Would you like to win a bit of money? Let’s wager on a card game for minor stakes. In front of you is a shuffled deck of cards. All 52 cards lie face down. Half the cards are red, and half are black. I will proceed to flip over the cards one by one. If the last card I flip over is red, you’ll win a dollar. Otherwise, you’ll lose a dollar.
Here’s the twist: you can ask me to halt the game at any time. Once you say “Halt,” I will flip over the next card and end the game. That next card will serve as the final card. You will win a dollar if it’s red, as shown in figure CS1.1.
Figure CS1.1 The card-flipping game. We start with a shuffled deck. I repeatedly flip over the top card from the deck. (A) I have just flipped the fourth card. You instruct me to stop. (B) I flip over the fifth and final card. The final card is red. You win a dollar.
We can play the game as many times as you like. The deck will be reshuffled every time. After each round, we’ll exchange money. What is your best approach to winning this game?
- Compute the probabilities of observable events using sample space analysis.
- Plot the probabilities of events across a range of interval values.
- Simulate random processes, such as coin flips and card shuffling, using Python.
- Evaluate our confidence in decisions drawn from simulations using confidence interval analysis.