What is a pity system in gacha games?

A pity system guarantees a high‑rarity item or featured character after a certain number of pulls without success. Some games use hard pity (guarantee at N pulls) and soft pity (increasing rates as you approach N).

How many pulls do I need for a 90% chance to get a 5★?

If the 5★ rate is p per pull and there is no pity, the number of pulls n needed for a target probability P is n = ln(1 − P) / ln(1 − p). For example, with p = 0.006 (0.6%), you need about 383 pulls for a 90% chance.

Does this calculator simulate soft pity or rate‑ups?

This tool models a hard pity threshold and constant per‑pull rates. Many real games add soft pity or 50/50 mechanics; you can approximate them by adjusting the base rate and pity threshold, but the exact behavior may differ from the official implementation.

Gacha / Loot Box Probability Calculator

Model your chances in gacha games: compute odds of getting a character, expected copies, pity probability, and run pull simulations.

Gacha Probability Calculator

Per-pull chance of target item (%)

Example: 0.6% for a 5★ rate-up, 1.5% for a general 5★ pool.

Planned pulls (tickets / rolls)

You can also use the budget helper below to convert currency to pulls.

Budget helper (optional)

Total currency (gems, primogems, stones…)

Cost per pull (currency)

Example: 14,400 primogems / 160 per pull ≈ 90 pulls.

Results

Key probabilities

Chance of at least one copy: –

Chance of zero copies: –

Expected number of copies: –

Simulation summary

Simulated players: –

% who reached target copies: –

Average copies per player: –

Median copies: –

Interpretation

Enter your banner rates and pulls, then click “Calculate” to see your odds.

How this gacha probability calculator works

This tool models gacha / loot box systems using basic probability theory. You can use it for games like Genshin Impact, Honkai: Star Rail, Fate/Grand Order, Arknights, and other gacha-style titles with banners, rate-ups, and pity.

1. Basic independent pulls (no pity)

If each pull has a fixed probability \(p\) of giving your target item and you do \(n\) independent pulls:

Probability of at least one copy

\[ P(\text{at least 1}) = 1 - (1 - p)^n \]

Probability of zero copies

\[ P(\text{0 copies}) = (1 - p)^n \]

Expected number of copies

\[ \mathbb{E}[\text{copies}] = n \cdot p \]

Example: if the 5★ rate-up is \(p = 0.006\) (0.6%) and you do \(n = 90\) pulls:

\(P(\text{at least 1}) = 1 - (1 - 0.006)^{90} \approx 41.7\%\)
\(\mathbb{E}[\text{copies}] = 90 \cdot 0.006 = 0.54\)

2. Approximating hard pity

Many gacha games guarantee a high-rarity item after a certain number of pulls without success (hard pity). This calculator approximates hard pity by assuming:

Each pull before pity has probability \(p\) of success.
If you reach the pity threshold without success, the next pull is guaranteed.

If your current pity count is \(c\), you will hit pity after at most \((\text{threshold} - c)\) additional failed pulls. The tool then combines:

Probability of getting at least one copy before pity.
Probability of failing all those pulls and being saved by pity.

3. Monte Carlo simulation

Even when we know the exact formulas, simulations help build intuition. The simulation mode:

Generates many “virtual players” with your chosen number of pulls.
For each player, simulates pulls with probability \(p\) and optional hard pity.
Counts how many copies each player gets and how many reach your target copies.

This shows how often people get lucky or unlucky compared with the average.

Practical tips for gacha players

Set a budget in pulls, not just money

Think in terms of total pulls you can afford on a banner. Use the budget helper to convert your gems or tickets into pulls, then check the probability of success. If the chance is lower than you’re comfortable with, consider saving for a future banner.

Understand that “pity” doesn’t erase bad luck

Pity systems protect you from extreme bad luck, but they don’t guarantee early wins. You can still be below average and only get your target at or near pity.

Gacha, loot boxes, and responsible play

Gacha mechanics are designed to be engaging and can feel similar to gambling. To stay in control:

Decide a hard spending limit before you start pulling.
Remember that even a 90% chance still means 1 in 10 players will miss.
Consider free-to-play or low-spend goals instead of chasing every banner.

FAQ

How do you calculate the chance of getting a character in a gacha game?

If the per-pull probability of the character is \(p\) and you do \(n\) independent pulls, the chance of getting at least one copy is:

\[ P(\text{at least 1}) = 1 - (1 - p)^n \]

This assumes no pity and constant rates. The calculator uses this formula in “Basic odds” mode.

How many pulls do I need for a 90% chance?

Rearranging the formula above, the number of pulls \(n\) needed for a target probability \(P\) is:

\[ n = \frac{\ln(1 - P)}{\ln(1 - p)} \]

Example: for \(p = 0.006\) (0.6%) and \(P = 0.9\) (90%):

\[ n \approx \frac{\ln(0.1)}{\ln(0.994)} \approx 383 \text{ pulls} \]

Does this calculator support multiple rarities or 50/50 mechanics?

This version focuses on a single target item or rarity at a time, with an optional hard pity. To approximate 50/50 systems, you can:

Multiply the base 5★ rate by the chance it’s the featured unit.
Adjust the per-pull probability \(p\) accordingly.

Is gacha the same as gambling?

Gacha and loot boxes share many features with gambling: random rewards, variable reinforcement, and often real-money purchases. Legal classification varies by country, but from a probability perspective they behave like gambling systems. Use tools like this to understand your odds and avoid overspending.