iterators – Iterative function – Mathematica Stack Exchange

I would like to write a bit of code that does the following.

Pick a random number from 1 to 20 (inclusive)

then if that number is < 15, stop

if that number is > 15 pick 2 numbers from 1-20, and check the highest number from the pair.

do the same check, if greater than 15, pick 3 numbers, then 4 then ectara.

f(n_) := Max(RandomInteger({1, 20}, n))

I made this function to give me the highest result from n rolls but I’m not sure how to iterate it .

thank you