This is the description and instructions for the Can You Beat Randomness?- The Lottery Game applet. It is a simulation of flipping coins. Students are asked to make conjectures about randomness and how certain strategies affect randomness. It strives to show the "growth of order out of randomness."
Source:
Email Address:
Technical Requirements:
Java-enabled browser
Content Quality Concerns:
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.
Content Quality Strengths:
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.
Ease of Use Concerns:
A short set of instructions could help the user despite the near self-explanatory nature of the applet.
Ease of Use Strengths:
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.
Potential Effectiveness Concerns:
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.
Potential Effectiveness Strengths:
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.
Potential Effectiveness Rating:
4
Source Code Available:
Source Code Available
Intended User Role:
Learner, Teacher, Author
Material Type:
Resource Type:
Statistical Topic:
Copyrights:
No
Cost:
Free for All
Format:
Math Level: