Loot Box Expected Value
Expected value per pull versus cost, and the chance of a rarity in N independent pulls.
Expected value is the average return of one pull if you could repeat it many times — not the next pull. Independent pulls, no pity. This is for reading the odds, not a reason to spend.
Expected value vs cost
-$0.68
EV $1.32 against $2.00 per pull.
EV per pull
$1.32
≥1 Legendary in 10
18.29%
Drop rates add up to 100%. They cover the full pull.
Worked example
A $2 pull with an 80% common worth $0.20, an 18% rare worth $2, and a 2% legendary worth $40 has an expected value of $1.32. Against the $2 cost, the pull is worth about −$0.68 on average. The chance of at least one legendary in 10 independent pulls is about 18%.
FAQ
- What does expected value mean?
- Each rarity’s chance times its value, added up. It is the average return of one pull if you could repeat it many times, not what the next pull will pay.
- How is the chance within N pulls worked out?
- One minus the chance of missing every time: 1 − (1 − rate)^N. Each pull is independent. There is no pity.
- Is this an encouragement to buy?
- No. It is a way to see that a rare prize can still leave the average pull below its price.