## Shuffle Board

Shuffle Board is authored in the NetLogo modeling-and-simulation environment. The model is part of ProbLab, a curricular unit designed to enrich student understanding of the domain. The online unit package will include a suite of models, student worksheets, and a teacher guide. Below is an applet of Shuffle Board. You can interact with this model by changing the slider values and then pressing SETUP and GO ONCE or GO to run this model under different settings. For more details, please download the model. Note that this model is still under development and is yet to undergo our rigorous checkout procedure.

CM ProbLab: Shuffle Board -- Attempts until success ("waiting time") and streaks of consecutive successes
Don't see nothin'?

Gist

Shuffle Board simulates an experiment in which a bounded number of elements with a fixed proportion of favored events is repeatedly shuffled. Here there are 121 candy boxes, and only some of them -- according to your setting of the slider AVERAGE-DISTANCE -- have prizes inside. If you set that slider at 5, then every fifth candy box, on average, will have a prize. In fact, if you press Setup, then literally every fifth bottle will have a prize, counting from the top left corner, running all the way to the right, then skipping down to the second row, and so on. The numbers in the "prize boxes" represent how many boxes had to be bought since the previous prize. The plots show two statistics: One plot, Frequency of Distances to Prizes, keeps accumulating the frequencies of runs since a previous prize to the next prize (as represented by the numbers on the prize boxes); The other plot, Frequency of Streaks by Length, shows how many times we have received single successes, a pairs of successes, a success triplet, etc. The COLUMNS FACTOR helps us look at the ratio between the heights of adjacent columns in the plot immediately above it. For instance, the value of .8 would mean that on average, each column is .8 as tall as the column to its left. You can use the slider TRUNCATE AFTER COLUMN to determine how many columns you want to include in this average.

Riddles

• Riddle #1: Is there a relationship between the value of AVERAGE-DISTANCE and the value of COLUMNS FACTOR? in the plot FREQUENCY OF DISTANCES TO PRIZES?

• Riddle #2: If each candy box is equally likely to contain a prize, why is it that you are more likely to wait just a single turn to get a prize as compared to waiting two turns?

• Riddle #3: Is there a relationship between the value of AVERAGE-DISTANCE and the value of COLUMNS FACTOR in the plot FREQUENCY OF DISTANCES TO PRIZES?

[last updated July 8, 2005]