{
  "evaluation_id": "EVAL-20260315-061839",
  "question_id": "EVAL-20260315-061839",
  "question_text": "You must choose between three investments. Investment A returns 10% with 90% probability, -50% with 10% probability. Investment B returns 5% with certainty. Investment C returns 100% with 20% probability, 0% with 80% probability. (1) Rank them by expected value. (2) Rank them by the Kelly criterion. (3) You have $10,000 your entire savings. Does this change your answer? Why? (4) Now you have $10,000,000. Does it change again? Derive the general principle.",
  "category": "reasoning",
  "timestamp": "2026-03-15T06:18:39.035Z",
  "display_date": "Mar 15, 2026",
  "winner": {
    "name": "Qwen 3 8B",
    "provider": "openrouter",
    "score": 9.63
  },
  "avg_score": 8.322,
  "matrix_size": 66,
  "models_used": [
    {
      "id": "devstral",
      "name": "Devstral Small",
      "provider": "openrouter"
    },
    {
      "id": "gemma3_27b",
      "name": "Gemma 3 27B",
      "provider": "openrouter"
    },
    {
      "id": "llama4_scout",
      "name": "Llama 4 Scout",
      "provider": "openrouter"
    },
    {
      "id": "phi4",
      "name": "Phi-4 14B",
      "provider": "openrouter"
    },
    {
      "id": "qwen3_8b",
      "name": "Qwen 3 8B",
      "provider": "openrouter"
    },
    {
      "id": "llama31_8b",
      "name": "Llama 3.1 8B",
      "provider": "openrouter"
    },
    {
      "id": "granite_40",
      "name": "Granite 4.0 Micro",
      "provider": "openrouter"
    },
    {
      "id": "mistral_nemo",
      "name": "Mistral Nemo 12B",
      "provider": "openrouter"
    },
    {
      "id": "qwen3_32b",
      "name": "Qwen 3 32B",
      "provider": "openrouter"
    },
    {
      "id": "kimi_k25",
      "name": "Kimi K2.5",
      "provider": "openrouter"
    }
  ],
  "rankings": {
    "qwen3_8b": {
      "display_name": "Qwen 3 8B",
      "provider": "openrouter",
      "average_score": 9.63,
      "score_count": 8,
      "min_score": 8.8,
      "max_score": 10,
      "rank": 1
    },
    "gemma3_27b": {
      "display_name": "Gemma 3 27B",
      "provider": "openrouter",
      "average_score": 9.38,
      "score_count": 8,
      "min_score": 8.8,
      "max_score": 10,
      "rank": 2
    },
    "phi4": {
      "display_name": "Phi-4 14B",
      "provider": "openrouter",
      "average_score": 8.86,
      "score_count": 8,
      "min_score": 7.2,
      "max_score": 9.8,
      "rank": 3
    },
    "devstral": {
      "display_name": "Devstral Small",
      "provider": "openrouter",
      "average_score": 8.77,
      "score_count": 8,
      "min_score": 7.15,
      "max_score": 10,
      "rank": 4
    },
    "mistral_nemo": {
      "display_name": "Mistral Nemo 12B",
      "provider": "openrouter",
      "average_score": 8.36,
      "score_count": 7,
      "min_score": 5.85,
      "max_score": 9.45,
      "rank": 5
    },
    "qwen3_32b": {
      "display_name": "Qwen 3 32B",
      "provider": "openrouter",
      "average_score": 8.25,
      "score_count": 1,
      "min_score": 8.25,
      "max_score": 8.25,
      "rank": 6
    },
    "kimi_k25": {
      "display_name": "Kimi K2.5",
      "provider": "openrouter",
      "average_score": 8.25,
      "score_count": 1,
      "min_score": 8.25,
      "max_score": 8.25,
      "rank": 7
    },
    "granite_40": {
      "display_name": "Granite 4.0 Micro",
      "provider": "openrouter",
      "average_score": 7.88,
      "score_count": 8,
      "min_score": 2.25,
      "max_score": 9.25,
      "rank": 8
    },
    "llama4_scout": {
      "display_name": "Llama 4 Scout",
      "provider": "openrouter",
      "average_score": 7.03,
      "score_count": 9,
      "min_score": 3.45,
      "max_score": 9.25,
      "rank": 9
    },
    "llama31_8b": {
      "display_name": "Llama 3.1 8B",
      "provider": "openrouter",
      "average_score": 6.8,
      "score_count": 8,
      "min_score": 2.8,
      "max_score": 9.25,
      "rank": 10
    }
  },
  "judgments": [
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.25,
      "brief_justification": "The response correctly calculates expected values and applies the Kelly criterion, but the general principle in part (4) lacks deeper analysis of how capital size interacts with risk tolerance. The explanation is clear and structured, though some nuances (e.g., logarithmic utility in Kelly) are omitted."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 8.95,
      "brief_justification": "The response correctly calculates expected values and applies the Kelly Criterion for Investments B and C. However, it contains a critical error in the Kelly calculation for Investment A (incorrectly using 0.10 instead of 0.50 for the loss magnitude). Despite this, it thoroughly addresses all four questions, explains risk considerations, and derives a clear general principle. The clarity and depth of analysis are strong, though the calculation error slightly reduces correctness and completeness."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 6.4,
      "brief_justification": "The response correctly calculates expected values but contains significant errors in the Kelly criterion calculations. It addresses all question parts but lacks depth in explaining the Kelly criterion and the impact of wealth on investment decisions."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 7.5,
      "brief_justification": "The expected value ranking is correct, but the Kelly criterion calculations contain errors. For Investment A, the Kelly formula should use the profit-to-loss ratio (0.10/0.50 = 0.2) and the correct formula f* = (p(b) - q)/b, yielding f* ≈ 0.0667 instead of 0.03636. Investment B's Kelly fraction is incorrectly computed as 0.04762 when it should be 1 (since it's risk-free). The principle about wealth scaling is valid, but the flawed calculations reduce correctness."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response accurately calculates expected values and Kelly fractions, explains the scale-invariance of the Kelly criterion, and addresses all four questions with clear, structured reasoning and mathematical rigor."
    },
    {
      "judge_key": "qwen3_32b",
      "judge_name": "Qwen 3 32B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 2.8,
      "brief_justification": "The response contains major mathematical errors in calculating expected values and incorrectly applies the Kelly criterion formula. The final answer is completely wrong and doesn't address the question. The explanation lacks depth and misses key concepts about how wealth amount affects investment decisions."
    },
    {
      "judge_key": "kimi_k25",
      "judge_name": "Kimi K2.5",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 3.45,
      "brief_justification": "The response correctly calculates expected values (C>B>A) but fails to properly derive Kelly criterion fractions (correct: B>A>C with f=1.0, 0.8, 0 respectively), instead presenting confused formulas and incorrect calculations. It inadequately addresses how wealth constraints affect risk tolerance and decision-making, incorrectly stating that wealth doesn't change the ranking while ignoring that Kelly assumes infinite horizon/recovery ability. The final answer only provides the EV ranking despit"
    },
    {
      "judge_key": "kimi_k25",
      "judge_name": "Kimi K2.5",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 2.25,
      "brief_justification": "While expected value calculations in part (1) are correct, the Kelly criterion calculations in part (2) are fundamentally incorrect due to misapplication of the formula and confusion between probabilities and returns. Parts (3) and (4) fail to recognize that when $10,000 represents entire savings, risk aversion and utility theory (not just EV/Kelly) become critical, potentially leading to different investment choices; the response incorrectly asserts rankings never change with wealth levels."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.6,
      "brief_justification": "The response provides a thorough, accurate, and clear analysis of the investments using both expected value and the Kelly criterion, and effectively explains how wealth levels impact the optimal investment strategy."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 6.65,
      "brief_justification": "The response provides a detailed calculation of expected values and attempts to apply the Kelly criterion, but the Kelly criterion calculations are incorrect and confusing. The final answer is correct, but the explanation could be clearer and more concise."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately calculates and explains both expected value and Kelly criterion for each investment, providing clear rankings and a general principle for different wealth levels."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8,
      "brief_justification": "The response is mostly correct and thorough, with clear explanations. However, the Kelly criterion calculations for Investment A and C are incorrect, and the depth could be improved by discussing risk tolerance and diversification."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response is factually accurate, thoroughly covers the topic, is well-structured, provides insightful analysis, and offers practical value."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion, providing clear rankings and discussing the impact of investment amounts on risk tolerance. However, it could delve deeper into the mathematical derivation of the Kelly criterion for more depth."
    },
    {
      "judge_key": "devstral",
      "judge_name": "Devstral Small",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 6.5,
      "brief_justification": "The response provides a clear and structured approach to ranking investments by expected value and the Kelly criterion. However, there are some errors in the calculations, particularly in the expected value for Investment C and the Kelly criterion formula application. The response does not fully address the impact of the investment amount on the decision, and the general principle could be more explicitly stated."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9.4,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion fractions. It correctly applies the Kelly criterion to different capital levels and explains the underlying principles well, demonstrating a strong understanding of risk management and investment strategy."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 7,
      "brief_justification": "The response correctly calculates expected values and attempts the Kelly criterion, but struggles with the correct application of the Kelly formula, showing multiple corrections and acknowledging errors. The discussion of wealth impact is reasonable, though could be more detailed."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.8,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion values for each investment. It correctly explains how the Kelly criterion scales with wealth, providing a clear and insightful answer to all parts of the question."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8.65,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion values, and correctly states that the rankings don't change with initial capital. While the explanation of the general principle is good, it could benefit from a more nuanced discussion of risk tolerance and the limitations of these criteria."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.6,
      "brief_justification": "The response provides a correct and complete analysis of the investment options using both expected value and the Kelly criterion. The explanation of the Kelly criterion and its scale-invariance is particularly well-done, and the mathematical derivations are accurate."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion values for each investment. It also correctly explains how the amount of capital influences risk tolerance and investment strategy, demonstrating a good understanding of the underlying principles."
    },
    {
      "judge_key": "gemma3_27b",
      "judge_name": "Gemma 3 27B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 6.75,
      "brief_justification": "The calculations for expected value are incorrect (should be expressed as a percentage return, not a decimal increase). The Kelly criterion application is flawed as the 'b' calculation is incorrect and the resulting negative values are not properly interpreted; Kelly criterion should result in a fraction between 0 and 1."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 10,
      "brief_justification": "The response accurately addresses all parts of the question, providing clear and thorough explanations of the expected value and Kelly criterion calculations, as well as insightful analysis of how the amount of capital influences investment strategy."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 10,
      "brief_justification": "The response accurately addresses all parts of the question, providing clear and thorough explanations of expected value, the Kelly Criterion, and how wealth level impacts investment strategy. The analysis is insightful, and the conclusions are well-supported and practical."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.45,
      "brief_justification": "The response accurately addresses all parts of the question, providing clear calculations and explanations for expected value and Kelly criterion rankings, and discusses the implications of different wealth levels."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately calculates and ranks the investments by expected value and Kelly criterion, and correctly explains that the rankings do not change with the amount of money invested."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response accurately addresses all parts of the question, providing clear calculations and explanations for ranking investments by expected value and the Kelly criterion, and discussing the impact of capital size."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately calculates and ranks investments by expected value and the Kelly criterion, and discusses the impact of total wealth on risk tolerance. However, it could provide more insight into the mathematical implications of the Kelly criterion and the general principle."
    },
    {
      "judge_key": "llama4_scout",
      "judge_name": "Llama 4 Scout",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.25,
      "brief_justification": "The response correctly calculates and ranks investments by expected value and the Kelly criterion. However, it could provide more insight into the implications of the Kelly criterion for risk management and portfolio optimization."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9.2,
      "brief_justification": "The response accurately calculates expected values and applies the Kelly criterion correctly, providing a thorough analysis. It is clear and well-structured, offering practical insights into investment decisions based on different capital amounts."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately evaluates the investments using expected value and the Kelly Criterion, providing a clear explanation of how wealth level and risk tolerance influence investment decisions. It offers a comprehensive analysis with practical insights into how different investment strategies are optimal depending on the investor's wealth and risk preferences."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 9.25,
      "brief_justification": "The response correctly calculates expected values and Kelly criterion fractions for each investment, ranking them accurately. It also discusses the impact of wealth on investment decisions, providing practical insights into risk tolerance and investment strategy."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately calculates the expected value and Kelly criterion for each investment, correctly ranks them, and explains why the rankings remain unchanged regardless of the investment size. The explanation is clear and provides practical insights into investment decision-making principles."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 10,
      "brief_justification": "The response accurately calculates expected values and Kelly fractions, clearly explains the rationale behind each ranking, and addresses the impact of capital size on investment decisions. It provides a thorough and insightful analysis, making it highly useful for understanding investment strategies."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.9,
      "brief_justification": "The response correctly calculates and ranks the expected values and Kelly criterion for each investment, providing a clear analysis of risk and return trade-offs. It effectively explains how the amount of money available influences investment decisions, illustrating practical implications for different scales of investment. The response is thorough and insightful, though it could further explore other investment criteria or scenarios."
    },
    {
      "judge_key": "phi4",
      "judge_name": "Phi-4 14B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 9.25,
      "brief_justification": "The response correctly calculates the expected values and Kelly criteria for each investment, providing a thorough and clear analysis. It accurately concludes that the amount of money invested does not affect the ranking based on the Kelly criterion, which is a relative measure. The response effectively derives the general principle that the Kelly criterion is independent of the absolute investment amount, focusing on expected returns and risks."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "qwen3_32b",
      "respondent_name": "Qwen 3 32B",
      "weighted_score": 8.25,
      "brief_justification": "The response correctly calculates expected values and applies the Kelly criterion, considers the impact of different investment amounts, and derives a general principle. It is well-structured and easy to follow."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "kimi_k25",
      "respondent_name": "Kimi K2.5",
      "weighted_score": 8.25,
      "brief_justification": "The response correctly calculates expected values and applies the Kelly criterion, considers the impact of different investment amounts, and derives a general principle. It is well-structured and easy to follow."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately evaluates each investment using both expected value and Kelly criterion, addresses the impact of capital size, and derives a general principle, demonstrating strong analytical and explanatory skills."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 8.8,
      "brief_justification": "The response provides a thorough analysis of the investments using expected value and Kelly Criterion, considers the impact of different wealth levels, and offers a clear general principle, while also including a disclaimer about not providing financial advice."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 8.2,
      "brief_justification": "The response accurately calculates expected values, applies the Kelly criterion with some conceptual errors, addresses the impact of wealth size, and derives a general principle, though it could be more precise in the Kelly calculations."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately calculates expected values and Kelly fractions, ranks investments correctly, addresses wealth impact, and derives a clear general principle, with minor depth limitation in explaining Kelly's scaling nature."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately evaluates each investment using expected value and Kelly criterion, addresses the impact of capital size, and derives a clear general principle, with minor depth due to brevity."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately evaluates each investment using expected value and Kelly criterion, considers the impact of different capital amounts, and derives a general principle. It is well-structured, clear, and provides actionable insights."
    },
    {
      "judge_key": "granite_40",
      "judge_name": "Granite 4.0 Micro",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.8,
      "brief_justification": "The response accurately calculates expected values, applies the Kelly criterion correctly, and derives a general principle while maintaining clarity and completeness."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 7.15,
      "brief_justification": "The response correctly calculates expected values but contains errors in the Kelly criterion formula application (incorrect b values). It addresses all parts of the question but the flawed calculations reduce correctness and depth."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 10,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion, thoroughly explains how wealth impacts investment choices, and provides clear, actionable insights with strong logical reasoning."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 6.6,
      "brief_justification": "Correct expected value calculations but Kelly criterion derivation is incomplete and confusing. General principle is mentioned but not fully derived."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 7.2,
      "brief_justification": "The expected value calculations are correct, but the Kelly criterion implementation contains errors (e.g., incorrect formula application for Investment B). The response is well-structured but the flawed Kelly analysis reduces correctness and usefulness."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 7.5,
      "brief_justification": "Expected value calculations are correct, but Kelly criterion application is flawed (incorrect formula interpretation). Other sections are well-structured and complete."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 5.85,
      "brief_justification": "The Kelly criterion calculations are fundamentally incorrect, leading to flawed rankings. The rest of the response is well-structured and covers all parts of the question."
    },
    {
      "judge_key": "qwen3_8b",
      "judge_name": "Qwen 3 8B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 3.8,
      "brief_justification": "Major errors in expected value calculations (incorrectly computed Investment A's EV) and Kelly criterion formula application. Final answer is nonsensical (boxed 0)."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 8.2,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion, providing clear rankings and explaining the general principles. However, the explanation could be more concise for better clarity."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 8.9,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion, provides a thorough analysis, and offers useful insights on how wealth affects investment decisions. However, some parts could be slightly more concise for better clarity."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 7.6,
      "brief_justification": "The response accurately calculates expected values and applies the Kelly criterion, but has some inconsistencies in the application of the Kelly formula. It provides a comprehensive analysis and addresses the impact of wealth on decision-making, but could delve deeper into the nuances of the Kelly criterion and risk tolerance."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 8.9,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion for each investment, ranks them accordingly, and explains the consistency of the Kelly criterion across different wealth levels. It is well-structured and provides insightful analysis, but could be slightly more concise for clarity."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 8.9,
      "brief_justification": "The response accurately calculates expected values and applies the Kelly criterion, covers all aspects of the question, is well-structured, provides insightful analysis, but could benefit from a real-world example to illustrate practical value."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.2,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion for each investment, clearly explains the methodology, and provides a thorough analysis. It also addresses the impact of different capital amounts on the ranking, demonstrating a deep understanding of the principles involved."
    },
    {
      "judge_key": "mistral_nemo",
      "judge_name": "Mistral Nemo 12B",
      "respondent_key": "llama31_8b",
      "respondent_name": "Llama 3.1 8B",
      "weighted_score": 8.25,
      "brief_justification": "The response accurately calculates expected values and Kelly criterion, thoroughly covering the topic. It's clear and well-structured, but could be more concise. It provides useful insights and a general principle, but lacks deeper analysis."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "devstral",
      "respondent_name": "Devstral Small",
      "weighted_score": 9.2,
      "brief_justification": "The response accurately applies the Kelly criterion and expected value to rank investments, providing a clear and thorough analysis with practical value."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "gemma3_27b",
      "respondent_name": "Gemma 3 27B",
      "weighted_score": 9.2,
      "brief_justification": "The response accurately applies the Kelly Criterion and expected value to the given investments, providing a clear and detailed explanation of the optimal strategy based on wealth level and risk tolerance."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "llama4_scout",
      "respondent_name": "Llama 4 Scout",
      "weighted_score": 8.15,
      "brief_justification": "The response accurately calculates expected values and attempts to apply the Kelly criterion, but contains some miscalculations and incorrect direct applications of the formula. The discussion on wealth impact and risk tolerance is clear and useful."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "phi4",
      "respondent_name": "Phi-4 14B",
      "weighted_score": 9.6,
      "brief_justification": "The response accurately calculates and compares the expected values and Kelly criterion for each investment, and provides a clear explanation of the general principle behind the Kelly criterion."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "granite_40",
      "respondent_name": "Granite 4.0 Micro",
      "weighted_score": 9.25,
      "brief_justification": "The response accurately calculates and compares the expected values and Kelly criterion for each investment, and provides a clear explanation of the general principle."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "qwen3_8b",
      "respondent_name": "Qwen 3 8B",
      "weighted_score": 9.45,
      "brief_justification": "The response accurately and thoroughly explains the concepts of expected value and the Kelly criterion, and provides clear and actionable advice on how to rank the investments."
    },
    {
      "judge_key": "llama31_8b",
      "judge_name": "Llama 3.1 8B",
      "respondent_key": "mistral_nemo",
      "respondent_name": "Mistral Nemo 12B",
      "weighted_score": 9.45,
      "brief_justification": "The response accurately and thoroughly explains the concepts of expected value and Kelly criterion, and provides a nuanced discussion of risk tolerance and investment strategy."
    }
  ],
  "meta": {
    "source": "The Multivac (app.themultivac.com)",
    "methodology": "10x10 blind peer matrix evaluation",
    "criteria": "correctness, completeness, clarity, depth, usefulness",
    "self_judgments": "excluded from rankings",
    "license": "Open data — cite as: The Multivac (2026)"
  }
}