Gacha Simulation: Understanding Pity Mechanics and Probability Psychology

Gacha Simulation: Pity Mechanics and Probability Psychology

The One-Sentence Essence

On the surface, it's a numerical adjustment to increase drop rates; in reality, the core mechanism uses "hard pity as a safety net" and "soft pity for smoothing" to eliminate the pain of extreme tail outcomes; this article focuses on how to verify the distribution via simulation and design emotional thresholds.

Traffic Reason: High controversy, naturally high engagement. Players will ask: "Is this probability actually a trap?"

1) Relying Solely on "2% Drop Rate" Will Fail

Players aren't broken by the "average probability," but by continuous failure.

Therefore, the gacha system usually needs to solve two things:

• Extreme non-lucky tail probability (Is P99 absurd?)
• The feeling of being stabbed in the back (Got a drop, but not the one you wanted)

2) The Most Common Combination: Hard Pity + Soft Pity + Directed

• Hard Pity: Guaranteed rare item after N pulls (baseline fairness)
• Soft Pity: Probability increases as you approach N (better perceived experience)
• Directed / Big Pity: If you get the wrong item, the next pull guarantees the target (reduces negative emotions)

Experience: The improvement in reputation from soft pity is often more noticeable than simply increasing the base probability.

3) Simulation Should Look at Distribution, Not Just Expectation

What you need is not "average 50 pulls to get an item," but:

• P50: How many pulls half the players need
• P90: How many pulls most players need
• P99: How many pulls extreme non-lucky players need (this decides whether public opinion explodes)

One-sentence summary: Gacha balance is about "reducing tail pain," not "increasing the mean."

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4) How to Implement Soft Pity (Smoother Perceived Experience)

The most common implementation of soft pity is not "sudden doubling," but a gradually rising probability curve, for example:

• Pulls 1~A: Base probability p0
• Pulls A~N: Probability increases by dp per pull (or rises via segments/exponential)
• Pull N: Hard pity guarantees the drop

What you are tuning is "player experience," not mathematical elegance:

• Rising too early: Makes the base probability look like a prop
• Rising too late: The tail remains painful (reputation risk)

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5) Directed / Big Pity: Solving "Got a Drop, But Not the One I Wanted"

Much of the controversy isn't "didn't get a rare," but "got a drop, but got the wrong one."

Common directed schemes:

• 50/50: If you get the wrong item this time, the next pull guarantees the target (big pity)
• Counter: Getting the wrong item adds 1 point; once full, guaranteed drop
• Redemption: Repeat rares exchange for "fragments," accumulating to redeem the target

Core Goal: Turn "bad luck" into accumulative progress.

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6) Using Monte Carlo to View Distribution (Minimum Executable Steps)

You don't need to start with complex mathematical derivation; use simulation first to uncover most problems:

1. Write a simulateOneUser() function returning "number of pulls required to get the target"
2. Run it 100000 times to get the distribution
3. Check P50/P90/P95/P99, then look at the distribution of "how many times you got the wrong item"

You will find: Some configurations may have a great mean, but P99 is extremely ugly—this is the "reputation explosion point."

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7) Review and Reputation Considerations (Product Side)

• Consistent disclosure wording: When displaying base probability, also explain pity and directed rules (otherwise players feel misled)
• Avoid "implicit weighting" causing unexplainability: Players fear most feeling "controlled by the system"
• Turn "bad luck" into progress: Even fragment redemption can significantly reduce negative emotions

Boundary Conditions

• Need to handle whether extreme non-lucky tail probability (P99) is absurd enough to cause reputation explosion.
• Need to handle the feeling of being stabbed in the back caused by continuous failure (got a drop, but not the one wanted).
• Need to handle the impact of soft pity probability curve rising too early or too late on perceived experience.
• Need to handle whether the "wrong item" situation in the directed mechanism converts into accumulative progress.
• Need to handle whether disclosure wording and implicit weighting rules are consistent, avoiding players feeling controlled.

Design Trade-offs

• Benefit: Soft pity improves reputation; Cost: Base probability looks like a prop; Alternative: Adjust the rising curve to avoid rising too early or too late.
• Benefit: Turning bad luck into accumulative progress (e.g., fragment redemption); Cost: Increased system complexity; Alternative: Directly increase base probability or rely solely on hard pity.