HandsOn 9 - Lottery Game

 You need the Winning Streak program to complete this activity. You can download it to your computer or use it online in a Java applet. This program is not available for Windows at this time. Download Winning Streak: Java Mac OS 7.x Not Available

Flip a coin over and over again until you get three heads in a row. Now choose one of these strategies and stick to it.

• Strategy #1: If you believe in a winning streak, bet that the next flip will be a head.

• Strategy #2: If you believe in luck running out, bet that the next flip will be a tail.

• Strategy #3: If you believe the next flip is random, bet on heads the first time, bet on tails the next, and so forth.

Now flip the coin a fourth time. How did it come out? Did you win or lose?

Again, flip the coin until you get three heads in a row, then make another bet, using the same strategy. Assume that a win brings you \$1.00 and a loss costs you \$1.00. Carry out this procedure again and again. Keep track of how much "money'' you win or lose.

 Q3.3: Can we speed up this process? Suppose you flip three different coins at once by shaking them in your cupped hands and throwing them on the table. Then just look to see if all three are heads. If not, shake them up and throw them down again and again until all three do come up heads. Then flip a fourth coin by hand and see if you win or lose according to your chosen strategy. Discuss the following question: Do you expect that this will give the same result as flipping a fourth time after the same coin has come up heads three times in a row?

Now move on to the computer program called Winning Streak. This time the computer program allows you to bet on the outcome of a coin-flip after four coins in a row land on the same side (four heads or four tails). With the computer flipping coins, you can test your strategy faster than you could flipping coins by hand. What is the result?

Is your strategy a winner? or a loser? Or do you break even? If your friends are doing the same activity, pool your results in order to compare the success rates of different strategies. Continue your discussion until there is general agreement that (i) winning streaks exist, (ii) losing streaks exist, or (iii) the next flip cannot be predicted: each flip is random.

Previous: 3.1 - Measuring Randomness

Next: 3.2 - Observed Distributions