# cf. e.g. 
 # Odd case: DOI:10.1016/0176-2680(93)90010-R
 # Even case with coinflip ties: DOI:10.1007/BF01718092
 library(tidyverse); options(scipen=999); library(ggthemes); library(extrafont)
 theme_set(theme_minimal()); theme_update(legend.position = "bottom", text=element_text(family="Lato"))
 
 f <- function(n,p) {
   h=floor(n/2)+1
   if(n %% 2) {
     return(sum(choose(n,seq(h,n)) * p^seq(h,n) * (1-p)^(n-seq(h,n))))
   } else {
     return((sum(choose(n,seq(h,n)) * p^seq(h,n) * (1-p)^(n-seq(h,n)))) +
       (choose(n,n/2) * p^(n/2) * (1-p)^(n/2)) * 1/2) 
   }
 }
 df = tibble(p = seq(0,1,0.01)) %>% rowwise() %>% 
   mutate("1" = f(1,p), "3" = f(3,p), "12" = f(12,p), "100" = f(100,p)) %>% 
   pivot_longer(c("1","3","12","100"), names_to="N", values_to="pg")
 
 df %>% ggplot(aes(p, pg, color=N)) + geom_line() +
   labs(title = element_blank(), x = element_blank(), y = element_blank()) + 
   scale_color_colorblind(breaks=c(1,3,12,100))
 
 ggsave("cjt.svg", width=1000, height=1000, units="px")