The transitive property is ingrained in our thinking. It gives our brains a simple, straightforward way to process the world — especially with numbers. If one thing is better or more valuable than another, and that second thing is better than a third, you KNOW that the first one is better than the third.
But it doesn’t always work that way. And if you fail to recognize when real life violates the pattern of transitivity, you’re going to run head first into a veridical paradox.
Efron’s non-transitive dice demonstrate that hard and fast rules about value don’t always exist. By toying with relative probabilities, Efron discovered that a die’s superiority or weakness can be relative — and as the dice values get more complex, it becomes nearly impossible to reason out which die is stronger against the others.
In math, our first impressions are often deceptive. Occasionally they’re just plain wrong. And sometimes a game is designed to deceive you into believing you’re in a position of strength when there’s no way to win. That’s the deception paradox.
Oh — and if someone wants to play a game with you and they let you go first… run.
*** LINKS ***
Talk Vsauce2 in The Create Unknown Discord: https://discord.gg/tyh7AVm
Vsauce2 on Reddit: https://www.reddit.com/r/vsauce2/
Hosted and Produced by Kevin Lieber
Research and Writing by Matthew Tabor
Tweets by TaborTCU
Editing by John Swan
Huge Thanks To Paula Lieber
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