Alice and Bob Case Study - Highest Card Wins - IT Computer Science Assignment Help

Assignment Task :

1. Q1) Alice and Bob are playing the following game: Both players put $1 each in the pot. Then both players draw one card each from a deck consisting of just three cards; an Ace, a King and a Queen. Alice may then check or bet $1. If Alice checks, the highest card wins the pot. If Alice bets $1, then Bob may fold (Alice wins the pot) or call – add $1 to the pot – and the highest card wins. We now look specifically at the situation where Bob has the King. Obviously, Alice will bet $1 if she has the Ace, but how often should Alice bet with the Queen and how often should Bob call? What is the value of this game – or rather the situation where Bob has the King? 

Comments:  

This can be solved in many different ways. It is obvious that Alice will always bet with a red card, so the task is to find out how often she will bet with a black card, and how often Bob will call. Solving shows that Alice should bet 1/3 of the time with a black card, and that Bob should call 2/3. With these strategies, Alice is expected to win $1/3 per game. 

Q2)

Alice and Bob are playing the following game: Both players put $1 each in the pot. Then both players draw one card each from a deck consisting of just three cards; an Ace, a King and a Queen. Alice may then check or bet $1. If Alice checks, the highest card wins the pot. If Alice bets $1, then Bob may fold (Alice wins the pot) or call – add $1 to the pot – and the highest card wins. We now look specifically at the situation where Bob has the King. Obviously, Alice will bet $1 if she has the Ace, but how often should Alice bet with the Queen and how often should Bob call? What is the value of this game – or rather the situation where Bob has the King? 

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