Code in C++

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

1 Points: 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

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.)

Note: in this example the choices points below 10 are random and suggested move for points=16 will not be optimal

Example 1 (user input is underlined): Option A range: 4 7 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