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 casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11 , the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the players loses? (Type an integer or a simplified fraction.) (b) What is the probability that the player wins? (Type an integer or a simplified fraction.) (c) What is the probability that the player progresses to the 'point' phase? (Type an integer or a simplified fraction.)arrow_forwardThe casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11, the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the player loses? The probability is nothing. (Type an integer or a simplified fraction.) (b) What is the probability that the player wins? The probability is nothing. (Type an integer or a simplified fraction.) (c) What is the probability that the player progresses to the 'point' phase? The probability is nothing. (Type an integer or a simplified fraction.)arrow_forwardThe 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_forward
- The casino game is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the 'come out' phase, and the second is called the 'point' phase. If the 'come out' roll of 2, 3, or 12, the shooter loses. If the 'come out' roll is a 7 or 11, the shooter wins. Otherwise, the game progresses to the 'point' phase. Complete parts (a) through (c) below. (a) What is the probability that the player loses?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_forwarda.Discuss five assumptions of game theory b.Explain three steps required to find a saddle pointarrow_forward
- Q. 4 GAME THEORYarrow_forwarda. In CSE230, there were 2 assignments this semester. The probability that you would NOT get above average marks in the first and the second assignments are 0.3 and 0.4 respectively. But if someone does NOT get the above average marks in the first assignment, the probability of NOT getting above average marks in the second assignment becomes 0.6. What is the probability of NOT getting above average marks in both the assignments? b. In a rational world, husband and wife are arguing over a matter. The probability of the husband being Wrong is 0.15 and the probability of the wife being Wrong is 0.13. And the probability of husband being Wrong provided that wife is Wrong is 0.18. What is the probability that the wife is Wrong provided that the husband is Wrong?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_forward
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