All of these huge numbers are basically un-comparable ergonomically to me. Why not make the distribution 1-10k instead?
Also, there is really no reason to have multiple boxes you have to click. You could just have a single "next" button along with a counter to show how many choices you have left before you run out.
'Next' button along with '# samples left' display would be much clearer.
Also, if the largest drawn so far were highlighted, manual play would be easier.