I need help with my game theory homework for my intro to AI class, any help is a

Question

I need help with my game theory homework for my intro to AI class, any help is appreciated!

1. Games I (10 points) A friend of yours offer to play with you the three games below that involve rolling a single 6-sided die: Game 1: You pay 3 cents and win in the cent amount on the roll. Game 2: You pay 1 cent and win 2 cents if the roll is odd. Game 3: You pay 2 cents and win 8 cents if the roll is at least a 5. Which game is the best in terms of expected payoff, and which game is the worst? Explain your reasoning or show your work.

Explanation / Answer

Game 1: Probability of winning or staying on no-loss = Chances of getting 3 or more than 3 / 6

= 4/6 = 66% you are on safe side. you either get more or 3 cents back

Game 2 Probability of win = Chances of getting odd number{1,3,5} / 6

=3/6 = 50% chance of winning the double amount ( you get 2 cents for 1 cent paid)

Game 3 Probability of win= chances of getting 5 or more than 5 {5,6} / 6

= 2/6 = 33% chance of winning Thrice the amount invested.

As the game can be played any number of times it is safe to go with Game 1, as you have a higher probability of win

By playing GAME 1maximum number of times you can get maximum payout.

If you wish to play a minimum number of times and get a maximum payout...

Game 2 can be preferred as it has 50%chances of winning the double amount.

Game 3 is the worst of all.. as it has very low chances of winning

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