pairs.r

pairsGame <- function(cards, maxTries){
  unknown_fields <- sample(c(1:cards, 1:cards), 2*cards, replace=FALSE)
  known_fields <- c()
  won_pairs <- c()
  
  playRound <- function(){
    # check if we already know a pair
    if(anyDuplicated(known_fields) != 0){
      # Open both Card of the pair
      card <- known_fields[duplicated(known_fields)]
      won_pairs <<- c(won_pairs, card)
      known_fields <<- known_fields[known_fields != card]
      return(TRUE) # Exit with found pair
    }
    
    # Open the first unknown card
    if(unknown_fields[1] %in% known_fields){ # If the card is known open it
      won_pairs <<- c(won_pairs, unknown_fields[1])
      known_fields <<- known_fields[known_fields != unknown_fields[1]]
      unknown_fields <<- unknown_fields[-1]
      return(TRUE) # Exit with found pair
    }else{ # If the card is new, move it to known cards...
      known_fields <<- c(known_fields, unknown_fields[1])
      unknown_fields <<- unknown_fields[-1]
      
      # ...and open the next one
      known_fields <<- c(known_fields, unknown_fields[1])
      unknown_fields <<- unknown_fields[-1]
      
      return(FALSE) # Exit without found pair
    }
  }
  
  
  #
  # Play until 3 errors
  #
  tries <- 0;
  while(tries < maxTries && length(won_pairs) < cards){
    if(!playRound()){
      tries <- tries +1
    }
  }
  
  outcome <- -1
  if(tries == 0) outcome <- 3
  else if(length(won_pairs) >= 7) outcome <- 2
  else if(length(won_pairs) >= 5) outcome <- 1
  else if(length(won_pairs) >= 2) outcome <- 0
  
  return(c(outcome=outcome, found_pairs=length(won_pairs)))
}

runAnalysis <- function(x){
  print(paste("Spiele", x,"mal Memory..."))
  data <- data.frame(t(replicate(x, pairsGame(8, 3))))

  print(paste("Erwartungswert (laut Gewinn-Schlüssel):", mean(data$outcome)))
  print("Verteilung der Anzahl der gefundenen Paare:")
  print(table(data$found_pairs))
  hist(data$found_pairs, col="gray", xlab="Gefundene Paare", main="Verteilung der gefundenen Paare", breaks=seq(-0.5, 8.5, by=1))
}

printHists <- function(x){
  data3 <- data.frame(t(replicate(x, pairsGame(8, 3))))
  data4 <- data.frame(t(replicate(x, pairsGame(8, 4))))
  data5 <- data.frame(t(replicate(x, pairsGame(8, 5))))

  hist(data3$found_pairs, col=rgb(1,0,0,1/4), breaks=seq(-0.5, 8.5, by=1))
  hist(data4$found_pairs, col=rgb(0,1,0,1/4), breaks=seq(-0.5, 8.5, by=1), add=T)
  hist(data5$found_pairs, col=rgb(0,0,1,1/4), breaks=seq(-0.5, 8.5, by=1), add=T)
  title(xlab="Gefundene Paare", main="Verteilung der gefundenen Paare")
}

runAnalysis(10000)