Exploring Probability Through Yahtzee Extensions. Chris Bolognese Upper Arlington High School firstname.lastname@example.org. Goals of the Talk. Motivation with Supportive Research Data Collection & Analysis via Nspires Java Simulation Showcase Sample Student Work Reflection. Motivation.
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Exploring Probability Through Yahtzee Extensions
Upper Arlington High School
Goal was to create cognitively-demanding tasks related to probability and statistics.
Roll five dice to get different combinations. The dice can be rolled up to three times in a turn, reserving dice as needed. The goal is to make one of thirteen different combinations (such as three-of-a-kind, or a large straight). The roll worth the most points is a Yahtzee (all five dice have the same value).
on the very first roll?
There are 65 possible rolls, with only 6 outcomes as Yahtzees, one for each of the six face values. Thus, the probability of a Yahtzee is 6/65 ≈ 0.077%
This is much harder as it requires a transition matrix. One can show that the probability is roughly 4.6029%.
In Yahtzee, we have to stop rolling after at
most three rolls… But that’s no fun!
What if we are determined to get a Yahtzee
and continue to roll. What is the expected
number of rolls to obtain a Yahtzee?
With a partner, experimentally determine the
number of rolls to get at least one Yahtzee,
reserving matching dice as needed. Then
share your data.
While we could continually roll to collect
data, let’s use technology to simulate this
How does this simulation compare to our
This graph (DataGenetics, 2012) shows the
chance of getting Yahtzee in n-rolls.
Probability of Yahtzee in at most 2 Rolls
7./8. Look for patterns and structure
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