Probability calculator

Expected Cost Calculator

Estimate the long-run average cost of one target outcome from a known success rate and price per attempt. Use the result to understand scale and risk, not as a spending recommendation.

Calculate expected cost

Expected cost $166.67
Expected attempts 33.33
Interpretation Long-run average

At a 3% rate and $5 per attempt, the long-run expected cost is about $166.67.

Formula

Expected attempts are estimated as 1 divided by the success probability. Expected cost is expected attempts multiplied by price per attempt.

Expected cost = (1 / success probability) x price per attempt

Example interpretation

At a 3% success rate, the long-run expected attempts are about 33.33. If each attempt costs $5, the expected cost is about $166.67. That number is not a target, a limit, or a promise. It is the average you would expect only across many repeated independent trials with the same rate and price.

A real person can hit the result early, miss far longer than the average, or stop before reaching the average. For random purchases, read the expected cost together with the miss chance and a fixed budget.

When not to use this calculator alone

Expected cost is less useful when the rate changes over time, attempts are not independent, prize pools are limited, pity rules apply, or the price per attempt changes with bundles. In those cases, use a tool that matches the specific model or read the official rules before making a decision.

Limitations

  • Expected cost is a long-run average, not a guarantee.
  • The model assumes independent attempts with a stable success rate.
  • It does not handle pity systems, changing rates, discounts, taxes, shipping, resale value, or shrinking prize pools.

FAQ

Does expected cost mean I will spend exactly that amount?

No. Expected cost is a long-run average across many similar situations. A single real outcome can be cheaper or much more expensive.

Can expected cost justify buying more attempts?

No. Use expected cost to understand scale and risk, not as a reason to exceed a budget.

What happens when the success rate is very low?

The expected attempts and expected cost rise quickly. That is a sign to compare alternatives before spending.

Privacy note

The expected cost calculator runs in the browser and does not require account registration. Inputs are normal calculator values.