Probability model index

Probability Calculators

Use this page when a decision depends on random outcomes. The goal is to read both the optimistic result and the remaining risk before acting on a probability estimate.

Quick selection

Start from the decision, then open the calculator.

This index groups working calculators with the supporting notes that explain formulas, assumptions, privacy, and limits. It is meant to be a starting page, not a thin list of links.

Calculator bench

Working tools in this index.

Each calculator below has an internal detail page and a direct browser-based tool page.

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Probability Tools

Repeated Attempt Probability Calculator

A browser-based calculator for estimating the chance of at least one success across repeated independent attempts.

  • probability
  • risk
  • repeated attempts
Open tool Details
Live

Probability Tools

Expected Cost Calculator

A browser-based calculator for estimating long-run expected cost from a single-attempt success rate and price per attempt.

  • expected cost
  • probability
  • collectibles
Open tool Details
Live

Planning Tools

Percentage Change Calculator

A browser-based calculator for finding percent increase, percent decrease, and the absolute difference between an old value and a new value.

  • percentage
  • change
  • comparison
Open tool Details
Use cases

When this index is useful.

Open this page when one of these situations matches the number you are trying to check.

You want the chance of at least one success after repeated independent attempts.

Use the linked calculator as a planning model, then read the notes before relying on the result.

You need to compare hit chance with miss chance before trusting a random outcome.

Use the linked calculator as a planning model, then read the notes before relying on the result.

You want to understand expected cost as a long-run average, not a promise.

Use the linked calculator as a planning model, then read the notes before relying on the result.

Worked example

Example: checking hit chance and miss chance together

A user is considering 12 independent attempts at a 4% single-attempt success rate. Looking only at 4% feels too pessimistic, while assuming 12 attempts guarantees progress is too optimistic.

  1. Use the repeated attempt calculator with a 4% single-attempt rate and 12 attempts.
  2. Read the at-least-one success chance and the miss chance together.
  3. If there is a cost per attempt, compare the expected cost with the amount the user would be comfortable losing.

Takeaway: Probability calculators are most useful when they show the risk that remains after repeated attempts, not only the best-case interpretation.

Selection rules

How to choose the right calculator.

  • Use repeated attempt probability when the single-attempt rate stays fixed.
  • Use expected cost when there is a cost per attempt and a visible success rate.
  • Read the probability guides when rates change, hidden rules exist, or a prize pool shrinks over time.
Limits

What can make the result wrong.

  • Changing rates, pity systems, limited pools, and hidden rules need different models.
  • Expected value is a long-run average and can differ sharply from one person's real result.
  • Probability tools explain risk; they do not predict or guarantee a specific result.
Review checklist

Before relying on the result.

  • Confirm whether attempts are independent or whether the rate changes after each attempt.
  • Look for hidden rules such as pity systems, limited pools, region-specific rates, or changing availability.
  • Treat expected cost as a model for understanding scale, not as a spending plan.
Related guides

Read the notes behind the formulas.

These pages explain assumptions, examples, common mistakes, and privacy handling.

View all guides
Probability

How Probability Calculators Work

Learn the basic models behind probability calculators, including repeated attempts, miss chance, expected cost, and prize pools without replacement.

 Probability

Repeated Attempt Probability Formula

Learn why repeated independent attempts use the miss chance formula, with examples for small probabilities and responsible interpretation.

 Probability

Miss Chance: The Probability Number People Ignore

A plain-English guide to miss chance, why it matters in repeated attempts, and how to use it when reading gacha, blind box, booster, and random draw odds.

 Probability

Expected Value vs Real Outcomes

Understand the difference between expected value, expected cost, and real individual outcomes before using averages for planning or random purchase decisions.
FAQ

Before using this calculator group.

Why does repeated probability not add up linearly?

Because each attempt can fail. A common model calculates the chance of missing every attempt first, then subtracts that from 100%.

Should I use expected cost as a budget?

No. Expected cost shows long-run scale. It is not a spending recommendation or guarantee.