here's a fun maths problem for you:
in Balatro, each hand gains a positive number of Chips and Mult, which are then multiplied together to get your final score. but on the Plasma Deck, the rules are altered such that Chips and Mult are "balanced", averaging the two before scoring.
does this "balancing" step always give you a better score than you would have gotten without the Plasma Deck? how would you prove this?
(I'll share my answer in a day or so)
@clarfonthey i thought about this
before
let x be the chips and y the mult
xy would be the score normally while ((x+y)/2)2 is the plasma deck score
xy - ((x+y)/2)2 is equal to ((x-y)/2)2, a positive number or zero (if x and y are real).
hence the plasma deck scores lower unless the chips and mult are the exact same number, in which deck scores the exact same as normal.
re: potential solution
@wallhackio your reasoning is correct but you swapped the sign in your solution and actually the answer is that (½(x+y))² - xy = (½(x-y))², meaning that it's always positive unless x=y, in which case it's zero
re: potential solution
@clarfonthey shit i did do that, my bad
re: potential solution
@wallhackio that said this is what I would consider the simplest solution, so, well done
my first attempt involved calculus because I was trying to prove that the result never decreased, but I didn't think to just subtract the two values and see what I got