/buffet_basketball.R
Last active Jan 4, 2016
What’s Warren Buffett’s $1 Billion Basketball Bet Worth? I look into it in this post http://wp.me/p1C5UP-gF
| ## Warren Buffet's 1B Basketball Challenge ## | |
| expected_value <- function(p,ngames=63,prize=1000000000){ | |
| p^ngames * prize | |
| } | |
| ## What is the expected value of an entry | |
| ## given a particular level of prediction accuracy | |
| expected_value(p=0.80) | |
| expected_value(p=0.85) | |
| ## Plotted ## | |
| par(lwd=3,cex=1.3) | |
| curve(expected_value(x), | |
| xlim=c(0.5,0.75), | |
| ylab='Expected Value (USD)', | |
| xlab="Probability of correctly predicting a single game") | |
| curve(expected_value(x), | |
| xlim=c(0.75,0.85), | |
| ylab='Expected Value (USD)', | |
| xlab="Probability of correctly predicting a single game") | |
| ## Odds that the prize will be awared | |
| winner_odds <- function(x,p=0.85){ | |
| 1-(1-(p)^63)^x | |
| } | |
| ## A million entries each with 80% accuracy | |
| winner_odds(x=1000000,p=0.8) | |
| ## A million entries each with 70% accuracy | |
| winner_odds(x=1000000,p=0.7) | |
| curve(winner_odds(x,p=0.8), | |
| xlim=c(0,1000000), | |
| xlab='# of Entrants', | |
| ylab='Probability of a winner', | |
| col='blue') | |
| curve(winner_odds(x,p=0.7), | |
| col='red',add=TRUE) | |
| legend("topleft", | |
| legend=c('80% accuracy','70% accuracy'), | |
| col=c('blue','red'), | |
| lty=1) |
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