Sure, here is some pseudo code to help you understand how to write a Python script to play the FizzBuzz game for a user-specified number of iterations:
``` 
1. Get user input for the number of iterations to run the game for (N).
2. Loop from 1 to N.
3. For each number in the loop:
   a. Check if the number is divisible by both 3 and 5.
   b. If yes, print "FizzBuzz".
   c. If not, check if the number is divisible by 3.
   d. If yes, print "Fizz".
   e. If not, check if the number is divisible by 5.
   f. If yes, print "Buzz".
   g. If not, print the number itself.
``` 
Here is how you can translate the above pseudocode to Python code:
```
N = int(input("Enter the number of iterations to run the game for: "))
for i in range(1, N+1):
    if i % 3 == 0 and i % 5 == 0:
        print("FizzBuzz")
    elif i % 3 == 0:
        print("Fizz")
    elif i % 5 == 0:
        print("Buzz")
    else:
        print(i)
```
This code should ask the user to input the number of iterations they want the game to run for, and then print out the corresponding output for each number from 1 to N.
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