Solving Modern Art: Master's Gallery

My favorite Reiner Knizia game is Modern Art: Master’s Gallery. I’ve always loved the min-max aspect of the game - a lot of the game is about playing the least number of cards at the early game, and building on plays from previous rounds in future rounds. Deciding whether to play a card in the early or late game is crucial part of the strategy for the game.

A long-running idea of mine had been to find the maximum score for Modern Art. I finally found some time for it, and learned some constraint programming to work on it. I’ve gotten a partial implementation and some decent results that folks here might be interested in. My personal highest scores would be around the 100-120 range, and getting anywhere near that is a great game for me.

Here is a 2p game where the first player scores 250 points:

Round Player A B C D E
1 1 4② 4② 0 0 0
1 2 1 0 3② 3② 1②
1 Ranking Scores 3 2 0 1 0
1 Total Scores 5 4 2 3 2
1 Player 1 Score 36
1 Player 2 Score 14
2 1 4 4 0 0 0
2 2 1 0 3 2 2■
2 Ranking Scores 3 2 1 0 0
2 Total Scores 8 6 3 3 2
2 Player 1 Score 56
2 Player 2 Score 17
3 1 4■ 3■ 0 0 0
3 2 1 1 3 2 0
1 Ranking Scores 3 2 1 0 0
3 Total Scores 11 8 4 3 2
3 Player 1 Score 68
3 Player 2 Score 31
4 1 5 2 0 0 0
4 2 0 2 3■ 2 0
4 Ranking Scores 3 2 1 0 0
4 Total Scores 14 10 5 3 2
4 Player 1 Score 90
4 Player 2 Score 35

Artists go from E->A = LiteMetal->Krypto.

Caveats
    ② denotes an artist was awarded
    ■ means a draw one card of that artist was played.
    - Total Score is calculated for this table cumulatively, but only top 3 artists are actually scored.

Here is a 3 player game where it manages to get 242 points (Took 21 hours for my PC to find this one). The columns on the right are scores for each artist for that round.

Player 1 Player 2 Player 3 A B C D E
AA② AA AA 5 0 0 1 2
AAAEE② BBCC②E D②EEEE 7 0 0 4 7
AAAAAEEEE ABBBDDDDE BBCCCCCA 10 0 0 5 9
AAAAAAEEE BBBBCCCDD B②CCDDDEE 13 0 0 6 11
242 = 10+35+86+111 65 = 10+4+39+12 87 = 10+32+5+40
Caveats
    ② denotes an artist was awarded
    Unlike previous result, there is no Draw One card implemented

The current solver implements most of the ruleset, but I’m still working on the remaining pieces:

  • Symbol (=) - Second card face up
  • Symbol (≂) - Second card face down
  • Symbol (✠) - Simultaneous play
  • Additional Card Play.

Once these are done, the solver should have the provable maximum score for the game. Note that it is already getting 200+ points easily without these additional rules. I expect all of these (especially additional card play) to get the score to ~300 range.

I’m looking for interesting challenges to throw at the solver once this is done. Things like:

  • Is it possible to win a game without playing any special cards?
  • What is the highest player average score?
  • Can you win the game a game where none of the artists you play are awarded (while the others are?)
  • Can you model a colluding 2 player system?
  • How many fewer cards can you plan from other players and still win?
  • Is it possible to win a game without playing any Lite Metal cards? What about other artists?
  • Given a unbiased draw of cards, what is the highest score?
  • What if everyone’s initial draws are identical, and draws after each round are identical. What’s the highest winning margin in that case?

If you have any suggestions, please reply. The Source Code is on GitHub and has more details on the implementation and current limitations.

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