Sure, I can help you write a test case generator for this problem. Here is the code for the test case generator:

```python
import random

def tcgen():
    # Generate a random number for X and Y within the given constraints
    X = random.randint(0, 10**18)
    Y = random.randint(0, 10**18)
    
    return X, Y

# For demonstration, let's generate a few test cases
for _ in range(5):
    print(tcgen())
```

This function `tcgen` generates random values for \(X\) and \(Y\) within the given range of \(0 \leq X, Y \leq 10^{18}\). Each call to `tcgen` will produce a new pair of \(X\) and \(Y\) which can be used as input for the game described in the problem statement.

If you'd like to see a few sample outputs from this generator, you can run the loop at the bottom of the code that prints out several test cases.

Here is more detailed implementation, including the sample output generation:

```python
import random

def tcgen():
    # Generate random values for X and Y within the given range
    X = random.randint(0, 10**18)
    Y = random.randint(0, 10**18)
    return X, Y

def main():
    # Generate a number of test cases
    num_cases = 10
    for _ in range(num_cases):
        X, Y = tcgen()
        print(f"{X} {Y}")

if __name__ == "__main__":
    main()
```

This script will generate 10 test cases and print them in the format expected by the problem statement. Each line will contain two integers \(X\) and \(Y\) separated by a space. You can adjust `num_cases` to generate more or fewer test cases as needed.