visualizing dreidel payoffs

dreidel.R

## https://forward.com/fast-forward/389673/finally-mathematical-proof-that-dreidel-is-a-terrible-game/
## Feinerman, Robert. “An Ancient Unfair Game.” American Mathematical Monthly 83, no. 8 (1976). https://www.jstor.org/stable/2319887.

library(emdbook)
library(ggplot2)
library(rayshader)
library(colorspace)

pvec <- 2:5
nvec <- 2:20
dd <- expand.grid(p = pvec, n = nvec)
dd$payoff <- with(dd,
     p/4 + (5/8)^(n-1)*(p-2)/8)

dd$payoff_sc <- with(dd,
                     (p/4 + (5/8)^(n-1)*(p-2)/8)/p)

gg0 <- ggplot(dd, aes(p, n)) + geom_raster(aes(fill=payoff_sc)) +
    labs(x = "number of players", y = "spin") +
    scale_x_continuous(position = "top", expand = c(0,0), breaks = pvec) +
    scale_y_continuous(expand = c(0,0)) +
print(gg0)

## flip labels so they look good when plot is rotated
flip <- element_text(angle = 180)
gg1 <- gg0 + theme(legend.position = "none",
                   axis.title.x = flip,
                   axis.title.y = flip,
                   axis.text.x = flip,
                   axis.text.y = flip)
                   
gg1R <- plot_gg(gg1, scale = 500)
rgl.snapshot("dreidel1.png")

theme_set(theme_bw(base_size=16))
gg2 <- ggplot(dd, aes(n, payoff_sc)) +
    geom_line(aes(colour = factor(p), group = p), linewidth = 3) + 
    labs(x = "spin", y = "payoff\n(scaled by number of players)") +
    scale_colour_discrete_sequential(palette = "Blues",
                                     name="number of\nplayers")
print(gg2)
ggsave("dreidel2.R")