Percentage isn't exactly an exact science so your results are correct. In theory 100 of 100 could still get the dagger, even though the percentage of that happening would be extremely low.

The question is: what do you need?

If you want 10% chance of getting the dagger the calculations you've made will do. If you want a more exact 1 out of 10 people will get the dagger, you should maybe make a random number between 1 and 10 and if it's number 6, the 6th person around will get it. And then do it again when the 10 first have passed.

Many solutions, which depends on what you really want :-)
A 10% chance will create variable results like you've got.
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Eriken