In statistics, you generally choose the confidence interval that you want to apply. Then you apply it and calculate the range that the data will be in. It isn't generally the reverse where you take numbers and estimate a confidence interval.

For example, if I want to be 100% confident, I need a large interval. Thus I can be 100% confident that your chest will be dropped between 0 times and 1000 times with 1000 attempts. Of course, that isn't a useful statistic, being 100% confident is just too strict. The lower and lower the confidence interval, the tighter and tighter the actual range will be.

I'm making up numbers here, but I could choose 90% confidence interval and the chest will appear between 5 and 15 times with 1000 attempts. Or I could be 80% confident and maybe then I could say the chest will appear between 6 and 14 times with 1000 attempts. Again, these are just example numbers.

If you want to know that you will get exactly 10 chests out of 1000 attempts, your confidence level is going to be virtually zero if it is truly a random occurrence.

For the close enough math, go here (there are better formulas but they are much more complex):

https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval
Suppose you want to be 95% confident of the result. Then you will be wrong 5% of the time. Thus, alpha = 0.05. From that it is just easier to look up a table and get z = 1.959963 when alpha = 0.05 (source of that number is beyond the scope of my post). If you think that you will get the chest 1% of the time, then p = 0.01. Enter into the formula in the link above and you get that you are 95% confident that the chest will appear between 0.38% and 1.61% of the time (in other words, you are 95% confident that the chest will appear 4 to 16 times with 1000 attempts).