高频题（0）
1. Optimal Strategy for a Probability-Based Machine Game
You have a row of machines numbered from 1 to 20. Each machine has a 50% chance of being genuine and a 50% chance of being fake. A genuine machine has a 50% chance of giving you money when you play it, with the cost being 1 dollar and the payout being equal to the machine's number (e.g., machine number x pays x dollars). Each machine can only pay out once. What should your strategy be to maximize your earnings?
2. Probability of Winning a Dice Game
In a dice game, two players roll two six-sided dice. The sum of the dice is even for one player to win, and exactly seven for the other player to win. If there is no winner, the dice are rolled again until a winner is determined. What is the probability of the first player winning? The interviewee's answer was 3/4.
3. Dice Game Strategy with Doubling Bet
In the dice game, there is a rule that allows you to spend $10 to double the number on your dice face after each roll. What strategy would you use to play this game?
4. Expected Dollar Gain from Dice Game
If you win the dice game mentioned above, you earn dollars equal to the number you rolled. What is the expected dollar gain from this game?
5. Dice Game Winning Probability
You and an opponent each roll a 100-sided dice once. You roll first, and whoever rolls the higher number wins. What is the probability of you winning?
