R-Cade Games: Simulating the Legendary Game of Pong

The legendary game of PongPong is one of the earliest arcade games on the market, first released in 1972. From the day I first saw this miracle box, I wanted to know more about computers.

I learnt how to write code from the 1983 book Dr. C. Wacko’s Miracle Guide to Designing and Programming your own Atari Computer Arcade Games. This book explains in a very clear and humorous way how to write computer games in Atari basic. I devoured this book and spent many hours developing silly games. This article is an ode to Dr Wacko, a computer geek’s midlife-crisis and an attempt to replicate the software I developed thirty years ago.

I showed in a previous post that R can be used for board games. The question is whether we create arcade games in R. My challenge is to recreate the look and feel of 1980s arcade games, or R-Cade games, using R? The code shown below simulates the legendary game of pong.

Playing Pong in R

The code is based on the Wacko’s Boing Program in the above-mentioned book. The R code is fully commented and speaks for itself. Please note that the animation is very clunky when you run it in RStudio. Only the native R Terminal displays the animation correctly.

Perhaps somebody can help me perfect this little ditty. I love to know how to read real-time USB input to control the game, so we get a step closer to the first R-Cade game.

The Pong Code

# Sound library
library(beepr) 

# Game parameters
skill <- 0.87 # Skill (0-1)
score <- 0
high.score <- 0

# Define playing field
par(mar = rep(1,4), bg = "black")
plot.new()
plot.window(xlim = c(0, 30), ylim = c(0, 30))
lines(c(1, 30, 30, 1), c(0, 0, 30, 30), type = "l", lwd = 5, col = "white")

# Playing field boundaries (depend on cex)
xmin <- 0.5
xmax <- 29.4
ymin <- 0.5
ymax <- 29.4

# initial position
x <- sample(5:25, 1)
y <- sample(5:25, 1)
points(x, y, pch = 15, col = "white", cex = 2)

# Paddle control
psize <- 4
ypaddle <- y

# Set direction
dx <- runif(1, .5, 1)
dy <- runif(1, .5, 1) 

# Game play 
while (x > xmin - 1) {
    sound <- 0 # Silence
    Sys.sleep(.05) # Pause screen. Reduce to increase speed
    points(x, y, pch = 15, col = "black", cex = 2) # Erase ball
    # Move ball
    x <- x + dx
    y <- y + dy 
    # Collision detection 
    if (x > xmax) {
        dx <- -dx * runif(1, .9, 1.1) # Bounce 
        if (x > xmin) x <- xmax # Boundary
        sound <- 10 # Set sound
        }
    if (y < ymin | y > ymax) {
        if (y < ymin) y <- ymin 
        if (y > ymax) y <- ymax
        dy <- -dy * runif(1, .9, 1.1)
        sound <- 10
    }
    # Caught by paddle?
    if (x < xmin & (y > ypaddle - (psize / 2)) & y < ypaddle + (psize / 2)) {
        if (x < xmin) x <- xmin
        dx <- -dx * runif(1, .9, 1.1)
        sound <- 2
        score <- score + 1
        }
    # Draw ball
    points(x, y, pch = 15, col = "white", cex = 2)
    if (sound !=0) beep(sound)
    # Move paddle
    if (runif(1, 0, 1) < skill) ypaddle <- ypaddle + dy # Imperfect follow
    # Draw paddle
    # Erase back line
    lines(c(0, 0), c(0, 30), type = "l", lwd = 8, col = "black")
    # Keep paddle inside window
    if (ypaddle < (psize / 2)) ypaddle <- (psize / 2) 
    if (ypaddle > 30 - (psize / 2)) ypaddle <- 30 - (psize / 2) 
    # Draw paddle 
    lines(c(0, 0), c(ypaddle - (psize / 2), ypaddle + (psize / 2)), type = "l", lwd = 8, col = "white") 
} 
beep(8) 
text(15,15, "GAME OVER", cex=5, col = "white") 
s <- ifelse(score == 1, "", "s")
text(15,5, paste0(score, " Point", s), cex=3, col = "white") 

Tic Tac Toe War Games: The Intelligent Minimax Algorithm

Tic Tac Toe War GamesIn a previous post, I shared how to build a randomised Tic Tac Toe simulation. The computer plays against itself playing at random positions. In this post, I will share how to teach the computer to play the game strategically.

I love the 1983 classic movie War Games. In this film, a computer plays Tic Tac Toe against itself to learn that it cannot win the game to prevent a nuclear war.

Back in those days, I devoured the wonderful book Writing Strategy Games on your Atari by John White which contains an algorithm to play Tic Tac Toe War Games. This is my attempt to relive the eighties using R.

You can find the code on my GitHub page.

Drawing the Board

A previous post describes the function that draws the Tic Tac Toe board. For completeness, the code is replicated below. The game board is a vector of length nine consisting of either -1 (X), 0 (empty field) or 1 (O). The vector indices correspond with locations on the game board:

1 2 3
4 5 6
7 8 9

draw.board <- function(board) { # Draw the board
    xo <- c("X", " ", "O") # Symbols
    par(mar = rep(0,4))
    plot.new()
    plot.window(xlim = c(0,30), ylim = c(0,30))
    abline(h = c(10, 20), col="darkgrey", lwd = 4)
    abline(v = c(10, 20), col="darkgrey", lwd = 4)
    pieces <- xo[board + 2]
    text(rep(c(5, 15, 25), 3), c(rep(25, 3), rep(15,3), rep(5, 3)), pieces, cex = 6)
    # Identify location of any three in a row
    square <- t(matrix(board, nrow = 3))
    hor <- abs(rowSums(square))
    if (any(hor == 3)) 
      hor <- (4 - which(hor == 3)) * 10 - 5 
    else 
      hor <- 0
    ver <- abs(colSums(square))
    if (any(ver == 3)) 
      ver <- which(ver == 3) * 10 - 5 
    else
      ver <- 0
    diag1 <- sum(diag(square))
    diag2 <- sum(diag(t(apply(square, 2, rev)))) # Draw winning lines if (hor > 0) lines(c(0, 30), rep(hor, 2), lwd=10, col="red")
    if (ver > 0) lines(rep(ver, 2), c(0, 30), lwd=10, col="red")
    if (abs(diag1) == 3) lines(c(2, 28), c(28, 2), lwd=10, col="red")
    if (abs(diag2) == 3) lines(c(2, 28), c(2, 28), lwd=10, col="red")
}

Human Players

This second code snippet lets a human player move by clicking anywhere on the graphic display using the locator function. The click location is converted to a number to denote the position on the board. The entered field is only accepted if it has not yet been used (the empty variable contains the available fields).

# Human player enters a move
move.human <- function(game) {
    text(4, 0, "Click on screen to move", col = "grey", cex=.7)
    empty <- which(game == 0)
    move <- 0
    while (!move %in% empty) {
        coords <- locator(n = 1) # add lines
        coords$x <- floor(abs(coords$x) / 10) + 1
        coords$y <- floor(abs(coords$y) / 10) + 1
        move <- coords$x + 3 * (3 - coords$y)
    }
    return (move)
}

Evaluate the Game

This code snippet defines the eval.game function which assesses the current board and assigns a score. Zero means no outcome, -6 means that the X player has won and +6 implies that the O player has won.

# Evaluate board position
eval.game <- function(game, player) {
    # Determine game score
    square <- t(matrix(game, nrow = 3))
    hor <- rowSums(square)
    ver <- colSums(square)
    diag1 <- sum(diag(square))
    diag2 <- sum(diag(t(apply(square, 2, rev))))
    eval <- c(hor, ver, diag1, diag2)
    # Determine best score
    minimax <- ifelse(player == -1, "min", "max")
    best.score <- do.call(minimax, list(eval))
    if (abs(best.score) == 3) best.score <- best.score * 2
    return (best.score)
}

Computer Moves

The computer uses a modified Minimax Algorithm to determine its next move. This article from the Never Stop Building blog and the video below explain this method in great detail.

The next function determines the computer’s move. I have not used a brute-force minimax algorithm to save running time. I struggled building a fully recursive minimax function. Perhaps somebody can help me with this. This code looks only two steps deep and contains a strategic rule to maximise the score.

The first line stores the value of the players move, the second remainder of the matrix holds the evaluations of all the opponents moves. The code adds a randomised variable, based on the strategic value of a field. The centre has the highest value because it is part of four winning lines. Corners have three winning lines and the rest only two winning lines. This means that the computer will, all things being equal, favour the centre over the corners and favour the other fields least. The randomised variables in the code ensure that the computer does not always pick the same field in a similar situation.

# Determine computer move
move.computer <- function(game, player) {
    empty <- which(game == 0)
    eval <- matrix(nrow = 10, ncol = 9, data = 0)
    for (i in empty) {
        game.tmp <- game
        game.tmp[i] <- player
        eval[1, i] <- eval.game(game.tmp, player)
        empty.tmp <- which(game.tmp ==0)
        for (j in empty.tmp) {
            game.tmp1 <- game.tmp
            game.tmp1[j] <- -player
            eval[(j + 1), i] <- eval.game(game.tmp1, -player)
        }
    }
    if (!any(abs(eval[1,]) == 6)) { # When winning, play move
        # Analyse opponent move
        minimax <- ifelse(player == -1, "max", "min") # Minimax
        best.opponent <- apply(eval[-1,], 1, minimax)
        eval[1,] <- eval[1,] * -player * best.opponent
    }
    # Add randomisation and strategic values
    board <- c(3, 2, 3, 2, 4, 2, 3, 2, 3) # Strategic values
    board <- sapply(board, function(x) runif(1, 0.1 * x, (0.1 * x) + 0.1)) # Randomise
    eval[1, empty] <- eval[1, empty] + player * board[empty] # Randomise moves
    # Pick best game
    minimax <- ifelse(player == -1, "which.min", "which.max") # Minimax
    move <- do.call(minimax, list(eval[1,])) # Select best move
    return(move)
}

This last code snippet enables computers and humans play each other or themselves. The players vector contains the identity of the two players so that a human can play a computer or vice versa. The human player moves by clicking on the screen.

The loop keeps running until the board is full or a winner has been identified. A previous Tic Tac Toe post explains the draw.board function.

# Main game engine
tic.tac.toe <- function(player1 = "human", player2 = "computer") {
    game <- rep(0, 9) # Empty board
    winner <- FALSE # Define winner
    player <- 1 # First player
    players <- c(player1, player2)
    draw.board(game)
    while (0 %in% game & !winner) { # Keep playing until win or full board
        if (players[(player + 3) %% 3] == "human") # Human player
            move <- move.human(game)
        else # Computer player
            move <- move.computer(game, player)
        game[move] <- player # Change board
        draw.board(game)
        winner <- max(eval.game(game, 1), abs(eval.game(game, -1))) == 6 # Winner, winner, chicken dinner?
        player <- -player # Change player
    }
}

You can play the computer by running all functions and then entering tic.tac.toe().

I am pretty certain this simplified minimax algorithm is unbeatable—why don’t you try to win and let me know when you do.

Tic Tac Toe War Games

Now that this problem is solved, I can finally recreate the epic scene from the WarGames movie. The Tic Tac Toe War Games code uses the functions explained above and the animation package. Unfortunately, there are not many opportunities to create sound in R.

# WAR GAMES TIC TAC TOE
source("Tic Tac Toe/Tic Tac Toe.R")

# Draw the game board
draw.board.wargames <- function(game) {
    xo <- c("X", " ", "O") # Symbols
    par(mar = rep(1,4), bg = "#050811")
    plot.new()
    plot.window(xlim = c(0,30), ylim = c(0,30))
    abline(h = c(10, 20), col = "#588fca", lwd = 20)
    abline(v = c(10, 20), col = "#588fca", lwd = 20)
    text(rep(c(5, 15, 25), 3), c(rep(25, 3), rep(15,3), rep(5, 3)), xo[game + 2], cex = 20, col = "#588fca")
    text(1,0,"r.prevos.net", col = "#588fca", cex=2)
    # Identify location of any three in a row
    square <- t(matrix(game, nrow = 3))
    hor <- abs(rowSums(square))
    if (any(hor == 3)) 
        hor <- (4 - which(hor == 3)) * 10 - 5 
    else 
        hor <- 0
    ver <- abs(colSums(square))
    if (any(ver == 3)) 
        ver <- which(ver == 3) * 10 - 5 
    else
        ver <- 0
    diag1 <- sum(diag(square))
    diag2 <- sum(diag(t(apply(square, 2, rev)))) # Draw winning lines if (all(hor > 0)) for (i in hor) lines(c(0, 30), rep(i, 2), lwd = 10, col="#588fca")
    if (all(ver > 0)) for (i in ver) lines(rep(i, 2), c(0, 30), lwd = 10, col="#588fca")
    if (abs(diag1) == 3) lines(c(2, 28), c(28, 2), lwd = 10, col = "#588fca")
    if (abs(diag2) == 3) lines(c(2, 28), c(2, 28), lwd = 10, col = "#588fca")
}

library(animation)
player <- -1
games <- 100
saveGIF ({
    for (i in 1:games) {
        game <- rep(0, 9) # Empty board
        winner <- 0 # Define winner
        #draw.board.wargames(game)
        while (0 %in% game & !winner) { # Keep playing until win or full board
            empty <- which(game == 0)
            move <- move.computer(game, player)
            game[move] <- player
            if (i <= 12) draw.board.wargames(game)
            winner <- max(eval.game(game, 1), abs(eval.game(game, -1))) == 6
            player <- -player } if (i > 12) draw.board.wargames(game)
    }
},
interval = c(unlist(lapply(seq(1, 0,-.2), function (x) rep(x, 9))), rep(0,9*94)), 
movie.name = "wargames.gif", ani.width = 1024, ani.height = 1024)

Tic Tac Toe Simulation — Random Moves

Tic Tac Toe Simulation - Part 1Tic Tac Toe might be a futile children’s game but it can also teach us about artificial intelligence. Tic Tac Toe, or Naughts and Crosses, is a zero-sum game with perfect information. Both players know exactly what the other did and when nobody makes a mistake, the game will always end in a draw.

Tic Tac Toe is a simple game but also the much more complex game of chess is a zero-sum game with perfect information.

In this two-part post, I will build an unbeatable Tic Tac Toe Simulation. This first part deals with the mechanics of the game. The second post will present an algorithm for a perfect game.

Drawing the Board

This first code snippet draws the Tic Tac Toe simulation board. The variable xo holds the identity of the pieces and the vector board holds the current game. Player X is denoted with -1 and player O with +1. The first part of the function draws the board and the naughts and crosses. The second part of the code check for three in a row and draws the corresponding line.

draw.board <- function(board) { # Draw the board
    xo <- c("X", " ", "O") # Symbols
    par(mar = rep(0,4))
    plot.new()
    plot.window(xlim = c(0,30), ylim = c(0,30))
    abline(h = c(10, 20), col="darkgrey", lwd = 4)
    abline(v = c(10, 20), col="darkgrey", lwd = 4)
    pieces <- xo[board + 2]
    text(rep(c(5, 15, 25), 3), c(rep(25, 3), rep(15,3), rep(5, 3)), pieces, cex = 6)
    # Identify location of any three in a row
    square <- t(matrix(board, nrow = 3))
    hor <- abs(rowSums(square))
    if (any(hor == 3)) 
      hor <- (4 - which(hor == 3)) * 10 - 5 
    else 
      hor <- 0
    ver <- abs(colSums(square))
    if (any(ver == 3)) 
      ver <- which(ver == 3) * 10 - 5 
    else
      ver <- 0
    diag1 <- sum(diag(square))
    diag2 <- sum(diag(t(apply(square, 2, rev)))) 
    # Draw winning lines 
    if (hor > 0) lines(c(0, 30), rep(hor, 2), lwd=10, col="red")
    if (ver > 0) lines(rep(ver, 2), c(0, 30), lwd=10, col="red")
    if (abs(diag1) == 3) lines(c(2, 28), c(28, 2), lwd=10, col="red")
    if (abs(diag2) == 3) lines(c(2, 28), c(2, 28), lwd=10, col="red")
}

Random Tic Tac Toe

The second part of the code generates ten random games and creates and animated GIF-file. The code adds random moves until one of the players wins (winner <> 0) or the board is full (no zeroes in the game vector). The eval.winner function checks for three in a row and declares a winner when found.

There are 255,168 possible legal games in Tic Tac Toe, 46,080 of which end in a draw. This implies that these randomised games result in a draw 18% of the time.

eval.winner <- function(board) { # Identify winner
    square <- t(matrix(board, nrow = 3))
    hor <- rowSums(square)
    ver <- colSums(square)
    diag1 <- sum(diag(square))
    diag2 <- sum(diag(t(apply(square, 2, rev))))
    if (3 %in% c(hor, ver, diag1, diag2)) return (1)
    else
        if (-3 %in% c(hor, ver, diag1, diag2)) return (2)
    else
        return(0)
}

# Random game
library(animation)
saveGIF ({
 for (i in 1:10) {
 game <- rep(0, 9) # Empty board
 winner <- 0 # Define winner
 player <- -1 # First player
 draw.board(game)
 while (0 %in% game & winner == 0) { # Keep playing until win or full board
   empty <- which(game == 0) # Define empty squares
   move <- empty[sample(length(empty), 1)] # Random move
   game[move] <- player # Change board
   draw.board(game)
   winner <- eval.winner(game) # Evaulate game
   player <- player * -1 # Change player
 }
 draw.board(game)
 }
 },
 interval = 0.25, movie.name = "ttt.gif", ani.width = 600, ani.height = 600)

Tic Tac Toe Simulation

In a future post, I will outline how to program the computer to play against itself, just like in the 1983 movie War Games.