User blog:MachineGunSuper/Breaking the odds really hardly?

I had a hard time figuring out the correct words  to use in this blog post but:

-pick any number, rational, irrational, just any number as long as it's finite.

-now, there will be a random number picked as well. If it's yours, then you win a prize.

But wait, what are the odds that it will be yours?

If you have to guess a random number between 1 and 10, the odds are 1/10

If it's 1-100, the odds are 1/100

If it's 1 to x, the odds are 1/x

But if it's 1-, then are the odds... 1/?

It wouldn't really work, as Infinity is not a number.

Let's follow this pattern instead:

If it's 1-100, then most likely the random number is in the tens.

If it's 1-1000, then most likely the number is in the hundreds.

If 1-10000, then most likely it is in the thousands.

etc

So, if it's 1- then the number will be... ? This would imply that  is finite, which it obviously isn't.

Another solution is that the random number would be finite BUT, it would be so big and so so massive, any of the currently uncomputable numbers would be overshadowed millions and millions of times.

An idea I thought of is: could we actually make a function out of this to generate numbers nobody thought of reaching before?

Pls tell me the solution to everything above this line