Portnoy’s 53 Under Bets

How much will Dave Portnoy win or lose on his 53 $10,000 bets today?

# Function to simulate 53 outcomes of over/under results (without any pushes)
portnoy.net <- function(){
    game <- c(1:53)
    wager <- rep(10000, 53)
    outcome <- sample(0:1, 53, replace = TRUE)

    df <- data.frame(game, wager, outcome)
    df$net <- 0
    for (i in 1:53){
        if(df$outcome[i] == 0) {df$net[i] <- -10000}
        if(df$outcome[i] == 1) {df$net[i] <- 9090.91}
    }
    sum(df$net)
}

# Set seed for reproducible results
set.seed(53)

# Simulating the net outcome of these 53 wagers if done 10,000 times
simulations <- 0
for (i in 1:10000){
    simulations[i] <- portnoy.net()
}

# Mean outcome
mean(simulations)

## [1] -24287.52

# Theoretical net outcome (probably not the most efficient way)
outcomes <- c(-10000, 9090.91)
px <- (c(0.5, 0.5))
xpx <- outcomes*px
sum(xpx)*53

## [1] -24090.89

His average overall outcome based on these simulations is to lose 24,288 bucks today. Which is close to the theoretical expected overall outcome of losing 24,091 dollars.

# Histogram showing range of results
options(scipen=5)
hist(simulations, breaks = 20)
abline(v = mean(simulations), col = "red")

A range of feasible expectations for his outcomes is anywhere from losing 133k to winning 100k. 5% chance it could be more extreme than that those boundaries.

# He needs 28 or more wins to come out in the black
# Probability of him winning 28+ of the 53 games
pbinom(27, 53, prob = 0.5, lower.tail = FALSE)

## [1] 0.3919232

He has a 39.1% chance of coming out net positive on the day.