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In Exercises 15–20, decide whether the game is strictly determined. If it is, give the players’ optimal pure strategies and the value of the game. [HinT: See Example 4.]
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- The point spread in sports betting is essentially a handicap towards the underdog, for example the point spread of the game this weekend between Cincinnati Bengals and Kansas City Chief in Cincinnati +3 or Kansas city is -3. If you place a bet on the bengals, Kansas city must win by less than 3 points for your bet to wim. If Kansas city wins by exactly 3 points then the bet is a push and your stake is returned. Now suppose you placed a bet of 100 dollars on the bengals on a website where they charge 10% commission (if you win $90) when line was CIncinati +3 or Kansas City -3 According to previous studies the final margin of victory for NFL team in a given game can be approximated as a normal variable with a mean of points spread line and a standard deviation of 12, however suppose the bengals just announced that their star receiver Chase would return this weekend which adds two points in favour of the bengals. In other words, we suppose that the winning margin now for Kansas City this…arrow_forwardedo exercises 17 and 18 in section 8.1 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data:If the animal is in the woods on one observation, then it is twice as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is three times as likely to be in the meadows as the woods on the next observation.Assume that state 1 is being in the meadows and that state 2 is being in the woods.(1) Find the transition matrix for this Markov process. (2) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (3) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?arrow_forwardAssume that the group has a portfolio of 6 stocks. There is 30% chance that any one of these stocks will increase in value. Find the proability that four of the six stocks increase in value.arrow_forward
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- 2.)A jar contains 2 red, 3 green, and 6 blue marbles. In a game a player closes their eyes, reaches into the jar and randomly chooses two marbles. The player wins the game if at least one of their marbles is red. Suppose it costs $1 to play the game and the winning prize is $3. Mathematically analyze this game and determine if it is in your financial interest to play the game.arrow_forwardFind the optimum strategy for player B. Choose the correct answer below and fill in the answer box(es) to complete your choice. OA. The game is strictly determined. Player B should choose column (Type a whole number.) OB. The game is not strictly determined. Player B should choose column 1 with probability, column 2 with probability ,and column 3 with probability (Type integers or simplified fractions.) The value of the game is (Type an integer or a simplified fraction.) # D L' 1. (10) Morearrow_forwardQ. 4 GAME THEORYarrow_forward
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