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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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