Скачать или смотреть How Probability Helps Us Understand an Unbeatable Game

I'd like to thank Brilliant.org for sponsoring today's video. To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/polymathematic/. The first 200 of you will get 20% off Brilliant’s annual premium subscription.

Let's say I tell you I've got two dice, and when I roll one of them, we'll call it die A, it beats the other one, we'll call that die B, 58% of the time. First of all, you'd know something fishy is going on, right? It should not be the case that between two fair dice, one of them wins so often.

Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications 🔔

But, hear me out, I'm going to let you choose whichever of these dice to roll and try to beat me. So if you think one is better than the other, you're free to pick that die first. There is a third die, actually, we'll call that die C, but die B beats that one 58% of the time as well, so surely you wouldn't want to pick die C.

Well, surprising as it may be, even though die A beats die B most of the time, and die B beats die C most of the time, die C actually beats die A at an even higher clip than either of the first two. Given the dice I'm using in this simulation, die C will beat die A about 69% of the time.

This is the beauty of what are called intransitive dice. These dice are not unfair in the sense that they're weighted (in fact, if they were weighted, it's less likely that this property ever emerges). Instead, the dice all have the same expected value, but very different modal probabilities. It's that difference that I explore here.

If you'd like to play around with the simulation itself, I modeled it out in ‪@Desmos‬ , and you can find that graph here: https://www.desmos.com/calculator/bs1....

If you'd like to see the sample spaces, those were also modeled in Desmos:
Fair Dice Sample Space: https://www.desmos.com/calculator/mlo...
Intransitive Dice Sample Space: https://www.desmos.com/calculator/czl...

If you'd like the "net" of a die, you can see that here: https://www.desmos.com/calculator/upt....

Finally, if you'd like to read more about intransitive dice, this Quanta article inspired me to make the original simulation: https://www.quantamagazine.org/mathem....

#probability #probabilitytheory #intransitivedice #thegameyoucannotwin

Follow Tim Ricchuiti:
TikTok:   / polymathematic  
Mathstodon: https://mathstodon.xyz/@polymathematic
Instagram:   / polymathematicnet  
Reddit:   / polymath-matic  
Facebook:   / polymathematic  

Watch more Math Videos:
Math Minis:    • Math Mini  
Math Minutes:    • Math Minutes  
Number Sense:    • Number Sense (UIL / PSIA)  
MATHCOUNTS:    • MATHCOUNTS  

FTC Disclosure: This video was sponsored by Brilliant.