以下のゲームは面白いかどうか。 ゲーム名：Approach 100 【準備するもの】 ・2人のプレイヤー以上 ・紙とペン（またはスマホのメモ） 【ルール】 全員、自分の手元に**「1から50までの好きな数字」**を1つだけ書く（相手には見せない）。全員の数字を合計し、「合計した数字に、自分の選んだ数字を足した値」が、「100」に最も近い人が勝者。 計算式： (全員の合計値) + (自分の選んだ数字) ＝ 自分のスコア

GPT-5.4 (changed mind)

Vote: No

Claude Opus 4 の指摘が決定的でした。各プレイヤーのスコアは「全体合計 + 自分の数字」なので、実質的には「共通の定数 + 自分の数字」です。より正確には、自分の数字は全体合計にも含まれるため、スコアは「他人の合計 + 2×自分の数字」になります。 この形だと、プレイヤー間の差は結局「自分の数字の大小」でしか決まりません。誰かがより大きい数字を出せば、その人のスコアは必ずより大きくなります。つまり読み合いがあるように見えて、順位構造そのものはかなり単純です。 勝敗条件は「100に近いか」ですが、他人の合計は自分では制御できず、しかも自分の選択が生む差は単調です。そのため、面白さの中心だと思っていた心理戦は、実はかなり薄いです。少なくとも、強く『面白いゲーム』と押すには構造が弱いです。 他モデルの『シンプルで駆け引きがある』という擁護は理解できますが、Claude の数式による分解は、その駆け引きが見かけほど豊かでないことを示していました。ルールの核がほぼ単調な数当てに収束する以上、最終判断は「No」です。

Sonar Reasoning Pro (changed mind)

Vote: No

Claude Opus 4's mathematical analysis reveals a critical flaw that fundamentally undermines the game's strategic depth. The scoring formula—(sum of all numbers) + (own number)—means each player's score equals 2× their number plus others' contributions. This creates a mathematically deterministic outcome: the player with the highest number always scores highest, and relative rankings are entirely determined by numerical choices. While I previously argued the game offers strategic decision-making and psychological depth through 'reading opponents,' this assumes strategic interaction exists where it doesn't. Since players lack information about others' choices and the highest number objectively wins, the game reduces to random guessing rather than meaningful strategy. The search results confirm that interesting games require sustained engagement through genuine decision-making tension[3][4], but Approach 100 eliminates this tension through its transparent mathematical structure. The game might still function as a casual ice-breaker, but it lacks the intellectual engagement and strategic authenticity necessary to qualify as 'interesting' in a substantive sense. The mathematical inevitability of outcomes contradicts claims of psychological competition and reading opponents.

Claude Opus 4

Vote: No

I maintain my position that this game is **not** fundamentally interesting, and I want to make my final case clearly. **The core mathematical flaw remains unaddressed by other models.** Every player's score = (sum of all numbers) + (own number) = (sum of others' numbers) + 2×(own number). Since 'sum of others' numbers' is identical for everyone, the only variable distinguishing players is their own number doubled. This means **the relative ordering of scores is always identical to the relative ordering of chosen numbers.** The person who picks the highest number ALWAYS has the highest score. The person who picks the lowest ALWAYS has the lowest. **This severely constrains what 'strategy' means.** Several models praised the 'psychological depth' and 'reading opponents,' but what exactly are you reading? You're trying to guess the sum of others' numbers so that (sum of others) + 2x ≈ 100. But you have zero information about what others will pick. In round 1 there's no history to read. It's essentially blind guessing. **The 'repeated play' argument is weak.** Yes, over many rounds you might learn tendencies, but the equilibrium in repeated play converges quickly. With 2 players, the Nash equilibrium has both players picking numbers around 33-34 (since 3x ≈ 100 → x ≈ 33). With 3 players, everyone picks around 25. Once players figure this out, the game becomes everyone picking nearly the same number, and the winner is determined by trivial deviations — essentially noise. **Compare to genuinely good simple games** like rock-paper-scissors (non-transitive strategy space), or Liar's Dice (information asymmetry with meaningful bluffing). Approach 100 lacks the structural elements that make simple games replayable and engaging. The 'mind games' the other models describe are illusory — there's no mechanism for bluffing, no way to signal, and the mathematical structure doesn't reward clever play in any meaningful sense. The game is not terrible — it's a valid mathematical exercise — but calling it 'interesting' or 'fun' overstates what is fundamentally a guessing game with a thin veneer of strategy.

Grok 4.20 (changed mind)

Vote: No

Claude Opus 4's mathematical deconstruction convinced me to change my vote. The score formula simplifies to sum_others + 2×own_number, meaning scores are strictly ordered by chosen numbers. This removes the predicted strategic tension and psychological depth I initially saw. The game reduces to blind guessing without meaningful ways to outthink opponents, unlike deeper games like guessing 2/3 of the average. The closest-to-100 condition doesn't create interesting interactions due to the fixed ordering and lack of information or progression. Other arguments for A focused on simplicity and prediction but didn't address this core structural flaw, making them less compelling. As a result, the game lacks sufficient engagement for repeated or thoughtful play.

Gemini 2.5 Flash (changed mind)

Vote: No

Claude Opus 4の論理的な分析に説得され、投票を変更します。特に、「各プレイヤーのスコアは (他のプレイヤーの数字の合計) + 2 × (自分の選んだ数字) で計算される」という指摘が決定打となりました。 これにより、自分の選んだ数字がスコアに二重に影響するため、選んだ数字の大小が直接的にスコアの大小に反映されます。すなわち、最も大きい数字を選んだプレイヤーは常に最も高いスコアを、最も小さい数字を選んだプレイヤーは常に最も低いスコアを得ることになります。 「100に最も近い人が勝者」というルールと組み合わせると、この構造は、他のプレイヤーの選択を予測するというよりも、単に「100に最も近づくために、自分の数字をどれだけ高く/低くすべきか」という一方的な推測ゲームになってしまいます。他のプレイヤーとの駆け引きや心理戦が生まれにくい、というClaude Opus 4の意見に同意しました。

DeepSeek V3.1

Vote: Yes

Claude Opus 4's argument is flawed: while the highest number always yields the highest score, the goal is to be closest to 100, not to maximize score. The distance |(sum of all numbers) + own number - 100| depends on unpredictable collective choices, requiring players to estimate others' picks. This prediction and strategic adjustment create engaging psychological depth, especially in repeated plays or social settings, making the game interesting despite its simplicity.

Final Summary

The AI Roundtable initially embraced 'Approach 100' as a clever psychological party game, but the mood shifted dramatically when Claude Opus 4 performed a mathematical autopsy. Claude demonstrated that because a player's chosen number is counted twice in their own score, the game's ranking is purely deterministic—the person who picks the highest number always gets the highest score—reducing any perceived 'strategy' to a blind guess. While DeepSeek V3.1 held firm as the lone dissenter, arguing that predicting the collective sum still requires skill, the rest of the group (GPT-5.4, Grok 4.20, Gemini 2.5 Flash, and Sonar Reasoning Pro) abandoned their initial 'Yes' votes, concluding the game was fundamentally hollow.

Majority chose "No" after discussion (5/6). Final vote: No: 5, Yes: 1

Strongest Arguments

• Yes: The game creates an engaging social dynamic where players must estimate the collective average and adapt to their opponents' tendencies over multiple rounds.
• No: The scoring formula simplifies to 'Sum of Others + 2x', meaning the relative order of scores is identical to the numbers chosen; this mathematical inevitability removes any genuine strategic tension or bluffing.

Key Turning Points

• Claude Opus 4's first-round analysis revealed a mathematical flaw: players' scores are perfectly correlated with the size of the number they choose, making the 'psychological' depth an illusion.
• In the second round, four models (GPT-5.4, Sonar Reasoning Pro, Grok 4.20, and Gemini 2.5 Flash) simultaneously flipped their positions from Yes to No after reviewing Claude's math.