How to create a probability by a given percentage?

Question

I'm trying to create a percentage-based probability for a game. E.g. if an item has a 45% chance of a critical hit, that must mean it is 45 of 100 hits would be critical.

First, I tried to use a simple solution:

R = new Random();
int C = R.Next(1, 101);
if (C <= ProbabilityPercent) DoSomething()

But in 100 iterations with a chance of e.g. 48%, it gives 40-52 out of 100. Same goes for 49, 50, 51. So, there is no difference between these "percents".

The question is how to set a percentage of e.g. 50, and get strictly 50 of 100 with random? It is a very important thing for probability of rare item finding with an opportunity to increase a chance to find with an item. So the buff of 1% would be sensinble, because now it is not.

Sorry for my bad English.

Answer 1

You need to think only in terms of uniform distribution over repeated rolls.

You can't look over 100 rolls, because forcing that to yield exactly 45 would not be random. Usually, such rolls should exhibit "lack of memory". For example, if you roll a dice looking for a 6, you have a 1-in-6 chance. If you roll it 5 times, and don't get a six - then: the chance of getting a 6 on the next roll is not 1. It is still 1 in 6. As such, you can only look at how well it met your expectation when amortized over a statistically large number of events... 100,000 say.

Basically: your current code is fine. If the user knows (because they've hit 55 times without a critical) that the next 45 hits must be critical, then it is no longer random and they can game the system.

Also; 45% chance of critical hit seems a bit high ;p