Backgammon

A money-game position with the dice rolled. GNU Backgammon rollouts score every legal play by cubeless equity; the answer is the whole play, e.g. 24/18 13/11. 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
30405060708090$0.0001$0.001$0.01Claude Haiku 5.5 Medium · 70.4% · <$0.01 · Pareto frontierClaude Sonnet 5.5 Medium · 26.3% · $0.01GPT-6 Luna high Medium · 36.8% · <$0.01GPT-6.1 Sol Medium · 56.9% · $0.01Claude Haiku 5.5 MediumGPT-6.1 Sol 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
Haiku 5.5Medium70.4100.0<$0.019
Sol (fewer samples)Medium56.9100.0$0.013
Luna highMedium36.888.9<$0.019
Sonnet 5.5 (fewer samples)Medium26.3100.0$0.013

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

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