The St. Petersburg paradox involves a coin-tossing game where payouts double with each flip, leading to an infinite expected value. To prevent the organizer from going bankrupt, the author proposes a model where the organizer issues shares instead of fixed currency. In this system, the bank's capital remains stable because payouts dilute the value of existing shares rather than depleting cash reserves.
The model limits the game's duration to a fixed number of flips, such as 24, ensuring the maximum payout and expected value remain finite. Participants pay a deposit in shares, which the bank destroys to increase the value of remaining shares. If the payout is lower than the deposit, the difference benefits shareholders, effectively creating a risk-adjusted mechanism similar to insurance.
The author compares this mechanism to Bitcoin mining, noting that both systems share underlying mathematics. In the proposed game, the probability of a specific payout sequence mirrors the difficulty of finding a hash with a certain number of leading zeros. The length of the game is determined by the bank's total share count, allowing for scalability while maintaining solvency.
