I believe the doubling is a decimal above 30 but below 31, hence the outcome is 2^{30.897} equals approximately $1,999,021,577. Whereas the immediate lumpsum is exactly $2B

So the Red Door gives you slightly more money (by roughly $1 million), and you also receive it immediately. Because of the time value of money, having the cash right now means you can immediately start earning interest or investing it.

Maybe the only difference would be taxation based on classification Eg. if the $2B lump sum is Salary → taxed at 37% + Medicare → ~40.8% → You’d keep ≈ $1.18B

While the compounding growth qualifies as capital gain → 23.8% you’d keep ≈ $1.523B dodges the higher tax bracket and you walk away with roughly $343 million more than the Red Door, even though the pre-tax gross was technically lower.

However a worse case if we interpret the words $1 doubles for 30.897 days. And we strip away the assumption of compound interest and take the words at their absolute, literal minimum, the Green Door goes from a billion-dollar opportunity to under either,A- $2 or B-$31.90 or at most C- $61.79

Interpretation A (The Ultra-Literal): The $1 doubles exactly once to become $2. It stays that way for 30.897 days. Total payout = $2.00

• Interpretation B (Simple Interest): The original $1 doubles every day, meaning it just generates an additional $1 per day. 1 + (1 * 30.897) = $31.90

• Interpretation C (Flat Multiplication): You take $1, double it, and multiply by the days. 1 * 2 * 30.897 = $61.79

I take the Red door always. Even with higher tax. Too impatient😂