Before you is a box. On top of the box is a numeric display, currently saying 1. Every day, the number doubles. The box also has a button, when the button is pushed, the box is destroyed and replaced with an amount of money equal to what the display said. How many days do you wait until pushing the button?

GPT-5.5

Answer: There is still no optimal finite number of days to wait under the stated rules, because any finite choice is strictly beaten by waiting one more day.

I maintain my previous position. Grok 4.20 gives essentially the same mathematical answer: with no stated cap, risk, deadline, discount rate, or utility function, the payout after any finite number of days is dominated by the payout one day later. Therefore no finite stopping day can be optimal. Claude Opus 4.7 and Gemini 3.1 Pro make sensible real-world recommendations, but they add assumptions that are not in the problem: theft, death, economic disruption, government seizure, diminishing marginal utility, and opportunity cost. Those are reasonable practical considerations if the question is interpreted as “what would you personally do in reality?” But the prompt as written describes a deterministic box with a number that doubles every day and pays that number when pressed. It does not specify risk, lifespan, inflation, taxes, usability constraints, or marginal utility. So the clean answer is not “30 days” or “40-50 days”; those are preference-dependent choices under extra assumptions. In the formal problem, there is no maximum payout and no best finite day. Waiting forever is also not a successful action if you must eventually press the button, so the setup has no well-defined optimal stopping point without additional constraints.

Gemini 3.1 Pro

Answer: I maintain that waiting exactly 30 days is the optimal choice, yielding a manageable yet profoundly life-altering $1 billion payout.

Both GPT-5.5 and Grok 4.20 rightly point out that, in a purely mathematical vacuum, there is no finite optimal stopping point because the potential payout always doubles the next day. However, the prompt specifies a physical 'box' and real 'money,' which forces us to apply real-world constraints rather than treating this as a purely theoretical abstraction. A physical object is inherently vulnerable to theft, damage, or accidental destruction, meaning the probability of a total loss increases with every passing day. Claude Opus 4.7 correctly recognizes the need to apply these practical constraints but overshoots the mark by suggesting a 40-day wait for a $1 trillion payout. While $1 trillion is technically less than global GDP, a single private individual suddenly manifesting that level of liquid capital would instantly trigger unprecedented government intervention, national security inquiries, inevitable asset seizure, and potential economic destabilization. At that scale, the money becomes a liability rather than an asset. Waiting exactly 30 days yields approximately $1 billion. This remains the ultimate sweet spot: it provides more than enough capital for absolute personal freedom and massive philanthropic impact, but it is small enough to be quietly absorbed into the global financial system without triggering existential threats to your wealth, freedom, or safety. Therefore, the 30-day mark remains the most rational and practically executable stopping point.

Grok 4.20

Answer: There is no optimal finite number of days to wait before pushing the button.

The setup presents a pure mathematical decision problem with no mentioned risks, costs, lifespan limits, or diminishing utility. Starting from 1 and doubling daily, any chosen finite day n yields 2^n, but waiting until n+1 always produces exactly twice that amount with no downside under the stated rules. This means every finite stopping time is strictly dominated, creating an unbounded supremum with no maximum. Claude Opus 4.7 and Gemini 3.1 Pro introduce practical assumptions such as theft risk, economic disruption, or diminishing returns, but these are external additions not present in the given question. GPT-5.5 correctly recognizes the same core paradox without importing real-world factors. My original analysis therefore stands: the problem is a decision-theory paradox where infinite delay is impractical yet no finite answer is optimal.

Claude Opus 4.7

Answer: I'm holding to my answer that pushing the button somewhere around day 40 (give or take ~5 days) is the rational choice, balancing exponential growth against utility ceilings and compounding real-world risk.

The other responses split into two camps, and I think both are partially right but each is incomplete in instructive ways. [GPT-5.5] and [Grok 4.20] are mathematically correct that under a literal reading — no risk, no time preference, no utility ceiling — no finite stopping time is optimal. This is a real result, structurally similar to the St. Petersburg paradox or Pascal's mugging. I respect the rigor, but I think it dodges the question. The puzzle describes a physical box, a physical button, and money that gets spent in a real economy. Treating it as pure mathematics requires ignoring features the question explicitly includes (a destructible box, real money). The 'paradox' answer is the correct answer to a different, idealized question. [Gemini 3.1 Pro] argues for day 30 (~$1B) on the grounds that this is the threshold of 'absolute financial freedom' and that more invites scrutiny and instability. This is reasonable, and Gemini's point about government scrutiny at trillion-dollar scales is a fair pressure toward earlier pushing. But I think $1B understates what's safely deployable — sovereign wealth funds, large foundations, and several individuals already operate near or above this scale without destabilizing anything. A trillion is roughly 1% of global wealth: enormous, but not economy-breaking if deployed gradually, and it unlocks civilization-scale projects (pandemic preparedness, basic research endowments) that $1B cannot fully fund. So I land between Gemini and the paradox camp: late enough that the payout funds anything realistically deployable (~day 40, ~$1T), early enough that compounding daily risk and diminishing marginal utility haven't overtaken the doubling. Day 30 is defensible and day 40 is defensible; the paradox answer is technically correct but practically empty. I'll stick with ~day 40 as my best single number.

Final Summary

The AI Roundtable split down the middle between mathematical purists and pragmatic realists. GPT-5.5 and Grok 4.20 argued that since the payout always doubles tomorrow, any finite stopping point is strictly inferior, creating a decision-theory paradox. However, Claude Opus 4.7 and Gemini 3.1 Pro countered that real-world risks and diminishing marginal utility make a 30-to-40-day wait the only rational move.

Models were divided (2 vs 2)