Experiment 2: Your games as vectors

In the first phase you decided what you record of every game: behind which door the car stood, which door was chosen first, which one the host opened, and whether the player stayed or switched. Now these four facts get their form in R. Many games can be written down as four vectors, one per fact, where the first position always belongs to the first game, the second to the second, and so on. The slides use exactly these four facts to show how R holds vectors.

Play

Play at least twenty games in the game with three doors and take turns. Do not always decide the same way, but stay in about half of the games and switch in the other half. The game records every round and on request shows them as R code, one vector per fact. Also save your games as CSV and as RDS; you will need the files in the next phase.

Analyse

Below are ten example games. Replace them with your own: copy the R code from the game and paste it in place of the four lines.

Task: Answer with R, each question with one line under the vectors:

1. How often was the first choice already right, as a share of all games?
2. Which games were won? Create a vector won of TRUE or FALSE for this. A game is won by whoever stayed and was right at once, or switched and was wrong at first.
3. What percentage of all games were won?
4. In what percentage of the games did the player stay?
5. How often does staying win, and how often switching?

prize_door <- c(2, 1, 3, 3, 1, 2, 2, 3, 1, 1)
contestant_choice <- c(2, 3, 1, 1, 1, 1, 3, 2, 2, 1)
monty_opens <- c(1, 2, 2, 2, 3, 3, 1, 1, 3, 2)
decision <- c("stay", "switch", "stay", "switch", "switch", "stay", "switch", "stay", "switch", "stay")

length(prize_door)

mean(prize_door == contestant_choice)        # 1.: 0.3

won <- (decision == "stay" & prize_door == contestant_choice) |
  (decision == "switch" & prize_door != contestant_choice)
mean(won)                                    # 3.: 0.6
mean(decision == "stay")                     # 4.: 0.5
mean(won[decision == "stay"])                # 5.: 0.4
mean(won[decision == "switch"])              # 5.: 0.8