesses from the filtered list then add to the filters.

What you are saying may be true, and helpful, but just isn't related. My initial comment was about an optimal play algorithm. So that's what I was discussing.

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?