Pull Probability Calculator
How many packs do you really need to pull your chase card? Select a product or enter custom odds to see the math — with confidence thresholds, cost estimates, and a clear verdict.
2024 Topps Chrome Hobby — Auto
How Many Packs Do You Need?
Based on geometric probability: P = 1 - (1 - 1/odds)^n
| Confidence | Packs Needed | Est. Boxes | Est. Cost |
|---|---|---|---|
50% | 8 | ~1 | $64.00 |
75% | 16 | ~2 | $128.00 |
90% | 27 | ~3 | $216.00 |
95% | 35 | ~3 | $280.00 |
99% | 53 | ~5 | $424.00 |
Calculate Your Odds
Enter the number of packs you plan to open:
How the Math Works
Each pack is an independent trial. The probability of not pulling the card from one pack is 1 - (1/12) = 91.6667%.
After n packs, the probability of never pulling it is (1 - 1/12)^n.
So the chance of pulling it at least once in n packs is: P = 1 - (1 - 1/12)^n
Note: This assumes each pack is independent (no box-level guarantees). Real products may have guaranteed hits per box, which improves your odds. This calculator gives the worst-case statistical baseline.
Should You Rip or Buy Singles?
If it costs $216.00 for a 90% chance of pulling the card, but the card sells for less than that on the secondary market, buying the single is always smarter.
Use this alongside the Wax vs Singles Calculator and Sealed Product EV Calculator for the complete picture.
Frequently Asked Questions
How many packs do I need to open to pull a specific card?▾
It depends on the card's pull rate. For a card with 1-in-100 odds, you need 69 packs for a 50% chance, 138 packs for a 75% chance, and 230 packs for a 90% chance. The formula is: packs = log(1 - desired_probability) / log(1 - 1/odds). Our calculator does this math instantly for any product and odds combination.
What are typical pull rates for chase cards?▾
Pull rates vary widely by product and insert level. Common inserts might be 1-in-4 packs. Numbered parallels like Silver Prizms are roughly 1-in-4 to 1-in-8 packs in hobby boxes. Autographs range from 1-in-6 (high-end hobby) to 1-in-72 (retail blasters). Ultra-rare cards like 1/1s or low-numbered parallels (/10, /25) can be 1-in-500 to 1-in-5000+ packs. Always check the product's official odds on the packaging or manufacturer website.
Is it cheaper to buy packs or just buy the card I want?▾
In most cases, buying singles is significantly cheaper than trying to pull a specific card. For example, if a card sells for $50 but the pull probability calculator shows you need $500 worth of packs for a 90% chance of pulling it, buying the single saves you $450. The exception is if you enjoy the ripping experience and value the other cards you pull along the way. Use our Wax vs Singles Calculator for a detailed comparison.
Do box-level guarantees affect these calculations?▾
Yes. Many hobby boxes guarantee a certain number of hits (e.g., "2 autographs per box"). Our calculator uses per-pack independent probability, which is the worst-case statistical baseline. If a box guarantees hits, your actual odds are better than what the calculator shows. However, the guarantee applies to the category (any auto) not a specific card, so for chasing one particular auto, the per-pack calculation is still useful.
Why do I need so many more packs to go from 90% to 99% confidence?▾
This is due to the diminishing returns of probability. Going from 0% to 50% requires about 69 trials for 1-in-100 odds. But going from 90% to 99% requires an additional 230 packs (from 230 to 460 total). Each additional percentage point of confidence requires exponentially more packs. This is why most collectors consider 90% a practical threshold — the cost to reach 99% rarely justifies the marginal confidence gain.