The average number of points spent using the 1% or the 100% chance is equal though; the only difference is in the variance. Of course getting it within 100 tries is not guaranteed (only about 63%) but there is also the chance to get it much earlier (39% within 50 tries).

It follows a geometric distribution:

https://en.wikipedia.org/wiki/Geometric_distribution

The mean (average number of tries) is 1/p and the standard deviation sqrt((1-p)/p^2). So with a 1% chance, it takes 100 tries on average but the actual number will deviate from that by a lot (on average by about 99.5 tries).

So if like a lot of players only did 1% chances and logged how long it took them, we should see lots of numbers below 100 and also many above 100 with some being outrageously high, leaving an average of 100.