Pokémon pull rates explained: what 1 in 85 packs means for a box

A pull rate such as "1 in 85 packs" is an average: across many packs, one card of that rarity turns up for every 85 opened. It is not a promise of one per 85. Treating each pack as a separate draw at that rate, a 36-pack booster box has about a 35% chance of at least one card of a 1-in-85 rarity and a 65% chance of none, and it takes about 59 packs to reach even odds.

This guide works through that arithmetic with real rates. Its example is Surging Sparks, whose Special Illustration Rares (SIRs) the site lists at 1 in 85 packs from published opening counts. The same steps apply to any rate on the pull rates page.

Where the rates come from

The site found no official pull rates for English sets. Every English rate with its own source is the midpoint of published pack-opening counts, mostly TCGplayer's, which open from about 1,000 to over 8,000 packs per set. Surging Sparks has its own published counts for four tiers; its Double Rares and ACE SPECs, which the source gives no rate for, use the era average, and the block marks those rows. The pull rates by set guide explains how the counts are taken and how far apart sources can be.

A rate is therefore an estimate. The arithmetic below is exact for the rate it starts from, but no more accurate than that rate.

From a rate to a chance

For a rarity at "1 in X packs", the chance that one pack holds it is 1 divided by X. The chance that a run of packs holds at least one is one minus the chance that every pack misses:

chance of at least one in N packs = 1 − (1 − 1/X) multiplied by itself N times

This treats every pack as an independent draw; a sealed box may behave differently from N separate packs, and the formula is the plain average case.

The table applies it to the rates Surging Sparks and Mega Evolution list, at the pack counts of the common products: 6 packs in a booster bundle, 9 in an Elite Trainer Box, 18 in a half booster box and 36 in a booster box.

Two things stand out. The chance does not grow in a straight line: 36 packs at 1 in 85 give 34.7%, not 36 in 85 (42%), because some boxes would hold two and some none. And the "average per 36 packs" column, which is just 36 divided by X, is an average over many boxes; a box with 0.42 SIRs does not exist.

How many packs for even odds

Turning the formula around gives the smallest number of packs that reaches a chosen chance of at least one:

A 90% chance at 1 in 85 takes 195 packs, a little over five booster boxes.

Surging Sparks, tier by tier

The site's rates for Surging Sparks are 1 in 13 packs for an Illustration Rare, 1 in 15 for an Ultra Rare, 1 in 85 for a Special Illustration Rare and 1 in 189 for a Hyper Rare. The block below shows them with the number of cards in each tier and the average per 36 packs, plus the Double Rare and ACE SPEC rows, which use the era average.

At those rates a 36-pack booster box has:

• a 34.7% chance of at least one SIR, a 65.3% chance of none and a 6.7% chance of two or more;
• a 17.4% chance of at least one Hyper Rare;
• a 94.4% chance of at least one Illustration Rare and a 91.7% chance of at least one Ultra Rare.

A 9-pack Elite Trainer Box has a 10.1% chance of at least one SIR, and a 6-pack booster bundle 6.9%.

The chance of one named card

A rate is for a whole rarity, and a rarity holds several cards. Surging Sparks has 11 SIRs, among them the Pikachu ex #238. If each of the 11 is equally likely, as the site assumes because the source gives one rate per tier, one named SIR turns up once in 11 × 85 = 935 packs. That gives:

• a 3.8% chance in one booster box;
• 648 packs, about 18 boxes, for an even chance;
• 2,152 packs, about 60 boxes, for a 90% chance.

The same step applies to any tier: multiply the rate by the number of cards in it. Mega Evolution lists its Mega Hyper Rares at 1 in 1,260 packs and has two of them, so one named Mega Hyper Rare, such as the Mega Lucario ex #188, is about 1 in 2,520 packs, a 1.4% chance in a 36-pack box.

What a rate does not say

• It does not schedule anything. At 1 in 85 a run of 100 packs with no SIR happens about 31% of the time, and two SIRs in one box about 6.7%. Neither means the rate is wrong.
• It does not fix a count per box. A rate is an average over many packs, not a number per box.
• It says nothing about value. Which card a rate gives, and what that card sells for, is a separate question; the sealed EV board combines rates with prices, and the methodology page explains how.

What changes and what stays

Dated figures: none of the chances here depends on prices, so they move only if the rates do. The site's rates were collected in September 2026 and change when a set's published counts are revised; the pull-rate block above always shows the rates the site uses.

Lasting facts: the formula, and the step from a rarity's rate to one named card's. They hold for any rate and any set; the chances change only if the rate they start from changes.

Bottom line

"1 in 85 packs" is an average. At that rate a 36-pack box has about a 35% chance of at least one card of the rarity and a 65% chance of none, and even odds take about 59 packs. For one named card, multiply the rate by the number of cards in its rarity: for one of Surging Sparks' 11 SIRs that is 1 in 935 packs, about 3.8% per box.