Puzzle Lab / Probability Puzzles
The Infinite Startup Payout
A probability puzzle about expected value, real-world constraints, and why math without context lies politely.
Puzzle
Challenge first.
A fair coin is tossed until the first heads. If heads appears on toss n, you win 2^n rupees. The expected value is mathematically infinite. Should you pay any finite amount to play?
Hints
- The expected value calculation is not the whole decision.
- Ask who can actually pay the largest outcomes.
- Utility is not linear in money.
Solution
The formal expected value diverges, but real decisions have bankroll limits, payout limits, risk preferences, and diminishing utility. The puzzle separates algebra from decision-making.