The Lottery game is an applet which displays the random outcome of a series of flips of a coin. It allows the user to guess the outcome of the next flip of the coin. The applet registers the number of wins and losses by the user. It also shows the number of heads and number of tails in the previous flips.
Type of Material:
This applet could be used at any level to demonstrate the concepts of randomness and unpredictability.
It requires a "Java-enabled" browser.
Identify Major Learning Goals:
The applet shows how the outcome of the flip of a coin cannot be predicted from previous flips. There is no strategy based on either ?winning streaks? or ?luck to run out? which could be used to predict the flip of a coin.
To demonstrate this fact, the author suggests two strategies for prediction and encourages the user to test them.
Target Student Population:
Any students being introduced to randomness.
Prerequisite Knowledge or Skills:
The page contains an introduction to randomness. It explains that the past outcomes in the throw of a coin cannot be used to predict future outcomes. It explains how the outcomes of future flips of a coin are independent of what happened before. The site tries to dispel two opposite misconceptions about randomness. One is the existence of "winning streaks" (a gambler in a winning streak is more likely to win than to lose). The other is the idea that "luck can run out" (since the average number of wins is 0.5, after a series of losses, a win is more likely than a loss). Students are encouraged to try these and other possible strategies.
The introduction is sketchy, which is probably deliberate. Yet this can cause problems with students who don?t go through the process that the author envisions.
Potential Effectiveness as a Teaching Tool
Students are asked to think about the correctness of several statements about randomness. Students are encouraged to devise a winning strategy and use it. The applet itself allows students to try to guess the outcome of the next (random) flip of a coin in a series of flips. After enough repetitions students will see that no strategy gives a true advantage. Thus the applet shows there is no strategy for guessing the outcome of the next flip of a coin.
It can require a large number of repetitions to see that a given strategy is neither advantageous nor non-advantageous. A way to overcome the need of a large number of repetitions is to ask students about their conclusions. Most likely some of the students will be doing well and some of the them will be doing poorly.
Ease of Use for Both Students and Faculty
The applet is very easy to use. It has several options. The basic function is to try to guess the outcome of the next flip of the coin. The applet scores the user?s number of wins and the number of losses. Coins can also be flipped without guesses made. This is possible one coin at a time and also until a streak of several (between one and 10) equal consecutive outcomes occurs. This latter option ?flip until k equal? is what can be used to test conjectures about the behavior of streaks.
A short set of instructions could help the user despite the near self-explanatory nature of the applet.
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