Worksheet

Game Studio: Balance the Score Engine

Build nonuniform probability models from game-test records, then use them to compare levels and evaluate scoring changes.

Grade 7MathInteractive · Printable

Aligned to7.SP.C.7.b

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1 Common Core standard
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14 questions
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Details

Format: Interactive · Printable
Grade: Grade 7
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

Students build probability models by dividing observed outcome counts by the total number of trials.
Students use frequency models to predict scores and compare game-level designs.
Students model how changes to score labels and outcome groups affect probabilities.

How to use

Have students tally the opening log before building its model. Discuss how changing a score value differs from changing how often an outcome occurs.

Curriculum

Common Core standard covered

7.SP.C.7.b

Build a probability model, which may not be uniform, from frequencies observed in a chance process.

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Game Studio: Balance the Score Engine

Use trial records to model random scores and guide design choices.

Read the Score Log

A studio tests a level with random moving platforms. An automated player repeats the same inputs each run. Use observed frequencies to estimate probabilities for comparable future runs. Give probabilities as fractions or decimals.

The score engine awards 0, 40, or 100 points per run. These are the scores from 16 test runs:
0, 40, 40, 100, 40, 0, 40, 100, 40, 40, 0, 100, 40, 40, 100, 40

Tally the log and build a probability model for the next comparable run.

P(0 points) =
P(40 points) =
P(100 points) =

A patch doubles every score without changing the platforms or the automated player's inputs. Which model follows from the original log?

A. The probabilities of 0, 80, and 200 points are 1/3, 1/3, and 1/3.
B. The probabilities of 0, 80, and 200 points are 3/16, 9/16, and 1/4.
C. The probabilities of 0, 80, and 200 points are 3/32, 9/32, and 1/8.
D. The probabilities of 0, 80, and 200 points are 3/8, 9/8, and 1/2.

Return to the original scoring rules. A designer plans 64 more comparable runs. Use the model to predict how many will score exactly 100 points.

Predicted number: runs

The studio compares two events: scoring exactly 40 points and scoring anything other than 40 points. Which comparison follows from the original log?

A. Other than 40 is more likely: its probability is 2/3 rather than 1/3.
B. Exactly 40 is more likely: its probability is 9/16 rather than 7/16.
C. Other than 40 is more likely: its probability is 13/16 rather than 3/16.
D. The events are equally likely: each has probability 1/2.

Eli proposes assigning probabilities of 0/140, 40/140, and 100/140 to scores of 0, 40, and 100. He says, “The probabilities add to 1, so this model fits our log.” Explain why adding to 1 is not enough. Use the log to give two pieces of evidence against his model.

Compare Level Layouts

The studio now tests two new layouts under the same automated-player conditions. Build a separate frequency model for each layout; do not assume their outcomes are equally likely.

New Layout Test Records
Layout	0 points	40 points	100 points
Tunnel	10	14	16
Bridge	6	9	5

Build the Bridge layout's probability model from its test record.

P(0 points) =
P(40 points) =
P(100 points) =

The studio wants a layout whose estimated probability of awarding exactly 100 points is at least 0.35. Which decision is supported by the records?

A. Choose Tunnel only; its estimate is 0.40.
B. Choose Bridge only; its estimate is 0.50.
C. Choose both layouts; each has an estimate of at least 0.35.
D. Choose neither layout; both have estimates below 0.35.

The studio wants a Bridge badge that the model predicts will be earned on at least 70% of comparable runs. Select every badge rule that meets this goal.

Earn the badge for a score of 40 or 100.Earn the badge for a score of exactly 100.Earn the badge for a score of 0 or 40.Earn the badge for a score of exactly 40.

A Tunnel results screen reports how many points short of 100 a run finishes. For example, scoring 40 means finishing 60 points short. Build a model for this new display.

P(0 points short) =
P(60 points short) =
P(100 points short) =

10.

The original 16-run log contained four scores of 100. Which comparison with the new layouts is correct?

A. Both new layouts have a higher estimated chance of 100 points than the original level.
B. Both new layouts have a lower estimated chance of 100 points than the original level.
C. Tunnel has the same estimated chance of 100 points as the original level.
D. Bridge has the same estimated chance of 100 points as the original level.

Test a Score Adjustment

A separate feature randomly adjusts a run's score. A negative adjustment removes points. Use the feature's trial records, not the earlier layout records.

11.

Build a probability model for the next comparable activation of the feature.

Original Adjustment Feature
Adjustment (points)	Observed count
−20	8
0	7
+30	5

P(−20 points) =
P(0 points) =
P(+30 points) =

12.

A run has 70 points before the original adjustment feature activates once. A reward requires a final score of at least 100. Use the feature's model to estimate the probability of receiving the reward.

Estimated probability:

13.

A proposed patch changes every −20-point adjustment to 0 points. It leaves all other adjustments unchanged and does not change how outcomes are generated. Which model for the patched feature follows from the original record?