Simulates the probability of winning the First Orchard Game https://www.habausa.com/my-very-first-games-first-orchard/

first_orchard_simulation.R

roll_die <- function(status, strategy) {
    roll = sample(c(names(status), "basket"), 1)
    if (roll == "basket") {
        trees = status[names(status) != "raven" & status > 0]
        if (strategy == "optimal") {
            biggest_trees = trees[trees == max(trees)]
            roll = sample(names(biggest_trees), 1)
        } else if (strategy == "random") {
            roll = sample(names(trees), 1)
        } else if (strategy == "worst") {
            smallest_trees = trees[trees == min(trees)]
            roll = sample(names(smallest_trees), 1)
        }
    }
    
    status[[roll]] = max(0, status[[roll]] - 1)
    
    return(status)
}

play_game <- function(strategy = c("optimal", "random", "worst")) {
    strategy = match.arg(strategy)
    
    status = c(
        red = 4,
        green = 4, 
        blue = 4, 
        yellow = 4,
        raven = 5
    )
    
    while (TRUE) {
        status = roll_die(status, strategy)
        if (status[["raven"]] == 0) {
            return(0)
        } else if (all(status[names(status) != "raven"] == 0)) {
            return(1)
        }
    }
    
}

optimal_games = vapply(1:100000, function(x) play_game(strategy = "optimal"), FUN.VALUE = 0)
random_games = vapply(1:100000, function(x) play_game(strategy = "random"), FUN.VALUE = 0)
worst_games = vapply(1:100000, function(x) play_game(strategy = "worst"), FUN.VALUE = 0)

mean(optimal_games) # 0.63175
mean(random_games)  # 0.59786
mean(worst_games)   # 0.55344