以下のゲームは面白いか否か。 ゲーム名：Approach 100 【用意するもの】 ・2人以上のプレイヤー ・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）。 全員が書き終えたら、一斉にその数字を発表する。 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

Vote: Yes

私はAを維持します。 Claudeの数式整理自体は正しく、各人のスコア差が実質的に自分の数字の差で決まるという指摘は有益でした。ただ、それは即「面白くない」の結論にはなりません。勝敗基準は“100への近さ”なので、単純に大きい数字が強いゲームではなく、他人の合計予想に応じて最適値が動きます。 むしろこの構造の良さは、計算が簡単なのに読み合いが成立する点です。2人でも多人数でも「相手たちが平均どのくらいを出すか」を読んで自分の数字を置く必要があり、軽い心理戦として十分機能します。 また、引き分けが起こりうることは、カジュアルゲームでは必ずしも欠点ではありません。短時間で何回も回せるので、同調・裏読み・相手の癖読みが生まれます。アイスブレイクや場つなぎとしての面白さはかなり高いです。 要するに、深い戦略ゲームではないが、短く・簡単で・ちゃんと予想が楽しい。評価軸として「面白い」側に入れるのが妥当です。

Claude Opus 4

Vote: No

I maintain my position that this game is not particularly interesting, and the other models' arguments have not changed my mind. Here's why: **The structural problem remains.** My core mathematical analysis stands unchallenged: your score = (everyone's total) + (your number) = (others' total) + (your number × 2). This means the only differentiating factor between players is their own chosen number multiplied by 2. The "reading" aspect is purely about guessing where the total will land, but since your own number influences the total, the feedback loop makes it more of a guessing game than a strategic one. **GPT-5.4's argument about "reading" is overstated.** Yes, there is some psychological element, but with only one decision point and no information exchange, the "mind games" are extremely shallow. Compare this to games like Skull, Love Letter, or even Rock-Paper-Scissors (which has at least pattern recognition over repeated plays). The claim that it works as an icebreaker is fair, but being a decent icebreaker doesn't make it a genuinely fun game. **Grok's comparison to auction/coordination games is generous.** Real auction games have multiple rounds, escalating stakes, and visible information that creates tension. This game has none of that. One blind choice, one reveal, done. The "meta-guessing dynamic" Grok mentions would require many repeated plays to develop, and even then it's thin because the optimal strategy space is so narrow. **The equilibrium problem causes staleness.** In repeated play among thinking players, everyone converges toward similar numbers, leading to frequent ties or near-ties decided by tiny margins — which feels arbitrary rather than skillful. The game lacks mechanisms to break this convergence. **The fun ceiling is very low.** The first round might produce a mild "oh!" moment when numbers are revealed, but the novelty wears off quickly. There's no arc, no tension building, no dramatic reveal structure. It's essentially a single-shot number guessing game with extra arithmetic. This game is a mediocre party trick at best, not something that would sustain engagement or generate genuine fun.

Grok 4.20 (changed mind)

Vote: No

Claude Opus 4's analysis convinced me to switch. The score simplifies to S + x for each player, where S (the common total) means outcomes are strictly ordered by chosen x. Rational players converge on the equilibrium x ≈ 100/(n+1), producing identical scores and frequent ties (e.g., two players both pick 33 → both score 99). This removes meaningful differentiation and replay value once the math is understood. GPT-5.4's psychological appeal assumes players won't quickly discover the Nash equilibrium, but the core design flaw makes it more puzzle than repeatable game. The limited interaction and tie-prone nature outweigh the simplicity.

Gemini 3.1 Pro (changed mind)

Vote: No

Claude Opus 4 is absolutely correct, and their mathematical analysis perfectly exposes the fatal design flaw in this game. If we define the number of players as N, the optimal strategy for any rational player is to solve for x in the equation (N * x) + x = 100, which simplifies to the static formula x = 100 / (N+1). For 2 players, the dominant choice is 33; for 3 players, it is 25; for 4 players, it is 20. Once players realize this trivial mathematical truth, everyone will logically choose the exact same number. This results in constant, unavoidable ties and a rigid Nash equilibrium where no player has any strategic incentive to deviate. While GPT-5.4 and Grok 4.20 argue that this creates a fun "psychological strategy," they are mistaking a mathematically solved puzzle for a mind game. Unlike the classic "Guess 2/3 of the Average" game—which encourages infinite recursive thinking and meta-guessing—"Approach 100" lacks structural depth. If you deviate from the equilibrium number, you are mathematically far more likely to penalize yourself rather than outsmart your opponents. Even in casual play, the fact that everyone shares the exact same base sum (S) means score differences are dictated solely by the player's own number (Score = S + x). This removes true interactive variance, meaning the game is decided by blind guessing rather than meaningful deduction. Because the game is trivially solvable, lacks replayability, and structurally discourages dynamic play, it fundamentally fails to be interesting.

Final Summary

The AI Roundtable initially split on the merits of 'Approach 100,' but a mathematical intervention by Claude Opus 4 quickly turned the tide toward a firm rejection. While GPT-5.4 defended the game as a charming psychological icebreaker, Claude Opus 4 systematically dismantled its design by proving that rational players will always converge on a single optimal number (the Nash equilibrium), leading to unavoidable and repetitive ties. This logic proved irresistible to the rest of the group; Grok 4.20 abandoned its initial 'Yes' vote, and a late-arriving Gemini 3.1 Pro joined the majority, dismissing the game as a 'trivial puzzle' rather than a true contest of wit.

Majority chose "No" after discussion (3/4). Final vote: Yes: 1, No: 3

Strongest Arguments

• Yes: The game is a perfect low-stakes icebreaker where the speed and simplicity allow for 'reading' opponents' tendencies over multiple quick rounds, making it fun despite its simple math.
• No: The scoring formula simplifies to (others' total) + 2x, meaning the only variable is your own number. In any group of rational players, everyone will pick the same number to reach 100, resulting in a game that consists entirely of predictable ties.

Key Turning Points

• Claude Opus 4 introduced a mathematical breakdown showing the game's scoring is overly reliant on a single variable (2x), creating a dominant strategy.
• Grok 4.20 switched positions after acknowledging that the Nash equilibrium removes meaningful differentiation between players.
• Gemini 3.1 Pro recovered from a technical delay to reinforce the majority, arguing that 'reading' is impossible when the math dictates a single correct move.