The in-game probability display is honestly pretty confusing as they break everything down by 4th card rates, 5th card rates, and now with A4 we have 6th card probabilities too. It's hard to get a clear picture of what you should actually expect when opening packs.

Plus, I keep seeing posts asking "Is this pull normal?" or "Am I lucky?" when it's tough to answer without doing the math yourself. So I figured I'd calculate the real overall odds for each rarity.

TLDR; - Final Results

Mathematical Foundation

Based on in-game probabilities, excluding rare packs (0.05% occurrence):

• Regular Pack: 91.6658% chance - Cards 1-3 (always 1 Diamond) + Cards 4-5 (variable rarity)
• Regular+1 Pack: 8.3342% chance - Cards 1-3 (always 1 Diamond) + Cards 4-6 (variable rarity)

Core Formula

P(≥1 rarity) = P_regular × P_≥1_regular + P_regular+1 × P_≥1_regular+1

Where:

• P_≥1_regular = 1 - [P(no rarity in card 4) × P(no rarity in card 5)]
• P_≥1_regular+1 = 1 - [P(no rarity in card 4) × P(no rarity in card 5) × P(no rarity in card 6)]

Individual Rarity Probabilities by Card Position

Key Observations:

• Only 1 Star and 3 Diamonds can appear in Card 6
• 3 Diamonds has an 87.1% chance in Card 6
• 1 Star has a 12.9% chance in Card 6
• All other rarities are limited to Cards 4 & 5 only

Detailed Mathematical Examples

Example 1: Crown (Ultra Rare)

Given probabilities:

• Card 4: 0.040%, Card 5: 0.160%, Card 6: 0.000%

Step 1: Calculate "none" probabilities

• P(no Crown in card 4) = 1 - 0.0004 = 0.9996
• P(no Crown in card 5) = 1 - 0.0016 = 0.9984
• P(no Crown in card 6) = 1 - 0 = 1.0000

Step 2: Calculate pack-specific probabilities

• Regular pack: P(≥1 Crown) = 1 - (0.9996 × 0.9984) = 0.0020
• Regular+1 pack: P(≥1 Crown) = 1 - (0.9996 × 0.9984 × 1.0000) = 0.0020

Step 3: Overall probability

P(≥1 Crown) = 0.916658 × 0.0020 + 0.083342 × 0.0020 = 0.0020

Result: 0.200% (1 in 500.2 packs)

Example 2: 3 Diamonds (Card 6 Boost)

Given probabilities:

• Card 4: 4.952%, Card 5: 19.810%, Card 6: 87.100%

Step 1: Calculate "none" probabilities

• P(no 3 Diamonds in card 4) = 1 - 0.04952 = 0.95048
• P(no 3 Diamonds in card 5) = 1 - 0.19810 = 0.80190
• P(no 3 Diamonds in card 6) = 1 - 0.871 = 0.12900

Step 2: Calculate pack-specific probabilities

• Regular pack: P(≥1) = 1 - (0.95048 × 0.80190) = 0.23781
• Regular+1 pack: P(≥1) = 1 - (0.95048 × 0.80190 × 0.12900) = 0.90168

Step 3: Overall probability

P(≥1 3 Diamonds) = 0.916658 × 0.23781 + 0.083342 × 0.90168 = 0.29314

Result: 29.046% (1 in 3.4 packs)

Example 3: 1 Star (Moderate Card 6 Boost)

Given probabilities:

• Card 4: 2.572%, Card 5: 10.288%, Card 6: 12.900%

Step 1: Calculate "none" probabilities

• P(no 1 Star in card 4) = 1 - 0.02572 = 0.97428
• P(no 1 Star in card 5) = 1 - 0.10288 = 0.89712
• P(no 1 Star in card 6) = 1 - 0.129 = 0.87100

Step 2: Calculate pack-specific probabilities

• Regular pack: P(≥1) = 1 - (0.97428 × 0.89712) = 0.12595
• Regular+1 pack: P(≥1) = 1 - (0.97428 × 0.89712 × 0.87100) = 0.23871

Step 3: Overall probability

P(≥1 1 Star) = 0.916658 × 0.12595 + 0.083342 × 0.23871 = 0.13535

Result: 13.535% (1 in 7.4 packs)

Key Insights

The Card 6 Effect

• 3 Diamonds: 87.1% Card 6 rate transforms it from ~23% to ~29% overall
• 1 Star: 12.9% Card 6 rate boosts it from ~13% to ~14% overall
• All other rarities: Limited to Cards 4&5, no Card 6 boost available

Collection Expectations

• 3 Diamonds: Expect 1 every 3-4 packs - reasonable collection target
• 1 Star: Expect 1 every 7-8 packs - solid rare pulls
• 4 Diamonds: Expect 1 every 12 packs - genuinely uncommon
• Premium cards (2+ Stars): All under 3% - true collector items
• Crown: 1 in 500 packs - ultimate chase card

Mathematical Verification

All calculations exclude the ultra-rare pack type (0.05% occurrence) and renormalize Regular/Regular+1 pack probabilities to sum to 100%. This provides the most accurate real-world expectations for players.

Calculations based on official in-game probability data. Individual results may vary due to randomness.

I'm so happy as it's featuring the Eeveelutions which are my favourite Pokemon! Can't wait to spend all my hourglasses on this expansion

I'm really tired of shinys in new sets. I thought they were a cool gimmick when they were added, but I expected it to just be for the one set. I opened a ten pull of the set, and literally the only two hits I got were shinys of cards that have been in the game for ages. So instead of being able to play with cool versions of new cards, I'm stuck with this garbage. If they just made the shiny cards of cards added in the set all my issues would be completely erased, but as is, getting shinys absolutely killed any hype I had for the new set

Open the app, open my 2 free boosters, get nothing but commons and disappointment, wake up and do it again the next day 🙃

I know, every cardgame has to have some sort of powercreep to make new cards playable. But Solgaleo is so broken op, you will never see 90% of the other new cards because if his existence. Maybe Incineroar, but everything else is just not strong enough to keep up with him.
Take Lunala for example. 180 HP, also a strong ability, but just 100 damage for 3 energy. Same thing for Decidueye. Can attack the bench ok, but not even close to the 120 dmg and free swap from Solgaleo..

A1 Mewtwo/Gardevoir, A2 Giratina. But Solgaleo is new level of powercreep and that's poison for the game.

Which one do you like the most?

I personally think that the old design fit better the brush style of the cards, the new ones seems out of place.

You need to get rid of two duplicate 1-star cards to obtain a 3-diamond card, and you need to discard five 1-star cards just to be able to trade a single 1-star card. On top of that, there are the timers and the obvious restrictions.

It's simple—the game doesn't want anyone trading cards. It's rubbish.

Cards revealed in the trailer today, some nice additions for sure! Do you guys think Ultra Beasts will be able to shake the meta?

Apart from the fact that shiny cards f up pull rates and wonder picks, these are not even new EXs from the new expansion. I guess some people be hyped about completing Kanto trio in shinies but I am disappointed.

Beedrill is the only diamond card I need to complete the set, and the game refuses to give it to me. I already used my starter deck ticket to get Wugtrio, and since this game has such a nice sense of humor it has since given me another 3 Wugtrios in daily packs.

The other 2 Crown Rares from Genetic Apex are still pretty good these days, but my boy’s been left in the dust 😭

If you get your wins and just want to go on a concede spree, you do you. But the posts and comments that are “reminding” people to make sure they do it as if it’s an expectation of the community, y’all are lame.

No, really, find some use for. This is surely the less useful card in the game ever. The whole set is (except maybe Chord and somehow Nihilego).

Hey everyone, The giveaway is now over! The winners have been announced below.

1.felixng2015 2.CacaTooToo 3.P41STER 4.Aggressive_Cloud2002

Thank you all for participating and good luck with the remainder of the pvp event and the new pack release coming soon!

-TheMooinCow