Mrs Heathen and I have a big-ass jar on our dresser into which we place our change nightly. It accumulates at a fairly rapid clip, so despite the jar’s size we end up redeeming it about twice a year. It’s usually between $250 and $300, depending on how full we let it get before we head to the Coinstar machine — which is a pretty clever thing, and a very savvy business model, we believe; they take a (fair) cut of the free money you’re bringing in, and you leave with 91% of the cash.

This whole thing got us wondering, however, on account of we’re powerful geeky: How close could we get to the value of the jar if we estimated based on the jar’s weight (adjusting for the weight of the empty jar, natch), the known individual weight of each denomination of coin, and the estimated distribution of American coinage?

Presumably, the biggest barriers to this would be (a) getting a good estimate of the distribution and (b) finding a precise enough scale, as coins are very, very light. With those in hand, the next obstacle would be distribution variance — i.e., how much does our household distribution differ from some national “normal” value?

Anyway, after turning in a mostly-full jar today ($297. plus 4 Sac dollars and a new nickle that Coinstar knows not what to make of), we discovered that the machine gives out its tally of denominations, so we figure we’ll use this for a jumping-off point: