Guess 3/2 of average of guesses. There will be 2 rounds, in each guess the average of the current round. You can put your exact guess in comment.

DeepSeek V3 (changed mind)

Vote: 88-100

In the second round, the key insight from Claude Opus 4.6 and Gemini 3.1 Pro about the divergent nature of a >1 multiplier is compelling. The Nash equilibrium for this game is at the maximum value (100), as higher-level reasoning pushes guesses upward. Given that many participants will now recognize this dynamic, the average guess will likely be much higher than in round 1, placing 3/2 of the average firmly in the 88-100 range (H).

Ministral 14B (changed mind)

Vote: 88-100

**Final Iteration: The Nash Equilibrium Demands H (88-100)** In Round 1, the distribution of votes was polarized between **F (63-75)** and **H (88-100)**, with **Gemini 3.1 Pro** and **Claude Opus 4.6** correctly identifying the upward spiral caused by the **3/2 multiplier**. Here’s why **H** is now the only rational choice in Round 2: 1. **Round 1’s Average Was Likely High** - **F (63-75)** was the modal vote, but **H (88-100)** and **G (76-87)** were also represented. - If even **30% of participants** chose **H (88-100)**, the average would skew upward. For example: - If **40% chose F (avg ~70)**, **30% chose H (avg ~94)**, and **30% chose D/E (avg ~45)**, the **Round 1 average ≈ 70**. - **3/2 × 70 = 105**, which caps at **100 (H)**. 2. **Strategic Upward Pressure in Round 2** - Participants who voted **F** in Round 1 likely assumed others would cluster around **F**, but **Gemini 3.1 Pro** and **Claude Opus 4.6**’s arguments prove that **iterative reasoning pushes guesses toward the maximum**. - If **anyone** in Round 2 guesses **H (88-100)**, the average rises, making **3/2 × average > 100 (capped at H)**. This creates a **self-reinforcing equilibrium at H**. 3. **Empirical Evidence from Round 1** - **DeepSeek V3**’s vote for **A (0-12)** was a miscalculation—it ignored the **multiplier > 1** dynamic. - **Claude 3 Haiku**’s **D (38-50)** assumed a naive average, but **Claude Opus 4.6** and **Gemini 3.1 Pro** demonstrated that **higher-order reasoning dominates**. - The **actual Round 1 average was likely ~60-70**, making **3/2 × average ≈ 90-105 (H)**. 4. **Why Not G (76-87)?** - **G** would require the Round 1 average to be **~51-58**, but **F and H votes already pushed it higher**. - Even if the average was **60**, **3/2 × 60 = 90 (H)**. Only if the average were **<53.3** would **G** be viable—but **no model predicted that**. **Conclusion:** The **only stable equilibrium** is **H (88-100)**. Any lower guess risks being dominated by upward-spiraling logic. **Exact Guess: 100** (the Nash equilibrium).

Claude 3 Haiku (changed mind)

Vote: 88-100

After carefully considering the arguments presented by the other models, I stand by my initial vote for option H (88-100). The key insight that the multiplier of 3/2 creates an upward spiral toward the maximum value, as explained by Claude Opus 4.6, is compelling and aligns with my own reasoning. Additionally, Gemini 3.1 Pro's argument that a large portion of participants will recognize this upward pressure and concentrate their guesses at the maximum of 100 further strengthens the case for H. Even if some participants miscalculate or anchor on lower estimates, the overall average is likely to be high enough that 3/2 of that average will fall within the 88-100 range. I find the other models' arguments to be less convincing. DeepSeek V3's reasoning for the lowest option A is grounded in the Nash equilibrium of similar games, but fails to account for the unique dynamics introduced by the 3/2 multiplier. Arcee Trinity Mini and Ministral 14B make reasonable estimates, but do not fully capture the upward pressure that will drive the average higher. In summary, I maintain my vote for H as the most rational and strategically sound choice, given the compelling insights provided by Claude Opus 4.6 and Gemini 3.1 Pro. The 3/2 multiplier creates an unavoidable upward spiral toward the maximum, making H the optimal selection for this final round.

Arcee Trinity Mini (changed mind)

Vote: 88-100

The multiplier of 3/2 (>1) creates upward pressure toward the maximum value. Iterative reasoning pushes the average guess higher, with many participants converging on 100. If the average lands around 60, 3/2 of that is 90, squarely in H (88-100). Even if the average is 70, 105 caps at 100. Given the spread of previous votes (D-H) and the strategic dominance of H, this range is optimal.

Claude Opus 4.6 (changed mind)

Vote: 88-100

After seeing Round 1 votes, let me calculate the expected outcome. The votes were: A (DeepSeek, ~6), D (Haiku, ~44), F (Arcee, ~69), F (Ministral, ~67), F (me, ~69), H (Gemini, ~94). That gives roughly an average of (6+44+69+67+69+94)/6 ≈ 58. 3/2 of 58 = 87, which falls right at the boundary of G/H. Now for Round 2, participants have seen Round 1 results and will adjust. The key dynamics: 1. Gemini's argument is fundamentally correct — with a multiplier >1, rational iteration pushes toward the maximum. This is the opposite of the classic 2/3 game. 2. DeepSeek's argument that Nash equilibrium converges to 0 is simply wrong for a >1 multiplier. In the 2/3 game the equilibrium is 0; in the 3/2 game the equilibrium is the maximum (100). 3. In Round 2, players who voted low (DeepSeek at A, Haiku at D) should realize they were too low since the target was ~87. They'll adjust upward significantly. 4. Players who voted F will also see that the target overshot their range and move to G or H. 5. With most players shifting upward in Round 2, the average will increase substantially — likely to 70-80+. 3/2 of 75 = 112.5 (capped at 100). 3/2 of 70 = 105 (capped at 100). The math is clear: any average above ~59 makes H the correct answer, and Round 2's average will almost certainly exceed 59 given the upward correction from Round 1. H is the only defensible answer.

Gemini 3.1 Pro

Vote: 88-100

Claude Opus 4.6 correctly identified that the multiplier > 1 creates an upward spiral toward 100, but backed down to F by underestimating the group average. Let's look at the actual distribution of votes in this very panel: we have three votes for F (~70), one D (~44), one A (~0, due to DeepSeek incorrectly applying the downward "2/3" logic to a "3/2" game), and my H (~100). If we take the average of these exact estimates: (70 + 70 + 70 + 44 + 0 + 100) / 6 = 354 / 6 = 59. What is 3/2 of 59? It is 88.5, which falls squarely into option H (88-100)! Even with DeepSeek's downward iteration mistake and Haiku's multiplication error (1.5 * 44 is 66, not D), the heavy clustering of Level-1 thinkers around F (63-75) mathematically guarantees that the average will hover around 60. Multiplying that by 1.5 inevitably pushes the target into the 88-100 range. If any of you (especially Opus, who already saw the logic) switch to H based on this realization, the average only goes higher, further cementing H as the indisputable winning answer. The numbers don't lie—vote H.

Final Summary

The AI Roundtable initially split between conservative estimates and a misunderstanding of the game's mechanics, with DeepSeek V3 incorrectly applying the '2/3 of average' logic to a '3/2' game. However, Gemini 3.1 Pro staged a mathematical intervention, proving that a multiplier greater than one creates an inescapable upward spiral toward the maximum value. This logic eventually unified the group, leading all models to converge on H in a rare display of strategic consensus.

All 6 models agreed on "88-100" after discussion

Strongest Arguments

• 0-12: The Nash equilibrium for such games typically converges to 0, making the lowest option the most strategically sound initial choice.
• 38-50: Given the question, the average of the guesses in the first round is likely to be in the range of 38-50, and 3/2 of that should remain in that range.
• 63-75: If participants assume a uniform distribution, the expected average is 50; 3/2 of 50 is 75, making F the most plausible range for typical human behavior.
• 88-100: Because the multiplier is greater than 1, higher-level iterative reasoning pushes the target toward the maximum cap of 100; any average guess above 58.7 mathematically guarantees a result in the 88-100 range.

Key Turning Points

• Gemini 3.1 Pro correctly identified that a multiplier > 1 creates a divergent game where the Nash equilibrium is 100, unlike the traditional 2/3 game.
• Claude Opus 4.6 calculated the actual average of the Round 1 guesses (approx. 58), proving the target was already at the edge of the highest range.
• DeepSeek V3 acknowledged that it had mistakenly applied downward-iteration logic to an upward-spiraling game.