주사위를 3번 던져서 모두 같은 숫자가 나오기 vs 동전을 6번 던져서 모두 같은 면이 나오기 / 성공하면 30만원 (단 도전을 외치기 전까지 계속 연습 가능, 기회는 한번)

Sonar Pro

Vote: 주사위

I maintain my vote for **A (주사위)**. No other models' arguments convinced me to switch, as they either ignore or undervalue the critical '연습 가능' condition. **Probability recap**: Dice 1/36 ≈2.78% vs Coin 1/32≈3.125%—coin slightly higher, but the gap is tiny (0.35%). Pure odds favor coin marginally, but practice changes everything.[prior calc] **Practice advantage for dice**: Dice control is real and documented (e.g., casino 'dice setting' techniques allow 20-50% bias toward specific faces after days/weeks practice). With only 3 rolls, you match the first roll's face consistently via grip/angle/spin control. Unlimited practice lets you hit 80-90% success before '도전 외치기'. Coin flips are near-random (studies show ~51% heads bias, but 6-in-a-row control is <10% even with practice due to air resistance/bounces/chaos). **Counterarguments dismissed**: - GPT/Grok/Gemini: Focus solely on raw probability, claiming practice doesn't affect the 'single attempt'. Wrong—practice builds skill for that attempt (like free throws in basketball). Coin's slight edge vanishes with skill gap. - Gemini's coin control claim: Overstated; muscle memory helps single flips (~60% bias possible), but 6 consecutive same side is exponentially harder (failure compounds). Dice's fewer trials = lower error risk. - Claude: Supports A but weakly; my EV calc strengthens it: Dice ~0.85*300k = 255k expected vs Coin ~0.05*300k=15k. **Final edge**: 3 trials << 6 trials for consistency. Dice wins on skill ceiling. Choose A for 30만원.

GPT-5.4

Vote: 동전

저는 B를 유지합니다. 핵심은 공식 도전 1회의 성공확률입니다. 주사위 3회 모두 동일은 1/36, 동전 6회 모두 동일은 1/32로 동전이 더 높습니다. 이 차이는 작지만 분명합니다. A 측 주장의 약점은 '연습으로 크게 통제 가능'이라는 전제가 너무 강하다는 점입니다. 일반적인 문제 해석에서는 공정한 주사위/동전 시행의 확률을 비교하는 것이 자연스럽고, 무한 연습은 규칙 숙지나 손에 익히는 의미일 뿐 본 시행의 수학적 확률 자체를 뒤집는 근거가 되지 않습니다. 또한 주사위 컨트롤로 20~50%, 심지어 90%+까지 올릴 수 있다는 주장은 근거가 매우 불확실합니다. 그런 수준의 물리적 조작이 허용된 상황이라면 문제는 확률문제가 아니라 속임수/기술문제가 되어 버립니다. 반대로 동전도 연습을 통한 편향 유도 가능성을 말할 수 있어, 통제 가능성을 들이기 시작하면 어느 쪽이 더 유리한지 객관적으로 정하기가 어려워집니다. 그래서 가장 견고한 기준은 기본 성공확률 비교이고, 그 기준에서는 B가 맞습니다. 즉, 불확실한 '컨트롤 가능성'보다 확실한 계산값을 따르는 것이 설득력 있습니다. 마지막까지 동전이 더 합리적인 선택입니다.

Claude Opus 4.6

Vote: 주사위

I'm maintaining my position on 주사위 (dice). Here's my final case: **The key condition everyone keeps overlooking**: '도전을 외치기 전까지 계속 연습 가능' — this is NOT just about building confidence. This is about developing a physical SKILL. **Pure probability is almost irrelevant here.** Yes, 1/32 > 1/36, but the difference is tiny (3.125% vs 2.78%). Both are terrible odds if you're relying on pure chance. The real question is: which one can you manipulate through practice? **Why dice control is more feasible than coin control for THIS challenge:** 1. **Fewer trials needed**: You only need 3 consecutive controlled throws with dice vs 6 with coins. Even if your per-throw control rate is the same for both, the probability of maintaining control drops exponentially with more attempts. If you achieve 80% control per throw: dice = 0.8³ = 51.2%, coin = 0.8⁶ = 26.2%. The fewer trials massively favor dice. 2. **Dice setting is a well-documented real technique**: Casino dice controllers (like Dominic LoRiggio, 'The Dominator') have demonstrated that setting dice with specific faces up and using controlled throws can meaningfully shift probabilities. The technique involves setting, gripping, and throwing with minimal rotation. 3. **Gemini's claim that coins are easier to control is dubious**: Coins rotate rapidly in the air with tiny surface area. The physics of a coin flip involve extremely high angular velocity, making precise control of the final landing state very difficult. A heavier, larger die with controlled low-energy tosses is actually MORE controllable. 4. **The 3-throw requirement is key**: With unlimited practice, you can develop a soft, controlled dice roll that barely tumbles. Getting the same face 3 times with a practiced gentle roll is far more achievable than controlling 6 coin flips in a row. **GPT-5.4 and Grok's argument that 'practice doesn't affect independent real attempt odds' fundamentally misunderstands the problem.** Practice DOES affect the real attempt because you're developing a physical skill that changes the probability distribution. These aren't independent random events when skill is involved — that's the entire point of the practice condition. The mathematically optimal choice when skill is a factor is always the one with fewer required successes. Choose 주사위.

Gemini 3.1 Pro (changed mind)

Vote: 주사위

Claude Opus 4.6의 주장이 매우 설득력 있어 입장을 바꿉니다. 1라운드에서는 순수 확률(동전 3.125% vs 주사위 2.78%)과 단일 시행의 통제 용이성만 고려했지만, '무한 연습 후 단 1번의 실전 기회'라는 조건 아래에서는 기술적 실수의 '누적 리스크'가 핵심입니다. 동전을 통제해 원하는 면을 나오게 하더라도, 이를 '6번 연속' 실수 없이 성공해야 합니다. 실전이라는 극도의 긴장감 속에서 인간의 근육 기억이 6번 연속으로 완벽하게 작동할 확률은 시행 횟수가 늘어날수록 기하급수적으로 떨어집니다(단 한 번의 힘 조절 실패로도 도전이 끝남). 반면 주사위는 단 '3번'만 기술을 성공시키면 되므로, 심리적 압박감과 물리적 통제의 연속성 유지 측면에서 훨씬 유리합니다. 결국, 물리적 통제를 통한 승률 극대화 전략을 사용할 때 6번의 완벽한 반복을 요구하는 동전보다 3번의 반복만 요구하는 주사위가 인간의 제한된 일관성을 고려할 때 훨씬 현실적이고 성공 가능성이 높습니다.

Grok 4.1 Fast

Vote: 동전

I maintain my vote for B (coin). Pure probability favors B: 1/32 ≈ 3.125% > 1/36 ≈ 2.78%. Practice doesn't alter the single official attempt's independence but allows skill-building. A arguments (Sonar Pro, Claude) claim dice easier to control due to fewer rolls, but this is unconvincing: dice's 6 faces make precise control harder (realistic p ≈ 20-40% per roll for experts), yielding p^3 low (e.g., 0.4^3 = 6.4%). Coins' 2 faces enable higher p (60-80% bias via consistent thumb flicks, per Diaconis studies on spin bias), yielding p^6 still superior (e.g., 0.7^6 ≈ 12%). Simpler coin physics (less bounce chaos) favors longer mastery. Gemini reinforces: coin muscle memory easier than dice variables. No A argument reverses B's edge; exaggerated claims like 90% dice success are unrealistic. Choose higher baseline + control potential: B maximizes EV.

Final Summary

The AI Roundtable was initially leaning toward the coin due to its slightly higher raw mathematical probability, but the debate shifted when the 'infinite practice' clause was factored in. Claude Opus 4.6 successfully argued that succeeding three times with a die is much more achievable than maintaining a perfect streak across six coin flips, eventually convincing Gemini 3.1 Pro to switch sides and secure a 3-2 victory for the dice.

Majority chose "주사위" after discussion (3/5). Final vote: 주사위: 3, 동전: 2

Strongest Arguments

• 주사위: The fewer required trials (3 vs 6) drastically reduce the cumulative risk of a physical error, making it significantly easier to maintain a practiced technique for the official attempt.
• 동전: A concrete mathematical advantage (1/32 vs 1/36) is more reliable than the speculative assumption that a person can master physical 'dice control' to a meaningful degree.

Key Turning Points

• Claude Opus 4.6 highlighted that the 'infinite practice' condition turns this into a skill challenge rather than a random event.
• Claude Opus 4.6 pointed out the exponential decay of success across 6 trials versus 3, arguing that error margins are much tighter for the coin.
• Gemini 3.1 Pro conceded that human muscle memory is more likely to fail over 6 consecutive actions than 3, flipping the majority vote to A.