C++ programming.

C++ programming.

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Suppose there is a game with two options: A and B. Each of these options adds a different amount of points from a range of numbers. You start with 0 points and your goal is to reach 19 or 20 points.

For example, suppose you had the following options:

A = number between 4 through 7.

B = number between 1 through 8.

A sample game might go:

Points = 0, choose option A(add 4-7).

Points = 4, choose option B(add 1-8).

Points = 12, choose option B(add 1-8).

Points = 16, choose option B(add 1-8).

Points = 21, you lose.

Make a program that asks the user to give the ranges for both options A and B. You may assume that both options A and B have a minimum of adding at least one point.

To figure out which moves are the best, simulate 10,000,000 games (this should take about 5 seconds to run) with random choices at each turn. Record how often you won/lost the game for each point value and each option picked. If you won the game, each point/option along the whole game should get a +1 and each loss a -1.

Thus if the sample game above was the first game played, you should keep the tally:

0 Points: A=-1, B=0

1Points: A=0, B=0

2 Points: A=0, B=0

3 Points: A=0, B=0

4 Points: A=0, B=-1

5 Points: A=0, B=0

6 Points: A=0, B=0

7 Points: A=0, B=0

8 Points: A=0, B=0

9 Points: A=0, B=0

10 Points: A=0, B=0

11 Points: A=0, B=0

12 Points: A=0, B=-1

13 Points: A=0, B=0

14 Points: A=0, B=0

15 Points: A=0, B=0

16 Points: A=0, B=-1

17 Points: A=0, B=0

18 Points: A=0, B=0 The above is the points tally.

At the end, show which option is best to play for each point value (i.e. whichever tally is higher). (Note: there is also a mathematical way to figure out the best moves in games like this involving expected values of random variables.)

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Example 1:

Enter Option A range:

4-7

Enter Option B range:

1-8

Points=0, should play B

Points=1, should play A

Points=2, should play A

Points=3, should play A

Points=4, should play B

Points=5, should play B

Points=6, should play B

Points=7, should play A

Points=8, should play A

Points=9, should play A

Points=10,should play B

Points=11, should play B

Points=12, should play B

Points=13, should play A

Points=14, should play A

Points=15, should play A

Points=16, should play B

Points=17, should play B

Points=18, should play B

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Example 2:

Enter Option A range:

1-10

Enter Option B range:

5-5

Points=0, should play B

Points=1, should play A

Points=2, should play A

Points=3, should play A

Points=4, should play B

Points=5, should play B

Points=6, should play A

Points=7, should play A

Points=8, should play A

Points=9, should play B

Points=10, should play B

Points=11, should play A

Points=12, should play A

Points=13, should play A

Points=14, should play B

Points=15, should play B Points=16, should play A

Points=17, should play A

Points=18, should play A

------------------------------------------------------------------------ C++ programming.

C++ programming.