Mr. Harless
Honors Geometry
Strategy Game Analysis
Game of 21
In class, you played the game of 21 several times and experimented with various strategies.
Based on this experience, you and your classmates stated several conjectures which seemed to be
true. Two of these conjectures were:
o If you leave four coins for your opponent, then you can always win the game.
o If you make the first move, then you can always win the game.
You task is to write a convincing argument of each of these conjectures. To do so, you will
reason deductively from specific set of assumptions – the rules of the game. Please write using
complete sentences. Complete parts I and II independently.
Part I: Postulates
State the rules of the game clearly and concisely. The rules are important because our
conjectures depend on the rules that we have chosen; they are unlikely to be true of different
games.
Part II: Proof
Based on the rules that you stated in Part I, explain why each of the conjectures must be true.
Your argument must be convincing; consider all of the possibilities, leaving no room for doubt.
Reason logically and organize your work so that each step in your thinking is clear.
Variation of the Game
Many variations of the game are possible if we allow small changes to the rules. When we
change the rules, however, the strategies often change as well and then a new set of conjectures
will emerge. You may complete Part III with a partner if you chose.
Part III: Variation
Explore a variation of the original game by changing one or more of the original rules. For
example, you might change the initial number of coins or allow players to take more coins on
each turn. Alternatively, you might declare the player to take the last coin the loser or allow
more than two players to compete at once. Once you have settled on the rules, play the new
version several times and describe what you discover. As part of your description, be sure to
answer the following questions:
o What rules did you choose for your variation? Why did you choose these rules?
o What strategies seem to work? What conjectures do you have?
o Why do you believe that your conjectures are true? Provide reasons when possible and
refer to your experience playing your variation.
o Which version of the game is the most interesting to play? Why?
Mr. Harless
Honors Geometry
Strategy Game Analysis Rubric
The rubric below describes various levels of performance. Use the rubric to self-assess your
strategy game analysis before submitting your final draft.
Part I:
Postulates
Part II:
Proof
Part III:
Variation
3
4
5
Some rules are
included
All rules are
included
All rules are included; rules are
stated accurately and concisely
6
8
10
Intuitive reasoning
is provided for
each conjecture
At least one
conjecture is
proved completely
Each conjecture is proved; each
proof is convincing, clearly written,
and considers all possibilities
6
8
10
Variation is outlined; at least one
conjecture is
included
Variation is
described clearly;
two or more
conjectures are
discussed
Variation is clearly described and all
questions are answered in detail;
several conjectures are included;
conjectures are relevant and welldefended