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a) Consider a set of r red cards and b black cards. b) The betting strategy is to always bet on red. c) If my guess is correct, I'll get back 2 times the amount I bet. For example, if I bet 10 Baht on red and the card turn out to be red, I'll bet back 20 Baht making 10 Baht profit. d) The betting amount is calculated with the following algorithm: i. If I win a turn I'll bet w times the previous bet on the next turn. ii. But, if I lose this turn, I'll bet / times the previous bet. For example, if the bet for this turn is 10 Baht, and I win this turn, the betting amount for the next turn would be 10w. Whereas if I lose this turn, then the betting amount for the next turn will bet 101. 2/3- 7.1) Show that if w+ 1 = 2 then the result of the game would be independent of the permutation of the card. 7.2) What would be the total gain/lose amount if w+ 1 = 2. (Answer in terms of r, b, w, and m the starting bet.) 7.3) (Optional) If there are 20 black cards and 18 red cards. What should w be to guarantee the maximum gain. (You will may computer for this. Numerical answer is OK.)

a) Consider a set of r red cards and b black cards. b) The betting strategy is to always bet on red. c) If my guess is correct, I'll get back 2 times the amount I bet. For example, if I bet 10 Baht on red and the card turn out to be red, I'll bet back 20 Baht making 10 Baht profit. d) The betting amount is calculated with the following algorithm: i. If I win a turn I'll bet w times the previous bet on the next turn. ii. But, if I lose this turn, I'll bet / times the previous bet. For example, if the bet for this turn is 10 Baht, and I win this turn, the betting amount for the next turn would be 10w. Whereas if I lose this turn, then the betting amount for the next turn will bet 101. 2/3- 7.1) Show that if w+ 1 = 2 then the result of the game would be independent of the permutation of the card. 7.2) What would be the total gain/lose amount if w+ 1 = 2. (Answer in terms of r, b, w, and m the starting bet.) 7.3) (Optional) If there are 20 black cards and 18 red cards. What should w be to guarantee the maximum gain. (You will may computer for this. Numerical answer is OK.)

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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a) Consider a set of r red cards and b black cards. b) The betting strategy is to always bet on red. c) If my guess is correct, I'll get back 2 times the amount I bet. For example, if I bet 10 Baht on red and the card turn out to be red, I'll bet back 20 Baht making 10 Baht profit. d) The betting amount is calculated with the following algorithm: i. If I win a turn I'll bet w times the previous bet on the next turn. ii. But, if I lose this turn, I'll bet 1 times the previous bet. For example, if the bet for this turn is 10 Baht, and I win this turn, the betting amount for the next turn would be 10w. Whereas if I lose this turn, then the betting amount for the next turn will bet 101. →→2/3 7.1) Show that if w+ 1 = 2 then the result of the game would be independent of the permutation of the card. 7.2) What would be the total gain/lose amount if w+ 1 = 2. (Answer in terms of r, b, w, I and m the starting bet.) 7.3) (Optional)If there are 20 black cards and 18 red cards. What should w be to guarantee the maximum gain. (You will may computer for this. Numerical answer is OK.)
Transcribed Image Text:a) Consider a set of r red cards and b black cards. b) The betting strategy is to always bet on red. c) If my guess is correct, I'll get back 2 times the amount I bet. For example, if I bet 10 Baht on red and the card turn out to be red, I'll bet back 20 Baht making 10 Baht profit. d) The betting amount is calculated with the following algorithm: i. If I win a turn I'll bet w times the previous bet on the next turn. ii. But, if I lose this turn, I'll bet 1 times the previous bet. For example, if the bet for this turn is 10 Baht, and I win this turn, the betting amount for the next turn would be 10w. Whereas if I lose this turn, then the betting amount for the next turn will bet 101. →→2/3 7.1) Show that if w+ 1 = 2 then the result of the game would be independent of the permutation of the card. 7.2) What would be the total gain/lose amount if w+ 1 = 2. (Answer in terms of r, b, w, I and m the starting bet.) 7.3) (Optional)If there are 20 black cards and 18 red cards. What should w be to guarantee the maximum gain. (You will may computer for this. Numerical answer is OK.)
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