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.

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?

A. The probabilities of 0 and +30 points are 0.50 and 0.50.B. The probabilities of 0 and +30 points are 0.35 and 0.65.C. The probabilities of 0 and +30 points are 0.75 and 0.25.D. The probabilities of 0 and +30 points are 7/12 and 5/12.

14.

Instead of applying that patch, the studio tests a redesigned generator. Build its model using only this new record. Which probability list fits?

Redesigned Generator: 50 Activations
Adjustment (points)	Observed count
−20	25
0	15
+30	?

A. For −20, 0, and +30 points, the probabilities are 0.50, 0.30, and 0.20.B. For −20, 0, and +30 points, the probabilities are 0.25, 0.15, and 0.10.C. For −20, 0, and +30 points, the probabilities are 0.40, 0.35, and 0.25.D. For −20, 0, and +30 points, the probabilities are 0.50, 0.20, and 0.30.