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1 22. (10 marks) In a game, three players A, B and C take turns to...
In a game of tennis if 2 players are tied at 40 it is called “deuce”....
In a game of tennis if 2 players are tied at 40 it is called “deuce”. You must win 2 points in a row in order to win the game at this point. If you win 1 point and then lose the next then you go back to deuce. Say players A and B are at deuce and player A wins a point then they are in the state called Advantage A. If A wins the next point then the...
In a game of tennis if 2 players are tied at 40 it is called “deuce”....
In a game of tennis if 2 players are tied at 40 it is called “deuce”. You must win 2 points in a row in order to win the game at this point. If you win 1 point and then lose the next then you go back to deuce. Say players A and B are at deuce and player A wins a point then they are in the state called Advantage A. If A wins the next point then the...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players pl...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects a Red marble first wins the gam...
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects a Red marble first wins the game. If Player 1 draws the first marble, what is the chance that Player 1 wins?
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects...
Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 m...
Consider a game in which two players, Fred and Barney, take turns removing matchsticks from a pile. They start with 21 matchsticks, and Fred goes first. On each turn, each player may remove either one, two, or three matchsticks. The player to remove the last matchstick wins the game. (a) Suppose there are only 5 matchsticks left, and it is Fred’s turn. What move should Fred make to guarantee himself victory? Explain your reasoning. (b) Suppose there are 10 matchsticks...
A game between two players A and B consists of 10 rounds. In each round, two...
A game between two players A and B consists of 10 rounds. In each round, two fair dice are rolled together. Let X denote the sum of two dice. If X>5, A wins. The player who wins the maximum number of rounds, wins the game. What is the probability that B wins the game?
Answer the following Nim game style questions. (Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone w...
Answer the following Nim game style questions.
(Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone wins. A player removes either one stone or p stones, where p is a prime dividing the number of stones in the pile at the start of the turn For which n does the First Player have a winning strategy? A winning strategy for the First Player...
explain the answer with clear handwriting please Questions: 1. [10 pts] There are two players A...
explain the answer with clear handwriting please
Questions: 1. [10 pts] There are two players A and B. The probability that A wins a game is 0.4, and the probability that B wins a game is 0.6. We randomly choose one player between A and B and let the chosen player play 10 independent identical games. An amount Xin dollars) is rewarded to each win, where X has a continuous uniform distribution over (0,60). Let X be the total amount...
(1 point) Three brothers play a game with a set of cards numbered 1 thru 10,...
(1 point) Three brothers play a game with a set of cards numbered 1 thru 10, they draw two cards with replacement and add the cards values. Scott will win if the sum of the cards is 13, Dave will win if 16, and Jim if 4. They will select 2 cards with replacement, then reshuffle until a winner is declared Part (a) What is the probability that on any particular two-card draw there is no declared winner? If rounding...
Exercise 1. Two players, 1 and 2, take turns choosing numbers; 1 goes first. On his...
Exercise 1. Two players, 1 and 2, take turns choosing numbers; 1 goes first. On his turn, a player may choose any number between 1 and 10, inclusive, and this number is added to a running total. When the running total of both players’ choices reaches 100, the game ends. The player whose choice of number takes the total to exactly 100 is the winner. (i) Who wins the game when we solve it using backwards induction? (ii) Provide a...
In a game of tennis if 2 players are tied at 40 it is called “deuce”. You must win 2 points in a row in order to win the game at this point. If you win 1 point and then lose the next then you go back to deuce. Say players A and B are at deuce and player A wins a point then they are in the state called Advantage A. If A wins the next point then the...
1. NIM game. This is a different version or easier version of NIM game Consider a pile of 5 matchsticks. Two people take turns removing 1 or 2 sticks each time from this pile. Suppose both players play smartly (nobody plays a fool move trying to let the opponent wins. But there is only one winner anyway) a)If the person getting the last stick wins, will the first player win? Why? Show the steps the first and second player will...
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects a Red marble first wins the game. If Player 1 draws the first marble, what is the chance that Player 1 wins?
10. (16 points) A jar contains 2 Red marbles and 5 Green marbles. Players 1 and 2 take turns withdrawing marbles from the jar (without replacing them). Whoever selects...
Answer the following Nim game style questions.
(Robert's Game) In this game, two players take turns removing stones from a pile that begins with n stones. The player who takes the last stone wins. A player removes either one stone or p stones, where p is a prime dividing the number of stones in the pile at the start of the turn For which n does the First Player have a winning strategy? A winning strategy for the First Player...
explain the answer with clear handwriting please
Questions: 1. [10 pts] There are two players A and B. The probability that A wins a game is 0.4, and the probability that B wins a game is 0.6. We randomly choose one player between A and B and let the chosen player play 10 independent identical games. An amount Xin dollars) is rewarded to each win, where X has a continuous uniform distribution over (0,60). Let X be the total amount...
(1 point) Three brothers play a game with a set of cards numbered 1 thru 10, they draw two cards with replacement and add the cards values. Scott will win if the sum of the cards is 13, Dave will win if 16, and Jim if 4. They will select 2 cards with replacement, then reshuffle until a winner is declared Part (a) What is the probability that on any particular two-card draw there is no declared winner? If rounding...
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