Pinball Simulation

This program simulates a pinball machine as illustrated in the Figure below. The ball is dropped at the top of the machine. When the ball rolls down, it strikes fixed pins and bounces to the left or to the right in a random fashion. At the end, the ball lands in one of the seven pockets. In this example, we’ll write a program to find the probability of landing in each pocket. We’ll drop the ball 1000 times and count how many times it lands in each pocket.

Figure: Illustrating the pin ball machine

We’ll use a variable, named pos, to refer to the ball’s position as it rolls down. The ball starts in the middle with pos=4 (i.e., above pocket 4). In its way down, the ball will hit six levels of pins. At each level, the ball hits a pin and bounces left or right with equal probability. If the ball bounces to the right, its position will increase by 0.5, otherwise its position will decrease by 0.5. The complete program is shown in the Listing below.

Listing:

 2 ' Simulates a pinball machine

 3

 4 For N = 1 To 7 ' seven pockets

 5   count[N]=0   ' zero balls in each pocket

 6 EndFor

 7

 8 For ball = 1 To 10000 ' Drops 10,000 balls. For each ball,

 9   pos = 4                      ' Starts in the middle

10   For level = 1 To 6    ' Drops six levels

11     If (Math.GetRandomNumber(2) = 1) Then

12       pos = pos - 0.5

13     Else

14       pos = pos + 0.5

15     EndIf

16   EndFor

17  

18   pos = Math.Floor(pos)         ' Makes it an integer

19   count[pos] = count[pos] + 1 ' Adds ball to pocket

20 EndFor

21

22 For N=1 To 7                         ' Displays result

23   TextWindow.WriteLine("Pocket" + N + ": " + count[N])

24 EndFor

    

Output:

Pocket1: 155

Pocket2: 920

Pocket3: 2338

Pocket4: 3131

Pocket5: 2343

Pocket6: 949

  

As you can see most of the balls landed in pocket 3.

 

TRY IT OUT!

Modify the pin-ball simulation program to have 15 pockets and 20 levels. Run the simulation to see what you get!

 

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- Ninja Ed & Majed Marji