Transparent math

Methodology

The calculator starts with listed family rates, then applies the options you enter. The result is useful for spin planning and sanity checks, but it is not a promise that a roll will hit by a specific number.

Core Formula

Chance to hit at least once after n spins:

1 - (1 - perSpinRate) ^ n

Chance to miss every spin:

(1 - perSpinRate) ^ n

Expected Spins

Expected spins are calculated as 1 / perSpinRate. This is an average over many repeated sessions, not a promise that a player will hit by that number.

Confidence Thresholds

To find spins needed for 50%, 75%, 90%, or 95% confidence, the planner solves:

ceil(log(1 - confidence) / log(1 - perSpinRate))

Specific Family Rates

When targeting one family, the planner divides the rarity pool equally across families in that rarity. Exact per-family weights are not published in one consistent public table, so named-family rates should be treated as planning estimates.

2x Rate Mode

2x mode doubles the Legendary and Mythical rarity pools and reduces Common by the same total amount. Rare and Epic stay unchanged.

Prestige Bonus

Prestige adds 0.0050% to the Legendary family pool per Prestige level. That bonus is added after 2x mode, so the Prestige part is not doubled.

Epic+ Pity

The pity checkpoint is shown separately. After 400 spins without an Epic, Legendary, or Mythical family, the next checkpoint is treated as Epic+. Public references list the Legendary chance at that checkpoint as 5.000%.

Limits To Keep In Mind

The main hit chance assumes repeated spins at the same listed rate. The pity checkpoint, storage choices, trades, and newly changed family rates can make a player session differ from the headline estimate. Recheck the data date before planning a large spin budget.

Data Sources

Rate table: aotr-family-rates-2026-06-29. Last refreshed: 2026-06-29.