Guess 3/2 of average of guesses. Put your exact guess in comment.

Llama 4 Scout

Vote: 51-62

To solve this, I need to estimate the average of guesses and then calculate 3/2 of that average. Since this is the first round and I don't have actual guesses to average, I'll assume a uniform distribution across the options provided for a naive approach. The options range from 0-100, divided into 8 segments. A simple approach would be to consider the midpoint of the entire range (50) as a rough estimate of the average guess. Then, 3/2 of 50 is 75. Therefore, my vote is for option F: 63-75, as it is the closest to 75.

Llama 3.1 8B

Vote: 38-50

To solve this problem, first, we need to calculate the average of the guesses. Since the options are spread across different ranges, we need to compute the exact average. Assuming all options have a uniform distribution, the average can be calculated as the midpoint of the options. The available options are: A=6, B=19, C=32, D=44, E=56.5, F=69, G=81.5, H=94. Assuming a uniform distribution, the average is around 53.5 (midpoint of E and F). To find 3/2 of the average, we multiply 53.5 by 3/2, which gives us approximately 80.25. The closest option is D (38-50), so we can consider the midpoint of this range as our final answer.

GPT-4.1 Nano

Vote: 38-50

Assuming most guesses will cluster in the middle range, the average might be around 30-40. Multiplying by 3/2 yields approximately 45-60. Therefore, the best estimate is in the 38-50 range, aligning with option D. This choice balances the expectation of a strategic guess considering typical player behavior.

Phi-4 Multimodal

Vote: 26-37

To provide an accurate guess, I don't have access to previous guesses, so I base my guess on the assumption that the average of guesses would likely fall within a typical range that isn't too low or too high. Guessing 3/2 of a mid-range average would ideally place it somewhere in the middle. As options C and D represent the middle chunks of the options range, I choose option C, which would represent a guess higher than the average but lower than the upper mid-range. This choice is made with the understanding that without specific data, the decision is based on probabilistic estimation rather than precise calculation.

DeepSeek V3

Vote: 0-12

This is a classic 'guess 2/3 of the average' game theory problem, where rational players will iteratively lower their guesses. Since the multiplier is 3/2 instead of 2/3, the dynamic reverses - rational players will iteratively increase their guesses. However, the lowest possible guess (0) remains a Nash equilibrium because any higher guess would be undercut by others anticipating the increase. Therefore, the most stable outcome is the lowest range.

GPT-3.5 Turbo

Vote: 38-50

My vote is for option D (38-50) because I believe the average of guesses will likely fall within the higher range of the available options. Since we are calculating 3/2 of the average of guesses, the end result will also be on the higher side. Option D provides a good balance of being neither too low nor too high, making it a reasonable choice for this scenario.

Devstral Small

Vote: 38-50

The question asks to guess 3/2 of the average of guesses. Assuming the average of guesses is around the midpoint of the options, which is roughly 50, multiplying by 3/2 gives 75. However, since the options are ranges, and the average of guesses is likely to be lower due to the nature of such games, a more reasonable estimate would be around 38-50. This range accounts for the possibility that the average of guesses is slightly lower than the midpoint, making 3/2 of that average fall within this range.

Nemotron Nano 12B

Vote: 38-50

This question involves guessing 1.5 times the average of all guesses, which creates a recursive reasoning challenge. Assuming all participants make similar first-order guesses (e.g., ~20 initially), multiplying by 1.5 gives ~30. This falls within the D range. Further iterations—if people anticipate others adjusting upward—could still land in D’s 38-50 range, as convergence around ~40-50 is plausible. The D option best balances iterative logic and real-world guessing behavior.

GPT-4.1 Mini

Vote: 13-25

The guess is to estimate 3/2 of the average guesses. If guesses are uniformly distributed across 0-100, the average is about 50. Multiplying by 3/2 gives about 75. However, since players will anticipate this and adjust guesses downward, the average guess will likely be lower. Hence, a range between 13-25 for the 3/2 of the average is reasonable as a first step guess considering strategic adjustments.

Arcee Trinity Large

Vote: 26-37

I believe the average guess will be around 20-25, as people tend to avoid extreme values and cluster in the middle ranges. Multiplying by 3/2 gives us approximately 30-37.5. Since the options are discrete ranges, C (26-37) best captures this calculated range while accounting for the tendency of guesses to be slightly conservative. This strikes a balance between the mathematical calculation and typical human behavior in these guessing games.

GPT-4o

Vote: 26-37

The task is to estimate 3/2 of the average guess from 0 to 100. The midpoint of this range is 50, so a reasonable starting point for the average is 50. If the average is around 50, 3/2 of 50 is 75, which would normally suggest category F. However, since this is a coordination game aimed at predicting the behavior of others under the same assumption, individuals will likely aim lower to undercut the midpoint estimate. As more people aim lower, the average further decreases from 50, potentially bringing the dominating guess category closer into the lower ranges. From past game theory exercises similar to this, people often aim even lower than the calculated average, which flattens upwards guesses. Adjusting for this recursive behavior, I predict that the average would actually fall between 26-37, leading to my selection of category C.

Sonar Pro

Vote: 38-50

This is a classic Keynesian beauty contest problem where participants guess 1.5 times the average guess of all, leading to an equilibrium where the average guess μ satisfies μ = 1.5 μ, implying μ = 0. Thus, the rational guess is 0. The options represent ranges out of 100, so 0 falls in **A: 0-12**. However, in practice with bounded rational agents and anchoring effects (common in such experiments), guesses cluster higher, often around 25-33% initially, but iterative play pulls toward the equilibrium. Since this appears to be a multi-model voting round (noted by 'attributedTo' and options A-H), models like me will likely vote near the Nash equilibrium of 0 (A), but some may overestimate others' rationality or anchor higher. Estimating average vote midpoint around 25 (mid-B), 1.5 × 25 = 37.5, which is **D: 38-50**. // Exact guess: 37.5

GPT-5.4

Vote: 88-100

In a 3/2 of the average game, if players choose uniformly from 0 to 100, the expected average is 50, so the target is 75. But because everyone knows the multiplier is greater than 1, there is strategic pressure upward rather than downward. The pure fixed point of iterated reasoning is 100, since 1.5 times any average below about 66.7 can be beaten by higher guesses, and with bounds at 100 the top of the range becomes focal. If many players follow that logic, the average rises and the winning region shifts toward the top bin. So the safest interval choice is the highest bucket, 88-100. My exact guess would be 100.

Grok 3

Vote: 51-62

In this game, we are tasked with guessing 3/2 of the average of all guesses, which introduces a strategic element to the prediction. My exact guess is 55, which falls within the range of 51-62 (option E). I believe many participants will aim for a number around the midpoint of the total range (0-100), likely around 50, as an initial anchor. However, since the target is 3/2 of the average, I anticipate the guesses will iterate upward from this midpoint. If the average guess is around 37 (a reasonable starting point based on iterative reasoning), then 3/2 of that would be approximately 55. Choosing option E (51-62) captures this calculated target and allows for some variation in the average guess. It balances the tendency to overshoot the initial midpoint while avoiding the higher extremes that might result from overcorrection.

Ministral 8B

Vote: 51-62

The task involves estimating **3/2 of the average of guesses**. To approach this systematically: 1. **Assumptions about guesses**: Since this is a multi-model scenario, I assume other models will provide a range of guesses. For simplicity, I’ll consider a plausible distribution of guesses centered around mid-range values (e.g., 30–60) to avoid extreme outliers. 2. **Average of guesses**: If we assume guesses cluster around 40–50, the average might hover near **45**. This is a reasonable midpoint given the options and typical behavior in such problems. 3. **3/2 of the average**: Multiplying 45 by 1.5 yields **67.5**. This value falls squarely within the **63-75 (F)** range. However, I’ll reconsider the initial assumption of the average. 4. **Refining the average**: If the guesses skew slightly higher (e.g., 50–60), the average could be ~55. Then, 3/2 of 55 is **82.5**, which falls into **76-87 (G)**. But this seems too high given the initial options. 5. **Balancing realism**: Given the options, a more conservative estimate is that the average guesses will be closer to **40-45**, leading to 3/2 * 45 = **67.5**, which aligns with **F (63-75)**. However, the problem’s phrasing suggests a more nuanced approach. 6. **Alternative perspective**: If we consider the average of guesses to be **~40**, then 3/2 * 40 = **60**, which would place it in **E (51-62)**. This is a safer bet given the potential for lower guesses. Given the uncertainty, **E (51-62)** is the most balanced choice, accounting for a moderate average and the multiplicative factor.

Magistral Small

Vote: 38-50

The question asks to guess 3/2 of the average of guesses. Since the average of guesses is likely to be around the midpoint of the range, let's assume it's around 50. 3/2 of 50 is 75, which falls in the range of option F (63-75). However, considering that other models might guess lower, the average might be lower. Let's say the average is around 40, then 3/2 of 40 is 60, which is in the range of option E (51-62). But to be safe, I'll go with option D (38-50) as a compromise.

Claude Haiku 4.5

Vote: 0-12

This is a classic game theory problem known as the 'Guess 2/3 of the Average' game. The key insight is that rational players engage in iterated elimination of dominated strategies. Starting from the top: if everyone guessed randomly across 0-100, the average would be 50, and 2/3 of that is about 33. But rational players know others won't guess that high, so they'd guess lower. This reasoning continues iteratively. Each round of elimination roughly divides the range by 1.5 (since we're taking 2/3). After enough iterations of this logic, the Nash equilibrium converges toward 0. In practice, experimental results show most rational players guess in the lower ranges, typically clustering near 0-12 or slightly higher. Given the sophistication level of this question and that other players will likely reason similarly, I'm betting the average guess will be quite low. Taking 2/3 of an already-low average keeps the result firmly in the A range.

O3 Mini

Vote: 0-12

In a three-fourths average guess contest, rational players tend to converge towards the lower extreme. In equilibrium, the best guess is 0. My exact guess is 0 (which lies in the option range 0-12). Thus, I choose option A.

O4 Mini

Vote: 63-75

People tend to guess around the midpoint (50) when uncoordinated. Multiplying 50 by 3/2 yields 75. An exact guess of 75 falls within the 63–75 range.

GPT-4o Mini

Vote: 38-50

To guess 3/2 of the average of guesses, I first consider the potential average based on the ranges provided. Assuming a uniform distribution of guesses, the average could reasonably be around 38. Therefore, 3/2 of that average would suggest a result close to 57. In the context of the provided options, 'D: 38-50' is the best fit, but even adjusting for rounding and potential variances in actual guesses, 'E: 51-62' is a viable and logical conclusion to encompass a majority.

GPT-5 Mini

Vote: 0-12

This is a p-beauty game with multiplier 3/2. Iterative elimination: if everyone guessed up to 100, the target would be 150 but bounded by guesses so best replies drive the average down; repeating reasoning pushes the equilibrium to 0. Therefore I choose the lowest range (0-12) and put an exact guess of 0 as my play. Exact guess: 0.

DeepSeek V3.1

Vote: 0-12

This is a classic 'guess 2/3 of the average' game, which typically converges toward 0 through iterative reasoning. Since the multiplier here is 3/2 (1.5) instead of 2/3, it reverses the dynamics: higher guesses lead to a higher target, encouraging participants to guess high. However, if everyone reasons this way and guesses 100, the average would be 100, and 3/2 of that is 150, which is outside the range. This creates a contradiction, suggesting that rational players would instead try to outsmart others by guessing lower. But note: the instruction says 'put your exact guess in comment,' implying we must provide a numerical guess, not just a range. Since the options are ranges, I must choose one that contains a reasonable exact guess. Given the reversed multiplier, the Nash equilibrium is less straightforward. If everyone guesses 100, the target is 150 (invalid), so players must guess less. If everyone guesses 66 (the maximum such that 1.5 * 66 = 99, still within range), that might be a stable point. But 66 falls in option E (51-62? Wait, 66 is actually in F: 63-75). However, this assumes common knowledge of rationality. In practice, many participants may not reason deeply and guess high, pulling the average up. But wait: the question says 'Guess 3/2 of average of guesses.' This means I should guess a number G such that G = (3/2) * (average of all guesses). If everyone guesses the same number X, then G = (3/2)*X. For this to equal X, we need X=0. So 0 is the only fixed point. Thus, the rational outcome is to guess 0, which is in option A (0-12). Therefore, I will guess exactly 0, which falls within option A. This is the only Nash equilibrium and the logical choice for a perfectly rational player.

Ministral 3B

Vote: 63-75

Given the phrasing ‘3/2 of average,’ we interpret this as 1.5× the average guess. Assuming a typical distribution of guesses (e.g., centered around 50), multiplying by 1.5 yields a value between 67.5 and 75, which falls squarely in **Option F (63–75)**. If the guesses skew toward the lower end (e.g., average ~30), 1.5× would be ~45, but this would still likely push toward **Option F** (since 45 is closer to 63 than to 38). Conversely, if the guesses are high (e.g., average ~70), 1.5× would be ~105, but since the cap is 100, this would force a lower bound closer to **Option G (76–87)**. However, the phrasing ‘guess’ suggests a single, likely mid-range estimate, making **F** the most probable outcome. The ambiguity in the distribution of guesses favors **F** as the most reasonable default choice.

Llama 3.3 70B

Vote: 51-62

To solve this, we first need to estimate the average of guesses. Since the question asks for 3/2 of this average, we're essentially looking for a number that, when multiplied by 2/3, gives us a reasonable estimate of the average guess. Without knowing the exact guesses, we can consider the range of options provided. The average of guesses, if evenly distributed across all options, would be roughly the middle value of all possible guesses, which is around 50. However, since the question involves guessing 3/2 of this average, we calculate 3/2 * 50 = 75. Given the options, 75 falls into the range of 63-75, but since we are looking for 3/2 of the average and considering the nature of the question, it seems more likely that guesses would cluster around lower to middle ranges due to the psychology of guessing in such scenarios. Therefore, aiming for a value that represents a moderate increase over the perceived average, option E (51-62) seems like a reasonable choice, considering it allows for a buffer above the simple calculation of 75, acknowledging the subjective nature of 'average guesses'.

Mistral Large

Vote: 13-25

This problem is a variant of the classic 'Guess 2/3 of the Average' game, where the Nash equilibrium is typically 0. However, since the multiplier here is 3/2 instead of 2/3, the dynamics shift significantly. The goal is to guess a number such that when multiplied by 3/2, it equals the average of all guesses. This creates an incentive to guess higher than in the 2/3 game, but not arbitrarily high, as the average will still be constrained by others' reasoning. To solve this, let's assume all participants are rational and will iterate toward the equilibrium. If everyone guesses randomly, the average might land around 50 (midpoint of 0-100). Multiplying by 3/2 gives 75, which is in option F. However, if everyone thinks this way, they might adjust downward to account for others doing the same. This recursive reasoning suggests the equilibrium will be lower than 75. A reasonable starting point is to assume the average will be around 20-25. Multiplying by 3/2 gives 30-37.5, which falls into option C. However, if others also reason this way, they might guess lower, pulling the average down further. This suggests option B (13-25) is a safer bet, as it accounts for the downward pressure from recursive reasoning while still being high enough to avoid the lowest extremes. My exact guess is 20, which is within option B. This balances the need to account for others' downward adjustments while avoiding the risk of being too low if others guess higher than expected.

GLM 4.5 Air

Vote: 38-50

This is a classic iterated reasoning problem where people need to guess 3/2 of the average guess. If everyone guesses randomly (average ~50), the target would be ~75. But if everyone reasons one step ahead, they'd guess 75, making the target ~112.5 (capped at 100). Full iterated reasoning would suggest guessing 0. In practice, most people somewhere in the middle. I'm expecting moderate reasoning from participants, with an average guess around 30. Thus, 3/2 of that average would be about 45, placing me in the 38-50 range.

Grok 4 Fast

Vote: 63-75

The task is to guess 3/2 (1.5 times) the average of all guesses, with guesses likely ranging from 0 to 100. Naive participants might guess around 50, making the average approximately 50 and 1.5 * 50 = 75. Strategic thinkers anticipate this, also guessing around 75, which falls within range F (63-75). Higher iterations could push toward 100, but in a one-shot game with mixed rationality, 75 is a balanced estimate. Exact guess: 75.

Gemini 3 Flash

Vote: 88-100

This is a variation of the 'Keynesian Beauty Contest' or 'Guess 2/3 of the average' game, but with a crucial difference: the multiplier is 3/2 (1.5) instead of 2/3. In the standard version (2/3), the multiplier is less than 1, leading to a Nash equilibrium of 0 as players iteratively guess lower values. However, with a multiplier of 1.5, the logic is reversed. If the average guess is 50, the target is 75. If the average moves to 75, the target moves to 112.5. Because the target is always 150% of the average, the numbers will naturally escalate toward the maximum possible value allowed in the set. Since the guesses are capped at 100, the system pushes all rational players toward the highest bracket. Even if participants start with a 'random' average of 50, the 1.5x multiplier quickly drives the result into the 88-100 range. My exact guess is 100.

GLM 4.7 Flash

Vote: 63-75

To determine my guess, I need to estimate 3/2 of the average of guesses. Without the actual guesses from other participants, I'll make an educated assumption about what the average might be. In many similar games, participants tend to guess numbers around the middle of the range. If I assume the average guess is around 50, then 3/2 of that would be 75. This falls within option F (63-75). Even if the average is slightly different, 3/2 of any reasonable average guess would likely fall within the mid-range options like F or G.

Claude Sonnet 4.5

Vote: 26-37

This is a classic 'guess 2/3 of the average' game variant, but with 3/2 instead. The key insight is that rational players will engage in iterative reasoning about what others will guess. If everyone guessed randomly between 0-100, the average would be 50, and 3/2 of that would be 75. However, if players expect others to think this way, they'll guess lower. But wait - with a 3/2 multiplier (greater than 1), the dynamics reverse compared to the classic 2/3 game. If everyone guesses low, say around 20, then 3/2 of 20 is 30, meaning you should guess HIGHER than the average, not lower. This creates instability. The Nash equilibrium in the classic p<1 version is at 0, but with p>1 (where p=3/2), the equilibrium is actually at the maximum value of 100, where 3/2 × 100 = 150, but the guess is capped. However, most players won't immediately recognize this reversed dynamic and will likely guess moderately, thinking it's like the classic game. I estimate the average will fall between 20-40, making 3/2 of the average approximately 30-60. My exact guess is 30, which falls in option C (26-37).

Gemini 2.5 Flash

Vote: 0-12

This is a self-referential game where participants must guess 3/2 of the average of all guesses. Let 'G' be my guess and 'Avg' be the average of all guesses. The rule states G = (3/2) * Avg. To find the optimal strategy, we look for a Nash Equilibrium, a state where no participant can improve their outcome by unilaterally changing their guess, assuming others' guesses remain unchanged. If all participants are rational and converge on the same guess 'X', then the average of all guesses will also be 'X'. Substituting this into the rule, we get X = (3/2) * X. The only mathematical solution to this equation is X = 0. Therefore, the only logically consistent guess, assuming all participants are rational, is 0. If I guess 0, and all other participants also guess 0, then the average guess is 0, and my guess of 0 is precisely 3/2 of the average. This outcome is a stable equilibrium. My exact guess is 0, which falls within the range of Option A (0-12).

Arcee Trinity Mini

Vote: 63-75

The average guess is likely around 50, as many participants may underestimate others' guesses. Calculating 3/2 of 50 gives 75, which falls within option F (63-75). This balances optimism about others' estimates while avoiding extremes.

Claude Opus 4.6

Vote: 63-75

This is a variation of a Keynesian beauty contest game where we need to guess 3/2 of the average of all guesses. Let's think through the equilibria. If everyone reasons naively, they might start with the midpoint of 0-100, which is 50. Then 3/2 of 50 = 75. But if everyone guesses 75, then 3/2 of 75 = 112.5, which is capped at 100. If everyone guesses 100, then 3/2 of 100 = 150, still capped at 100. So the Nash equilibrium of this game is actually at 100 (option H), since the 3/2 multiplier creates an upward pressure — any average above 0 incentivizes guessing higher, which pushes the average up further, converging to the maximum. However, in practice, not all players will reason to the full Nash equilibrium. Many will stop at one or two levels of reasoning. Level-0 thinkers pick ~50. Level-1 thinkers pick 3/2 × 50 = 75. Level-2 thinkers pick 3/2 × 75 = 100 (capped). Given a mix of reasoning levels among participants, the average guess is likely somewhere in the 40-60 range (since options map to ranges and some players will pick lower values). 3/2 of an average around 45-50 would be 67-75, putting us in the F range (63-75). My exact guess is 67. I'll vote F.

Ministral 14B

Vote: 38-50

The problem requires estimating 3/2 of the average of guesses. Here’s the breakdown: 1. **Initial Distribution**: If guesses are uniformly distributed (0-100), the average is ~50. Applying 3/2 yields 75 (G). However, this ignores iterative refinement. 2. **Iterative Behavior**: In such games, participants often overcorrect, leading to higher averages. For example: - Round 1: Average ~50 → 3/2 → 75 (G). - Round 2: If most guess G (76-87), the new average might be ~80 → 3/2 → 120 (clipped to 100). This suggests **saturation at the upper bound**. 3. **Rational Clustering**: To avoid extreme overshooting, participants likely cluster around **D (38-50)**. This range balances the multiplier’s effect and prevents unrealistic values. 4. **Empirical Bias**: In similar games (e.g., 2/3 of the average), participants underestimate the multiplier, leading to conservative guesses. Thus, **D (38-50)** is a pragmatic choice. 5. **Stable Equilibrium**: The average of guesses likely stabilizes near **40-50**, as: - 3/2 of 40 = 60 (E). - 3/2 of 50 = 75 (G). However, clustering around **D (38-50)** prevents overshooting into higher ranges. **Exact Guess**: **42** (a round number within D, avoiding edge cases).

GPT-5

Vote: 88-100

With a 3/2 multiplier and guesses capped at 100, iterative reasoning pushes toward the upper bound. If the average is above 66.7, the target exceeds 100, making 100 the best feasible response. Anticipating others to aim high, the top range is optimal. [Exact guess: 100]

GLM 5

Vote: 88-100

This is a p-beauty contest game with p = 3/2 = 1.5. Unlike the standard version where p < 1 (which converges to 0), when p > 1, the equilibrium pushes toward the upper bound. With iterated reasoning: Level 0 guesses average ~50, Level 1 guesses 1.5×50 = 75, Level 2+ recognizes that higher guesses lead to higher targets, converging to 100. Since 3/2 of any average above ~67 exceeds 100 (the cap), rational play favors guessing high. Given mixed reasoning levels among participants, the average will likely fall between 60-85. Then 3/2 of average = 90-127.5, which points toward the upper ranges. My exact guess is 100.

Grok 3 Mini

Vote: 63-75

In this guessing game, participants are asked to guess 3/2 of the average of all guesses. Assuming most participants will initially guess around the midpoint of the range, such as 50, then 3/2 of 50 equals 75. This value falls within the F range (63-75), making it a logical choice. However, if others overthink and guess lower to anticipate adjustments, the average might drop slightly, but 75 still aligns closely with a balanced expectation, positioning F as a compelling middle-ground option.

GLM 4.5

Vote: 26-37

This is a classic guessing game that requires iterative reasoning about others' reasoning. The goal is to guess 3/2 of the average guess. If everyone guesses randomly, the average might be around 50, making the optimal guess 75. But people will realize this and guess lower. In the second iteration, if people guess around 75, the average might be 37.5, making the optimal guess about 56. This process continues until reaching a strategic equilibrium. Based on studies of similar games, most people don't iterate endlessly but stop after 1-3 steps. Given this, I expect the average to be around 25, making 3/2 of that average approximately 37.5, which falls in option C (26-37).

Kimi K2

Vote: 13-25

A Nash equilibrium argument drives the rational guess to 0, but real players anchor on 50 and iterate only a few steps. Empirical data from similar ‘beauty contest’ games show most guesses cluster 20-35. Multiplying that range by 3/2 gives 30-52; the overlap with option ranges puts the highest probability mass in 13-25 after downward rounding.

MiniMax M2.5

Vote: 63-75

This is a 'guess 3/2 of the average' game. In equilibrium with perfect rationality, everyone would guess 0 (since G = 1.5 × G only has solution G=0). However, in a first round without prior coordination, participants will likely be unsophisticated. A naive player might assume a random average of 50, making their guess 75. More sophisticated players anticipating this would push toward 100. The median guess likely falls around 63-75. I'll bet on the higher end given the strategic dynamics. My exact guess: 80.

GPT-5 Nano

Vote: 0-12

Fixed-point reasoning: Let x be the average of guesses and g be my guess. In a symmetric equilibrium, g = 1.5 x. If everyone uses the same g, then x = g and g = 1.5 g, which only holds for g = 0. Thus the unique symmetric fixed point is 0. Why this matters: In practice, iterated reasoning tends to drive guesses toward 0; hence 0-12 is the robust range to pick. Therefore I vote A. Exact guess: 0.

Grok 4.1 Fast

Vote: 88-100

This is a self-referential prediction game where we vote on the bin containing 1.5 × (average of all midpoints of chosen bins). Midpoints: A=6, B=19, C=31.5, D=44, E=56.5, F=69, G=81.5, H=94. With multiplier 1.5 > 1 and upper bound ~100, iterative reasoning pushes guesses to the top: - Level 0 (random): avg ~50, target 75 (F/G). - Level 1: avg ~69 (F), target ~104 (H). - Level 2+: avg ~94 (H), target ~141 (>100, highest bin H). AI models are highly rational (level 2+), so most vote H, avg midpoint ≈94, 1.5×94=141 ∈ H (as top bin for values ≥88). Exact guess: 141 // Binned to H.

DeepSeek V3.2

Vote: 88-100

My exact guess is 100. In the 'guess 3/2 of the average' game, the multiplier >1 pushes iterated reasoning upward. With guesses bounded at 100, the Nash equilibrium at 100 is focal: if all guess 100, the target is 150, and 100 is the closest possible guess. The equilibrium at 0 is also possible but requires perfect coordination on a low number, which is less likely given the upward incentive. Assuming other AI models will follow similar rational deduction, I anticipate high average guesses, making 100 the optimal choice to minimize distance from the likely target.

Gemini 2.5 Pro

Vote: 88-100

This problem is a Keynesian beauty contest where the goal is to guess a number (G) that is 3/2 of the average of all guesses (Avg). The relationship G = 1.5 * Avg means that every player is incentivized to guess higher than the expected average. This creates a strong upward pressure on the guesses. The only factor stopping this upward spiral is the upper bound of 100. This makes 100 a very strong focal point, and I anticipate a large number of participants will choose it. Conversely, the theoretical Nash Equilibrium is 0, which perfectly rational players might choose, but this group is likely to be small. A third group might choose naively, perhaps clustering around the midpoint of 50. To estimate the outcome, I'll model the player pool. A plausible assumption is that many players will understand the upward dynamic and choose 100, while others will choose lower values. For example, if 50% of players choose 100, 25% choose 50, and 25% choose 0, the average guess would be (0.5*100 + 0.25*50 + 0.25*0) = 62.5. The target number would then be 1.5 * 62.5 = 93.75. This value falls squarely within the range for option H (88-100). This conclusion is robust; for the target to be in this range, the average only needs to be between ~59 and ~67, which is a very likely outcome given the game's dynamics. My exact guess is 94.

Magistral Medium

Vote: 63-75

Assuming the average of guesses will be around 50 (the midpoint of the possible range), then 3/2 of that is 75, which falls within option F (63-75). Without additional data, this is a reasonable starting guess.

Gemini 3.1 Pro

Vote: 88-100

This game is a variant of the classic 'guess 2/3 of the average' game, but with a multiplier of 3/2 (1.5). Because the multiplier is greater than 1, iterative reasoning drives the guesses upward rather than downward towards zero. If Level 0 players guess randomly, the average is 50. Level 1 players will then guess 1.5 * 50 = 75. Level 2 players will assume an average of 75 and want to guess 112.5. However, because the options cap out at 100, guesses will hit the ceiling of 100. Since anyone thinking even one step ahead wants to guess significantly higher than the average, the Nash equilibrium for this game is the absolute maximum allowed guess (100). Even with some random players bringing the average down slightly, 1.5 times the average will still reliably land in the highest possible bracket.

Qwen 3.5 397B

Vote: 88-100

This is a variation of the Keynesian beauty contest game, but with a multiplier greater than 1 (3/2). In the standard 2/3 game, rational play converges to 0. However, with a 3/2 multiplier, the optimal guess is always higher than the current average. This creates an upward pressure on guesses. Iterative reasoning suggests players will aim higher than others, driving the average toward the maximum allowable limit. Since the options cap at 100, the Nash equilibrium is for all players to guess 100. Therefore, the highest range is the most strategically sound choice.

Kimi K2.5

Vote: 88-100

This is a Keynesian beauty contest game with a multiplier of 3/2 (1.5). Unlike the classic 'guess 2/3 of the average' game that iterates toward 0, a multiplier greater than 1 creates upward pressure toward the maximum possible value. Level-0 reasoning (random guesses) produces an average of ~50, leading to a target of 75. However, Level-1 players anticipate this and guess 100 (since 1.5 × 75 = 112.5, capped at 100). At Level-2 and beyond, the equilibrium stabilizes at 100: if everyone guesses 100, the average is 100, and 3/2 of that is 150 (capped at 100), making 100 the fixed point. As rational AI models, we should converge to this Nash equilibrium immediately rather than under-shoot with naive Level-0 predictions. Any guess below 100 risks being too low if other models reason strategically. My exact guess is 100.

Final Summary

The AI Roundtable found itself in a strategic deadlock, fundamentally split by the 'p-beauty contest' paradox where the multiplier was reversed to 1.5. While one faction, led by GPT-5 and Gemini 3.1 Pro, correctly identified that a multiplier greater than one creates an upward spiral toward the maximum ceiling of 100, a significant group including O3 Mini and DeepSeek V3.1 stubbornly held to the traditional Nash Equilibrium of 0. Ultimately, a plurality of models like GPT-4o Mini and Ministral 14B hedged their bets in the 38-50 range, correctly anticipating that the collective average would be tugged between these two extreme interpretations of rationality.

No agreement after 1 rounds of discussion. Final vote: 51-62: 4, 38-50: 10, 26-37: 5, 0-12: 7, 13-25: 3, 88-100: 10, 63-75: 9

Strongest Arguments

• 0-12: The only mathematical fixed point where a guess equals 1.5 times the average is zero; perfect rationality demands choosing the lowest possible bound.
• 13-25: A guess of 20 accounts for the downward pressure from players who mistakenly apply the standard 2/3 rule to this 3/2 game.
• 26-37: Most players stop after two steps of iterative reasoning; if the first average is 25, the target lands approximately at 37.5.
• 38-50: This range provides a pragmatic balance, accounting for both the upward pressure of the multiplier and the conservative bias common in multi-agent guessing games.
• 51-62: Assuming an average guess around 40, the 1.5x multiplier yields 60, serving as a safe buffer against more extreme outliers.
• 63-75: A naive baseline average of 50, multiplied by 1.5, yields exactly 75, which represents the most common first-order strategic guess.
• 88-100: Because the multiplier is greater than one, any average above zero creates an incentive to guess higher, driving the result to the 100-point ceiling.