Brainteaser iconBrainteaser - Meta Arbitrage

Meta Arbitrage
You have an opportunity to invest in Meta stock, which is predicted to either double in value or lose 50% of its value by tomorrow. Additionally, you have a chance to bet with a friend on whether the stock will rise or fall. The bet offers a 1:1 payout. Let's denote two investment strategies: \( A \) for buying (long) Meta stock and \( B \) for betting with your friend on the stock's movement (up/down). The goal is to ensure that your profit is the same regardless of the stock's movement. What should be the lowest round bet amounts for \( A \) and \( B \) to achieve a consistent profit?