library(readr)
library(dplyr)

betsAugust <- read_csv("betsAugust.csv")
betsJuly <- read_csv("betsJuly.csv")

bets <- rbind(betsAugust, betsJuly) %>% as.data.frame
bets <- arrange(bets,bets.settledAt)

bets$running_mean <- cummean(bets$bets.winLoss)
bets$running_sd <- lapply(1:nrow(bets), sequence) %>% sapply(function(I) bets[I, "bets.winLoss"] %>% sd)
bets$running_se <- bets$running_sd / sqrt(1:(nrow(bets)))


library(ggplot2)
g <- ggplot(bets, aes(x = 1:nrow(bets), y = running_mean)) + geom_line()
g <- g + geom_ribbon(aes(ymax = running_mean + 2*running_se,
                    ymin = running_mean - 2*running_se),
                alpha = 0.4)
g <- g + xlab("N") + ylab("EV estimate (95% CI)")
g + ggtitle("Running EV estimate and 95% confidence interval")