Principalities: what follows from the measurements

The numbers on this page come from measuring AI opponents. The articles they are from repeat it: an AI is not a person, and the strategy of people could not be measured. The rules are on the page Principalities.

The first move

Two equally good AI opponents that alternate in a duel give the starting one 93.3% of the games; with 3 players 61.3%, with 4 players 41.8% (the fair share is 25%) and with 8 players 15.8% (12.5%). With 4 players it was 400 games per cell (±5 percentage points). That is why the game draws who starts; with 4 players the seats won in order 24.8, 22.8, 28.0 and 24.5%. The alternative, extra dice for the second player, was too sensitive: without them the first wins about 95%, with +25% 56% and with +50% 9%. In a duel the game tells the player that it matters most who starts.^[1]

Skill

With two players skill hardly shows (52% for an average AI and 55% for a good one), because a duel is decided by the order. The more players, the more decisions: a good AI (level 3) wins 51% with 4 players (the fair share is 25%) and 47% with 8 players (13%). More about the AI is on the page Opponents.

Reinforcements and placing them

By the rule the reinforcements go to random territories (Principalities); in Free play there is the option "I place them". In the measurement an AI that put all the new dice into the biggest stack at the front won 99% of the games in 6 rounds in the basic setup, while with the random placement of the AI it won 35% in 10 rounds and with a fully random one 34% in 34 rounds. The opponents in the game do not stack dice. The game therefore values manual placement at −41 points of the score (earlier +2). Stacking as a human practice is an observation of the author, only AI opponents were measured.^[2]

What makes a game longer and easier

• The length of a game against a level-3 AI is raised by: reinforcements by half of the territories ×2, at most 36 dice per territory ×1.7 and the archipelago map ×3; moving half of the dice changes nothing.
• The difficulty of settings is measured in points: 1 point is a drop of 0.125 in the log-odds, about 3 percentage points near 50%. The defender bonus +4 costs about 8.6 points. The points do not add up exactly: the result differs by 15 to 40%, so they serve for comparing settings, not for predicting a chance.^[3]

What was not measured

A simple "best move" in Principalities was not found. Attempts with tuned weights and Monte Carlo did not beat the Strong AI, and the game is largely luck.^[4]