Loot Box Economics: Gacha Pull & Pity Timer Simulator

Crate Pulls

Drop Model

Base rare-drop rate 2.0%

Soft-pity start (pull #) 70

Hard pity (guaranteed at) 90

Price per pull $1.00

Pity Progress

Pull 0P(rare) = 2.0%

No pulls yet. Pull to begin.

Economics

Total spent

$0.00

Rares won

Cost / rare

—

Theoretical EV

—

Pull history appears here…

How it works

Each pull is an independent Bernoulli trial at the base rate p, except a "soft pity" ramp raises the effective probability linearly once the player crosses a threshold, and a hard-pity ceiling guarantees a rare on that exact pull if none has landed yet — the exact mechanic used by gacha games like Genshin Impact:

p_eff(n) = p                                    for n < softStart
p_eff(n) = p + (n − softStart) × step            for softStart ≤ n < hardPity
p_eff(hardPity) = 1.0                            (guaranteed)

Without pity, the expected number of pulls to a first success is 1/p (geometric distribution), and the expected real-money cost is:

E[cost] = price × E[pulls] ≈ price / p   (no pity)
E[cost] with pity  <  price / p          (pity caps the tail, lowering variance and EV)

Pull ×1 / ×10 — spends `price` per pull and resolves each independently against the pity-adjusted probability.
Simulate 1,000 — runs a fast Monte-Carlo batch (no per-pull animation) to show the long-run average cost-per-rare converging toward the theoretical EV — the same law of large numbers a game studio relies on for predictable revenue per player.
Soft/hard pity sliders — show how publishers tune "bad luck protection" to keep spend bounded while still using variance (the thrill of an early rare) to drive purchases.

Real-world relevance: loot boxes and gacha pulls are one of the dominant monetization mechanics in free-to-play games, generating billions annually; regulators in several countries now require disclosed drop rates, which is exactly the number this simulator exposes and lets you tune.

Rare item Common item

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