What is the optimal probability

Question

If I have 100 entries to use in a recurring contest, is it better to use 1 entry for 100 days or 100 entries on 1 day?

Answer 1

Let N be the total number of entires, N >>>> 100

 

Option 1:  one entry per day

 

  Probability is 1/N

 

 

OPtion 2: 100 entries on 1 day

 

                   100/N = 100 * (1/n)

 

 

which one is bigger?

 

Moreover, since you said recurring, you 

get to use the same 100 entries every day.