## 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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