Today in #Logic: #expectedValue/utility

Student calculations determined whether to kick a field goal or go for first down, whether to buy smartphone #insurance, how to optimize #retirement #savings, and where to deploy troops to minimize losses.

Then they determined which part of a #trip to a country with known terrorist activity is riskiest: #driving to the airport, #flying to the country, or being in the country. (Driving was the riskiest part.)

If you play an infinite number of rounds you'll have infinite payoff (#probability theory #ExpectedValue)
But if you paid $1k to play each round your real world expected value is negative rather than the #infinity $ that math says it is.

Because...
Like #Martingale betting strategy, you don't have an infinite bankroll...
Nor infinite time.

As you keep tossing tails, you have exponential payoff growth, BUT you also have linear cost growth
And you cant buy time with $

3Blue1Brown on Wordle, probability, information theory, and expected value.

Or: Shannon, von Neumann, and Pascal walk into a word game...

Whether or not you've been sucked into this word game fad, this is a really good explanation of the relationships between probability and expected information value (I = -log2(p)), as well as how to optimally find one element within a known search space.

It explains the logic behind selecting starting words for Wordle, as well as how and why optimisers choose their own guesses, and what an optimal solver's ultimate limits would be.

https://yewtu.be/watch?v=v68zYyaEmEA

HN discuussion: https://news.ycombinator.com/item?id=30232413

#Wordle #3Blue1Brown #Video #InformationTheory #Probability #ClaudeShannon #JohnVonNeumann #BlaisePascal #ExpectedValue