HandsOn 9 - Lottery Game
a coin over and over again until you get three heads in a row. Now
choose one of these strategies and stick to it. See the Java Applet Page
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.
flip the coin a fourth time. How did it come out? Did you win or
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?
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.
3.1 - Measuring Randomness