Rent Divider

Because envy-free splits usually aren't unique. For a given room assignment, there's typically a whole range of prices that are all simultaneously envy-free and add up to the total rent — not just one right answer.

For example, with roommates valuing three rooms as (5000, 3000, 2000), (4500, 3000, 2500), and (3500, 3300, 3200) out of a $10,000 rent, the first room's envy-free price can be anywhere from about $4,367 to $4,833 — a $466-wide range — and every price in it is equally valid. "Enter valuations myself" always lands at one particular point in that range (a property of how the underlying math is solved); "ask us one at a time" lands wherever the back-and-forth bidding happens to settle, which is usually a different point in the same range. Neither is more correct than the other.

Not by itself. "Envy-free" doesn't mean nobody would have paid more for your room in the abstract — it means nobody would be better off swapping places with you, taking your room and your price.

Say your room costs $4,366.66 and a roommate says they'd value it at $4,500. That sounds like they're being shortchanged — until you check what they'd give up: if their own room nets them $133.33 (value minus what they pay), and swapping into yours would net them $4,500 − $4,366.66 = $133.34, they're not missing out on anything — those numbers are, for all practical purposes, identical. Your room costs a lot precisely because they also wanted it enough to bid it up that high; the price rose until they stopped caring whether they got it or not.

No — envy-free and equitable (everyone walking away equally happy) are different things, and a split can be the first without being the second. Someone who gets their favorite room can end up with hundreds of dollars more surplus than a roommate who settles for their second choice, and the split can still be fully envy-free: what matters is that nobody wants to trade places, not that everyone's deal is equally sweet.

This tool (like essentially every rent-division method, including the NYT calculator) assumes a dollar is worth the same to you no matter how many you have — so "value minus price" is a single comparable number. A hard budget doesn't work that way: below your limit it's a normal trade-off, and at your limit a room becomes completely unavailable, not just "less good." The math here can't see that cliff.

If a room being above your real budget would matter to you, don't enter your abstract enjoyment of it — cap your number for it at the most you'd actually pay, even if you'd love it more than that in the abstract. Otherwise the tool might assign it to you anyway.

Because a round where nobody wants to switch can still be wrong — at a coarse price step, two people with close-but-different preferences can settle into a pairing that looks stable but isn't the best one (a full swap would make both of them happier, the price gaps just weren't fine enough yet to reveal it). So a round is only offered as a "settled" checkpoint once the same pairing repeats several rounds in a row; if it hasn't, the tool quietly narrows the price step and asks everyone again rather than locking in a result that might be wrong. When preferences are close, refining a few more times past the first checkpoint is worth doing.