Introduction to the craps data

In this investigation we will continue using the game of craps to unravel the laws of probability. At the same time we will begin building an understanding of how casinos make sure to build games that keep the odds in their favor in the long run. This will be critical for you as you begin thinking about how you will build your own casino game.

Recall that on Friday you all played craps as a class. While playing craps, you played the game many times and recorded the outcomes as you went. Bradshaw compiled the outcomes from most of your games into a large spreadsheet so that we can take a closer look at the data. Our goal in this investiation is to estimate the probabilities associated with each outcome in the game.

Part I: Understand the sample space and outcomes of the game

  1. Recall the sample space is the set of all possible outcomes in a probability experiment. What is the sample space of the game of Craps? In other words, what are the possible outcomes that can happen in the game? Write these down.
  2. Recall that disjoint event are events that cannot happen simultaneously. Are each of the events found in the contingency table in the spreadsheet disjoint from one another? Write down an explanation.

Part II: Count the number of times each outcome occurred

  1. Use the COUNTIF() function and the contingency table found in the spreadsheet to count the number of times each event occurred in each of our 257 trials.
  2. Use the SUM() fuction to count the number of times the game ended in the come out round and list this in the contingency table. 3.Use the SUM() fuction to count the number of times the game ended after the come out round and list this in the contingency table.
  3. Use the SUM() fuction to count the number of times the shooter won and list this in the contingency table.
  4. Use the SUM() fuction to count the number of times the house won and list this in the contingency table.

Part III: Calculate the empirical event probabilities

Recall that we can estimate the probability of an event by counting the number of times an event happened and dividing that by the total number of times we conducted a probability experiment.

  1. Calculate the probability that the shooter wins on the come out roll and list this probability in the probabilities table in the spreadsheet. 2.Calculate the probability that the house wins on the come out roll and list this probability in the probabilities table in the spreadsheet.
  2. Calculate the probability that the shooter wins after the come out roll and list this probability in the probabilities table in the spreadsheet.
  3. Calculate the probability that the house wins after the come out roll and list this probability in the probabilities table in the spreadsheet.

Part IV: Calculate the empirical union probabilities

Recall that we can calculate the probability of the union of disjoint events using the addtion rule for disjoint events.

  1. Write down the possible events where the player wins in craps.
  2. Use the addition rule for disjoint events alongside the events you listed in (1) to calculate the probability that a player wins in craps.
  3. Write down the possible events where the house wins in craps.
  4. Use the addition rule for disjoint events alongside the events you listed in (3) to calculate the probability that the house wins in craps.
  5. Write down the possible events that lead to the game ending in the come out round.
  6. Use the addition rule for disjoint events alongside the events you listed in (5) to calculate the probability that the the game ends in the come out round.
  7. Write down the possible events that lead to the game ending after the come out round.
  8. Use the addition rule for disjoint events alongside the events you listed in (7) to calculate the probability that the the game ends after the come out round.

Part V: Synthesize your results.

We now need to analyze the probabilities we calculated in order to make sense of them. What do the numbers have to tell us?

  1. As a player, are the odds in your favor playing craps if you play many times? In the end will you end up making money or losing money?
  2. Take a look at the probability the game ends in the come out round vs the probability the game ends after. Why do you think the game is structured this way?
  3. Write down any take aways you have that you can apply to your own casino game. How can you borrow aspects of craps to design your game?