So long as you don't have to turn it in for serious credit in Math class... I have one solution: Cheat.
Since you're the one pouring b/w balls in jars, what does it matter? You were the one who placed them in the first place, so you've already tainted the "pure" aspect of random. For the purposes of my short discussion though, I assume Random is purely random, not pseudo--like how humans can toss heads 100 times in a row with practice.
Thinking on a broader level, there's no difference between randomly picking between 2 containers (jars) holding the same overall content and randomly picking from 1,100 containers holding the same overall content. We tend to think too narrowly... limiting our own options too much by the most natural "common sense" methods we're most comfortable in.
Change your perspective: What's the difference between randomly picking between 100 balls or randomly picking between 2 then randomly picking 50 of those two.
In Mathematical proof-like equations terms:
Given: Chance Random 100, and Chance of Random 2 (jars) * Random of 50
Since Random * Random = Random,
--like true infinity * infinity = infinity or true zero * zero = zero.
There's no difference, no "maximizing" at all and if you think you can you're just blinding yourself with smoke and mirrors-- or just near-sightedness. Borrow my pair of glasses, see from my perspective and there's no difference.
*Yawn. If anyone would care to prove me wrong successfully, I'd like to see it. Until then, there is no spoon here.
Since you're the one pouring b/w balls in jars, what does it matter? You were the one who placed them in the first place, so you've already tainted the "pure" aspect of random. For the purposes of my short discussion though, I assume Random is purely random, not pseudo--like how humans can toss heads 100 times in a row with practice.
Thinking on a broader level, there's no difference between randomly picking between 2 containers (jars) holding the same overall content and randomly picking from 1,100 containers holding the same overall content. We tend to think too narrowly... limiting our own options too much by the most natural "common sense" methods we're most comfortable in.
Change your perspective: What's the difference between randomly picking between 100 balls or randomly picking between 2 then randomly picking 50 of those two.
In Mathematical proof-like equations terms:
Given: Chance Random 100, and Chance of Random 2 (jars) * Random of 50
Since Random * Random = Random,
--like true infinity * infinity = infinity or true zero * zero = zero.
There's no difference, no "maximizing" at all and if you think you can you're just blinding yourself with smoke and mirrors-- or just near-sightedness. Borrow my pair of glasses, see from my perspective and there's no difference.
*Yawn. If anyone would care to prove me wrong successfully, I'd like to see it. Until then, there is no spoon here.