Loot Box Expected Value Calculator
Expected value of a loot box, case, pack or crate from its drop chances and item values — three quick tiers or your own full drop table — compared with the price plus any key cost, after marketplace fees. Shows the house edge, the spread per box, what N boxes cost and return, the chance of at least one rare and of breaking even, boxes and money per rare, a pity guarantee and the rare value needed to break even.
How it works
EV = Σ (drop chance × item value × (1 − marketplace fee)); net = EV − (box cost + key cost); return = EV ÷ cost; house edge = 1 − return; SD per box = √(Σ p·v² − EV²); P(at least one rare in n) = 1 − (1 − p)ⁿ; boxes per rare = 1 ÷ p; with pity every N boxes: p_eff = p ÷ (1 − (1 − p)ᴺ); break-even rare value = (cost − EV of the other drops) ÷ p_rare
Expected value weights every possible drop by its probability and sums the results, giving the average payout of a box over the long run. Use the three quick tiers — the leftover probability falls to the common drop, and the total is capped at 100% so the odds stay valid — or switch to your own list and paste a full drop table with each item’s published chance and value. A separate key price and the cut a marketplace takes when you sell both count against you, so they are included. Almost every real loot box has an expected value below its price — that gap is the house edge — and the spread per box is large because most of the value sits in rare drops. That is why the calculator also looks at a run of boxes: what you spend, what you should expect back, the chance of at least one rare (or the rarest item on your list), and the chance that the items are worth at least what you paid, worked out from the full drop distribution rather than the average. For pity systems that guarantee a rare within a set number of boxes, the long-run rare rate is raised accordingly. A positive net here usually means you have overvalued the items.
Worked example
A $2.50 box: 5% rare at $30 = $1.50, 20% uncommon at $3 = $0.60, and the remaining 75% common at $0.50 = $0.375. Expected value is $2.475, just under the $2.50 cost, for a net of about −$0.03 per box — a 1% house edge. Opening 10 boxes costs $25 and returns $24.75 on average, but the spread is large ($6.39 per box): only 40.1% of players get at least one rare in 10 boxes, and the items are worth at least $25 for 40.1% of them. A rare takes 20 boxes ($50) on average and 45 boxes to be 90% sure. With a 15% selling fee the same box is worth $2.10.
Sources: Expected value (Wikipedia)
Frequently asked questions
What is expected value?
The probability-weighted average of all outcomes. If you opened thousands of identical boxes, the average value you received per box would converge on this figure — even though any single box is all-or-nothing.
Why is it usually below the cost?
Publishers set drop rates so the average payout is less than the price; the difference is their margin. A box with expected value above its cost would let players profit indefinitely, which no operator allows.
Should I trust in-game item values?
Only if items are tradeable for real or in-game currency. Cosmetic-only rewards have no resale value, so their worth is purely subjective and the money-based expected value does not apply. If you sell on a marketplace, enter its fee under More options — values then reflect what you actually receive.
Can I enter a full drop table?
Yes. Switch the drop table to “My own list” and put one item per line as name, chance in percent and value, for example “Covert, 0.64, 25”. Chances that add up to less than 100% leave the remainder as worthless; more than 100% is rejected.
How many boxes until I get a rare?
On average 1 ÷ the rare chance — 20 boxes at 5% — but that is not a guarantee: 90% of players have one within 45 boxes and 1 in 100 still has none after 90. A pity system caps the wait; enter its count under More options.
What is the chance I come out ahead?
Because most value sits in rare drops, the typical result of a few boxes is below the expected value. The calculator works out the exact chance that the items from your boxes are worth at least what you spent by adding up the drop distribution box by box; only for very long lists or thousands of boxes does it fall back to a close normal approximation.
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This calculator is for educational purposes. Double-check important results before acting on them.