Kalah

Kalah(6,4), the common mancala. An exact solver scores every house by the final store difference; the answer is a house number. See Methodology.

Fewer puzzles than the other models, so results are noisy.

Quality is the mean oracle score of the moves played, × 100. The best move scores 100; an illegal move or no move scores 0. Protocol boardbench-0.2.

Quality vs cost

4 of 4 models
  • Anthropic
  • OpenAI
4050607080$0.0001$0.001$0.01$0.1Claude Haiku 5.5 Medium · 33.3% · <$0.01 · Pareto frontierClaude Sonnet 5.5 Medium · 33.3% · $0.01GPT-6 Luna high Medium · 33.3% · <$0.01GPT-6.1 Sol Medium · 66.7% · $0.04 · Pareto frontierGPT-6.1 Sol MediumClaude Haiku 5.5 MediumGPT-6 Luna high MediumClaude Sonnet 5.5 Medium
  • Pareto frontier: nothing plotted is both cheaper and better
  • Anthropic
  • OpenAI

Horizontal axis is logarithmic.

Table

ModelQualityLegalityCostn
Sol (fewer samples)Medium66.7100.0$0.043
Haiku 5.5Medium33.3100.0<$0.019
Sonnet 5.5 (fewer samples)Medium33.3100.0$0.013
Luna highMedium33.3100.0<$0.019

Headline is the mean move score × 100. n is answers: puzzles × samples.

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