How Many Hat Combinations Are Possible on ROBLOX?

30, 2014

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Pop quiz! How many different combinations of hats can you possibly wear on ROBLOX? Go on, take a wild guess.

At ROBLOX we love hats, which is apparent from the thousands of them filling the catalog. When it comes to character customization and showing off your individual style, combining hats with clothing and gear provides a lot of ways to stand out. But we were curious: how many different ways?

Editor’s note: Huge thanks to ROBLOX user Siccity, who helped me exercise my brain with a hefty amount of math.

For the sake of simplicity let’s only consider the current, obtainable hats — excluding the retired and promotional. ROBLOX users can wear up to three different hats simultaneously, so we’re working with that idea. And with over 2,500 of them in the store, that’s a lot of options.

To calculate the number of different three-hat combos, we’re using the nCr formula for combinations. It’s a little tricky, and involves factorials. If you’d like an explanation on combinations and permutations, check out this helpful guide.

Using that formula, we arrive at  3.886 billion combinations. Specifically 3,886,685,656 combinations of hats.

To put that in perspective, that’s about half the population of the planet Earth. If you had that much money you would have to spend \$133,000 every day for your entire life (if your life was 80 years long) to spend it all.

And that’s just hats. If we add in, say, the 799 pieces of gear, then the combinations jump massively.

3.886B x 799 = 3,105,461,839,144

We end up with over three trillion combinations! How big is three trillion?

441 planet Earths would create that many human beings. If you tried to count to that number out loud, it would take you over 98,000 years to do it.

Oh good, we’re one sixth of the way there! Only 70,000 years to go!

But wait, hold on! Hats and gear are great, but they don’t even comprise the biggest clothing selection on ROBLOX. You guys, our talented ROBLOX creators, have made thousands upon thousands of shirts, t-shirts, and pants. So, let’s go ahead and add in all your hard work to the equation. And let’s not forget that the hundreds of different faces, even if you can’t see them with certain hats, count as well.

Hang on, this is going to get crazy.

• Faces: 259
• Shirts: 452,337
• T-shirts: 506,671
• Pants: 220,056

So that’s…

3.886B x 799 x 259 x 452,337 x 506,671 x 220,056 x 17

Which gives us a whopping…

689 Nonillion. Or…

6.896e^32. Or…

689,598,419,909,508,494,000,538,823,099,584.

That’s not even a number that you can really fathom. That’s the kind of number you get when you’re calculating the number of atoms in the galaxy. We’re into some next level math here. But let me try and break it down.

If every single ROBLOX user — all 60 million accounts — changed their outfits once a second, 24 hours a day, every day, it would take us all 364 quadrillion years to wear every combination. With the theory that the universe has a lifespan of about 20 billion years, that’s enough time for the universe to die out, be reborn, and repeat the process all over again 18 million times.

If you’ve gotten this far in this math lesson, awesome! And you’re probably thinking that there is something we’re leaving out…

Body packages.

We’ve got dozens upon dozens of packages, each with five interchangeable parts (arms, legs, and a torso). Adding those into the mix gives us a number so huge that it ruptures the fabric of space and time in the sheer overpowering force of its immensity. So, we won’t. But feel free to try and calculate it yourself for a fun side project that will probably impress your math teacher.

Next time someone is wearing the same outfit as you in ROBLOX, take a screenshot and think for a moment about how astronomical the odds of that are.

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