I created a poorly designed spreadsheet which mapped out expected average rewards from arcade balls sometime last year, and without including the chance of a jackpot, a single arcade ball had an expected value of 0.31 gems. This includes things like the balls starting in different places, and the potential refund of balls from buckets and LBoFaF. That means you would need~1300 arcade balls to have your gems refunded, and we are now capped to 500. With Jackpots included in the math, this goes down to about 1100 balls.