Is this probability calculation and product correct?

[late pumice]

I need to calculate the chance of:

If 29 people and yourself each roll a 100-sided die, what is the chance of you rolling higher then the all other 29 people?

This is the result I got:
½²⁵⁻¹≈5.96×10⁻⁸

[viscid bolt]

Why 25 in the exponent?

In any case, this is not right. Heuristically, there are thirty people rolling, so your chance of winning is about 1/30. It doesn't work out to that because of ties, but 1/30 is about the right order of magnitude.

[hallow geyser]

My idea for an answer (excuse poor notation):
You roll a 100-sided die, meaning you can get results ranging from 1 to 100. The mean of these results is 50,5 meaning you can be assumed to roll a 50,5 which is impossible and all that but works in the context. So, you rolled a 50,5. Now for you to win everyone has to roll 50 at max, which is 1/2 of a hundred (quick logic jump there sorry I'm lazy). Now, everyone of the 29 people has to roll this 1/2 of the dice. So, the answer should be around 1/2^29, give or take some accuracy mistakes I may have made. I am essentially asking you to check my answer as well because I know 1/2^29 is pretty far from 1/30 and I agree with the logic for that.

[viscid bolt]

That's a good idea and a good explanation. Unfortunately, it doesn't work.

The probability of winning with a roll of 50 is nearly zero, as is the probability of winning with a 12, but the probability of winning with 98 or 99 is very high. You can't take the average roll and say that its probability of winning is the average probability of winning.

[hallow geyser]

If I did that right, it should open a calculator program or whatever it's called and show the brute-forced answer. If I'm not mistaken, we are all off by quite a lot with our guesses.

[viscid bolt]

Can you share a screenshot of the calculation?

[olive terrace]

$\sum_{n=1}^{100} P(\text{max}=n)*(100-n) \ \approx 2.85747$

[thorn jungle]

someone1010

[olive terrace]

So, not even close

1/30 is a good guess tbh