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Pack Odds Calculator

The Pack Odds Calculator shows the probability of pulling at least one card of each rarity level from a trading card pack. Input your pack size (1–20 cards) and see exact probabilities for Common (50%), Uncommon (30%), Rare (10%), Holo Rare (7%), and Secret Rare (3%) pulls.

23 cardsneeded for a 50% chance of pulling at least one Secret Rare at 3% odds
60M+Pokemon TCG Pocket downloads, popularizing digital pack probability mechanicsThe Pokemon Company

Real math, not guesswork. This calculator uses binomial probability distribution to show your exact odds, the same math behind every pack opening simulator and TCG probability analysis.

100% FreeNo sign-upRuns in your browser
15101520
5cards per pack
RarityDrop RateExpected
Common50%~2.5
Uncommon30%~1.5
Rare10%~0.5
Holo Rare7%~0.4
Secret Rare3%~0.1
Total100%5.0

Expected value = pack size × drop rate. Over many packs, the average number of each rarity converges to these values. Individual packs will vary, and that's what makes opening them exciting.

How the Math Works

Each card in a pack is an independent draw with a fixed probability per rarity. The chance of pulling at least one card of a given rarity uses the complementary binomial formula:

P(at least 1) = 1 − (1 − p)n

Where p is the rarity's drop rate and n is the pack size. For a 5-card pack, the chance of at least one Rare (10% base) is 1 − 0.95 = 40.95%.

Ready to test your luck? Open a pack and see what rarity you pull.

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Features

What Makes This Tool Special

Binomial Distribution Math

Uses the binomial probability formula P(X≥1) = 1 - (1-p)^n to calculate exact odds. Not approximations, but the real math behind TCG pull rates.

Visual Probability Bars

Each rarity level gets a color-coded progress bar showing your probability. Bars animate as you change pack size, making the math intuitive to understand.

Expected Value Breakdown

See how many cards of each rarity you'd expect in a given pack size. In a 10-card pack: ~5 Common, ~3 Uncommon, ~1 Rare, ~0.7 Holo Rare, ~0.3 Secret Rare.

All 5 Rarity Tiers

Covers MakeACard's complete rarity system: Common (50%), Uncommon (30%), Rare (10%), Holo Rare (7%), and Secret Rare (3%). Each tier uses its signature color.

Client-Side Computation

All calculations run in your browser. Adjust the pack size slider and see results update in real-time. No server round trips, no loading spinners.

FAQ

Frequently Asked Questions

How are the pack odds calculated?
The calculator uses the complementary binomial probability formula: P(at least 1) = 1 - (1 - p)^n, where p is the rarity's drop rate and n is the pack size. For example, the chance of getting at least one Rare (10% base rate) in a 5-card pack is 1 - (0.9)^5 = 40.95%.
Are these the same odds as real Pokemon booster packs?
MakeACard uses its own rarity distribution: Common 50%, Uncommon 30%, Rare 10%, Holo Rare 7%, Secret Rare 3%. Real Pokemon TCG packs use different rates and guaranteed rarity slots. This calculator models MakeACard's system specifically.
What pack size gives me the best chance at a Secret Rare?
At 3% base rate, you need about 23 cards for a 50% chance at one Secret Rare, and 76 cards for a 90% chance. The calculator will show you the exact probabilities for any pack size from 1 to 20.
What is expected value in pack opening?
Expected value (EV) is the average number of cards of each rarity you'd get over many packs. It's calculated as n × p (pack size × drop rate). In a 10-card pack, you'd expect 5 Commons, 3 Uncommons, 1 Rare, 0.7 Holo Rares, and 0.3 Secret Rares on average.
Does this calculator apply to other TCGs?
The math is universal: binomial probability works for any independent random draw. However, the pre-set rates match MakeACard's rarity system. Real TCGs like Pokemon, MTG, and Yu-Gi-Oh use different rate structures and often include guaranteed rarity slots per pack.
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