DICEWARS by R

dicewars.R

library(scatterplot3d)

p <- function(n) {
  m <- matrix(0, ncol=n, nrow=n*6)
  m[1:6, 1] <- 1/6

  val <- function(i, j) if(i < 1) 0 else m[i,j]

  for (j in 2:n) {
    for (i in j:(6*j)) {
      m[i,j] <- 1/6 * sum(sapply(i - 6:1, function(k) val(k, j-1)))

    }
  }
  m
}

m <- p(8)

plot.dists <- function(local.m=m) {
  oldpar <- par(mfrow=c(2, 4))
  for (i in 1:8) {
    x <- local.m[i:(6*i), i]
    names(x) <- as.character(i:(6*i))
    barplot(x, main=sprintf("N=%d", i))
  }
  par(oldpar)
}

dice.dist <- function(n1, n2, local.m=m) {
  p.n1 <- local.m[n1:(6*n1) ,n1]
  p.n2 <- local.m[n2:(6*n2), n2]

  p.mat <- outer(p.n1, p.n2)

  d.mat <- matrix(0, nrow=5*n1+2, ncol=5*n2+2)
  d.mat[2:(5*n1+2), 1] <- p.n1
  d.mat[1, 2:(5*n2+2)] <- p.n2
  d.mat[2:(5*n1+2), 2:(5*n2+2)] <- p.mat

  df <- data.frame(cols=as.vector(col(d.mat)),
                   rows=as.vector(row(d.mat)),
                   value=as.vector(d.mat),
                   color=as.vector(color.mat(n1,n2)))
  
  scatterplot3d(df, type="h", lwd=5, pch=" ",
                main=sprintf("%d vs %d", n1, n2),
                xlab=as.character(n2),
                ylab=as.character(n1),
                zlab="probability",
                label.tick.marks=F,
                scale.y=n1/n2,
#                x.ticklabs=as.character(n2:(6*n2)),
#                y.ticklabs=as.character(n1:(6*n1)),
#                xlim=1:(5*n2+1), ylim=1:(5*n1+1)
                )
}

color.mat <- function(n1, n2) {
  no.color="gray"
  color.p1 = "orange"
  color.p2 = "yellowgreen"
  color.win1 = "tomato"
  color.win2 = "green"
  color.draw = "yellow"
  
  c.mat <- matrix(no.color, nrow=5*n1+2, ncol=5*n2+2)
  c.mat[2:(5*n1+2), 1] <- color.p1
  c.mat[1, 2:(5*n2+2)] <- color.p2

  for (i in 2:(5*n1+2)) {
    for (j in 2:(5*n2+2)) {
      if (i + n1 > j + n2) {
        c.mat[i, j] <- color.win1
      }
      else if (i + n1 < j + n2) {
        c.mat[i, j] <- color.win2
      }
      else {
        c.mat[i, j] <- color.draw
      }
    }
  }
  c.mat
}

win.prop <- function(n.off, n.diff, local.m=m) {
  p <- 0
  for (i in n.off:(6*n.off)) {
    for (j in n.diff:(6*n.diff)) {
      if (i > j)
        p <- p + local.m[i, n.off] * local.m[j, n.diff]
    }
  }
  p
}

#  sapply(1:8, function(n1) sapply(1:8, function(n2) as.double(sprintf("%.4f", win.prop(n1,n2)*100))))
  
direct.8 <- function() {
  p.8 <- rep(0, 8 * 6)
  for (d1 in 1:6) {
    for (d2 in 1:6) {
      for (d3 in 1:6) {
        for (d4 in 1:6) {
          for (d5 in 1:6) {
            for (d6 in 1:6) {
              for (d7 in 1:6) {
                for (d8 in 1:6) {
                  i <- d1+d2+d3+d4+d5+d6+d7+d8
                  p.8[i] <- p.8[i] + 1
                }
              }
            }
          }
        }
      }
    }
  }
  p.8 / 6**8
}