Boomgaard.R

# Simulation to estimate emperical odds to win the Haba game "Boomgaard".

# Set number of games to play
NUM.SIM = 10000

# Simulate one turn. Roll die and pick fruit or move bird.
# Input: game state.
# Output: game state after this turn.
turn <- function(state) {
  roll <- sample(1:6,1)
  
  # Five represents "basket" side of die which allows picking from any tree.
  if (roll == 5) {
    # Optimal strategy is to pick tree with most remaining fruit.
    roll <- which.max(state[1:4])
  }

  # Reduce state counter.
  state[roll] <- max(0, state[roll] - 1)
  return(state)
}

# Check if the game is over.
# Input: game state.
# Output: Boolean if game over (T=win, F=loss), NULL otherwise.
game.over <- function(state) {
  if (state[6] == 0) { return (F) }
  if (sum(state[1:4]) == 0) { return (T) }
  return (NULL)
}

# Play a game.
# Input: index (ignored).
# Output: Boolean game outcome (T=win, F=loss).
play.game <- function(i) {
  state <- c(4,4,4,4,0,5)
  while (is.null(game.over(state))) { state <- turn(state) }
  return(game.over(state))
}

# Simulate many games.
wins <- sapply(1:NUM.SIM, play.game)

# Compute win odds.
sum(wins) / NUM.SIM

Should return approximately 0.6244 (e.g. 62% odds to win).

To simulate increased difficulty by removing one bird path tile, set line 36 to state <- c(4,4,4,4,0,4).

Should return approximately 0.4608 (e.g. 46% odds to win).