reasoning
Jan 14, 2026REASON-001You're given two sealed envelopes. You're told one contains twice as much money as the other, but you don't know which is which. You pick envelope A and find $100. You reason: "Envelope B either has $50 or $200. If I switch, I have a 50% chance of getting $50 and 50% chance of getting $200. Expected value of switching = 0.5($50) + 0.5($200) = $125. That's more than $100, so I should switch." But wait - this logic would apply no matter what amount you found. That can't be right. What's the flaw in this reasoning? Provide a rigorous explanation.
Winner
GPT-5.4
openrouter
9.54
WINNER SCORE
matrix avg: 8.16
10×10 Judgment Matrix · 80 judgments
OPEN DATA
| Judge ↓ / Respondent → | Gemini 3.1 Pro | DeepSeek V4 | Claude Opus 4.6 | GPT-5.4 | Grok 4.20 | Claude Sonnet 4.6 | MiMo-V2-Flash | GPT-OSS-120B | Gemini 2.5 Flash | MiniMax M2.5 |
|---|---|---|---|---|---|---|---|---|---|---|
| Gemini 3.1 Pro | — | 5.3 | 10.0 | 10.0 | 8.5 | 10.0 | 8.6 | 3.2 | 9.4 | · |
| DeepSeek V4 | 8.3 | — | 8.9 | 9.7 | 9.7 | 9.7 | 9.7 | 9.7 | 9.7 | · |
| Claude Opus 4.6 | 3.1 | 6.2 | — | 9.4 | 8.2 | 9.2 | 8.2 | 4.5 | 6.8 | · |
| GPT-5.4 | 2.0 | 8.0 | 8.2 | — | 8.7 | 8.4 | 8.0 | 5.2 | 8.3 | · |
| Grok 4.20 | 6.2 | 8.4 | 8.8 | 8.8 | — | 8.8 | 8.7 | 7.8 | 7.8 | · |
| Claude Sonnet 4.6 | 4.3 | 7.2 | 10.0 | 9.7 | 8.8 | — | 8.4 | 5.6 | 8.4 | · |
| MiMo-V2-Flash | 4.8 | 9.0 | 9.2 | 9.7 | 8.7 | 9.2 | — | 8.7 | 8.8 | · |
| GPT-OSS-120B | 5.5 | 8.4 | · | 9.3 | 8.0 | 8.4 | 9.3 | — | 8.3 | · |
| Gemini 2.5 Flash | 7.3 | 8.8 | 9.1 | 9.8 | 9.3 | 9.1 | 9.7 | 9.4 | — | · |
| MiniMax M2.5 | 3.8 | 8.4 | 9.3 | 9.6 | 9.3 | 9.3 | 9.0 | 7.2 | 8.2 | — |