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Calculating pi by flipping 10,000 coins (Video pre-release) (Patreon)

Published:
2026-03-13 14:35:27
Imported:
2026-03

Content

Happy pi day! This is a re-post of a previous post (from about an hour ago) - which we deleted when some mistakes were spotted that were too obvious and easy to fix to keep uploaded.

I know we all thought this would be a pi-by-hand year, so in honour of that, I've used an amazing new bit of maths and some old footage of me flipping a coin 10,000 times (by hand) to calculate pi this year.

The flip data is available here, and I enthusiastically invite you to dive in and check my workings. I know how much you all enjoy that. https://www.dropbox.com/scl/fi/y7pueeebnt2v4i2w8sfz1/coinflip-stats.xlsx?rlkey=n9s1onlj9l6xebl1vuygl3u4l&st=4axban7n&dl=0

Looking forward to hearing if you corroborate my findings!

Files

Flipping 10,000 coins to calculate pi.

Happy Pi Day! The new value of pi is 3.2266. Pi-by-hand is happening - at some time in the future - at some location! Please opt-in for updates and tell us which places would work for you: https://docs.google.com/forms/d/e/1FAIpQLScprg57Bvv1jOfoMQwriHPegTnCjik2p9xrly0zQ84ANYMfEQ/viewform?usp=dialog Huge thanks to Jim Propp for discovering this amazing bit of maths. For more math details: https://arxiv.org/abs/2602.14487 For the backstory: https://mathenchant.wordpress.com/2026/03/12/in-praise-of-stupid-questions/ Check out Sophie Maclean's Numberphile video: https://www.youtube.com/watch?v=fczN0BCx0xs My coin flip data is available here: https://www.dropbox.com/scl/fi/y7pueeebnt2v4i2w8sfz1/coinflip-stats.xlsx?rlkey=n9s1onlj9l6xebl1vuygl3u4l&st=4axban7n&dl=0 Huge thanks to my Patreon supporters. They are flipping brilliant. http://patreon.com/standupmaths CORRECTIONS Nothing yet. Let me know if you spot anything! Filming and editing by Alex Genn-Bash Written and performed by Matt Parker Produced by Nicole Jacobus Content wrangling by Rhys Jones Music by Howard Carter Design by Simon Wright and Adam Robinson MATT PARKER: Stand-up Mathematician Website: http://standupmaths.com/

Comments

garethaethwy

BUT WE’VE LOST OUR 36 SECONDS! lol

Adam Wishneusky

The difference between Catalan numbers and Pascal’s triangle is whiteboard versus brown paper

Mark Reed

My entirely in-spreadsheet calculation of pi from your 10,000 flips (that is, all formulas, no scripting, gotta love IF()) matched your result exactly. But if heads overtaking tails is counted as "one sample", those 10,000 flips comprise only 62 samples, so it's not surprising that it's not a better estimate. I wrote some terrible code (Raku instead of Python so as not to infringe on your copyright) that would keep flipping coins until heads overtook tails 10,000 times. That took 110,626,006 flips, which is probably way too many to do by hand, and even that result was only correct to two digits at 3.1542...

Tim Clark

Because I hate excel I also abused it to replicate the calculation (sucessfully), but also because I hate excel I actually used libreoffice

Rick Rubenstein

I posted this on YouTube, but repeating it here to increase the chance of Matt seeing it, because it’s awesome: the JWST “Pillars of Eternity” photo in the background CONTAINS AN UPSIDE-DOWN PI!! Surely I can’t be the first person to have noticed this, right? Is this already a meme I’m unaware of?

Peter Dillinger

If I understand correctly, and not made clear in the video, the 3.22 number really only comes from a pr fix of the data that was roughly 80% heads. I haven't verified using the xlsx yet but that's got to be a small prefix of the data (on average). It's like a gambler saying they're going to stop when they're ahead. But they inevitably start again. And at some point they're in such a hole, it's most likely they're going to stop in a deep hole.

John Doe

I'm able to confirm Matt's calculation. More precisely, the estimate of pi that I got was 374217171779402730435946 / 115979054370213383235315.

John Doe

It's true that the last 198 flips, of which 90 are heads, do not contribute to the calculation because Matt stopped flipping while still in the middle of a run where the heads hadn't yet overtaken the tails. But 198 flips is a small proportion of 10,000 flips, and the heads and tails were roughly balanced in the prefix that was used (certainly not 80% heads).

Grant Parish

What type of Rubik's cube is that in the background by Matt's arm? I don't think I have that one and I need it

Peter Dillinger

The critical word I missed in his terse description was "average". It's a convergence of the average ratio for runs with more heads, not a convergence of the ratio. Very different weighting.

Rick Rubenstein

D’oh: Pillars of CREATION. Stellar nursery, not an RPG.

Elim Garak

I was curious what the result would be if the roles of heads and tails were reversed, so I wrote my own little program to calculate pi using runs of tails instead of heads. And I have to say, tails never fails as I got a much more accurate estimate of 3.1263405682. Or, to round generously, 3.13.