The shown multiplier is not the threshold

390. Lesson identity

Module

1.9 — Basic economy

Lesson

The shown multiplier is not the threshold

Academic type

Case Study / Systems

Schema type

case-study

Order

Lesson 2 in the module

Estimated time

25–40 minutes, including practice

This lesson uses a hypothetical display-versus-threshold systems exercise. The word Survival names a fictional mode in the exercise; it is not the verified CONTRABAND Survival progression theme and is not production evidence. Its purpose is to separate a displayed reward multiplier from the simulation value used by an unlock rule.

391. Learning objective

After this lesson, you can explain why a displayed number may be the wrong input for an unlock rule by distinguishing a reward multiplier from the progression threshold that controls the unlock.

This is a systems exercise using a hypothetical or explicitly labelled example. It is not documented CONTRABAND production history unless a verified theme is named.

392. Why this matters

The player acts on what the game shows, but the game decides from state and rules. A Survival screen can display a reward multiplier such as ×8 while an unlock rule checks a separate threshold such as eight completed Survival runs. Treating those values as interchangeable creates misleading feedback and incorrect unlock behavior. This distinction also makes an AI-directed implementation request precise: name the authoritative state value, the operation, and the comparison.

393. Prior knowledge

You should already be able to identify a resource source and a resource sink from 1.9 — Sources and sinks. In particular, you should know that a displayed resource icon is presentation, while an award or purchase changes the resource balance.

394. Core concept

A display value and a rule input can describe related parts of a system without being the same value.

In this Survival case:

• A multiplier changes an economy amount, such as baseReward × 8.
• A threshold is the condition used to decide whether progression has reached a required point, such as survivalRunsCompleted >= 8.

The 8 in ×8 means “multiply the reward by eight.” The 8 in >= 8 means “unlock when the tracked count reaches eight.” The shared numeral does not make the two values interchangeable.

395. Mental model

Use the display–simulation–rule model:

Trace the value from the rule backward. Do not assume that the number in a label is the source of truth.

Use this test sequence: ACT → RESPOND → CHANGE → AGAIN:

1. ACT: complete or attempt the relevant Survival action.
2. RESPOND: observe the reward display and the unlock result.
3. CHANGE: alter one relevant state value or rule assumption.
4. AGAIN: repeat the action and compare the result.

396. Concrete example

A Survival screen displays:

Survival reward: ×8

The simulation stores:

baseReward = 5
payoutMultiplier = 8
survivalRunsCompleted = 7

Compare the displayed value with the calculated simulation payout. The display says ×8, but the authoritative simulation calculates the payout from baseReward and payoutMultiplier:

reward = baseReward × payoutMultiplier
reward = 5 × 8 = 40

Thus, the displayed ×8 corresponds to a calculated payout of 40 in this state; it is not itself the payout amount and it is not the progression threshold.

The unlock rule is separate:

unlock when survivalRunsCompleted >= 8

The player receives a reward of 40, but the unlock remains locked because 7 >= 8 is false. The displayed ×8 is a reward multiplier, not the unlock threshold and not a progress count.

Now change only survivalRunsCompleted from 7 to 8. The reward display can remain ×8, and the reward calculation can remain 5 × 8 = 40. The unlock now succeeds because 8 >= 8 is true. This controlled change shows that the unlock responds to the tracked count.

To test the multiplier independently, keep survivalRunsCompleted = 8 and change only payoutMultiplier from 8 to 10. The payout changes from 40 to 50, while the unlock remains available because the comparison is still 8 >= 8. Taken together, these controlled comparisons distinguish the multiplier's economy effect from the completed-run count's progression effect.

If the interface is meant to communicate unlock progress, it should show a separate value such as Survival runs: 7/8. That additional display may help the player, but it does not replace the authoritative state or change the rule.

397. Common mistake

The common mistake is treating every visible number as the same game variable: “The screen shows ×8, so the unlock threshold must be eight,” or “Because the threshold is eight, the reward must be multiplied by eight.” Those conclusions confuse an economy calculation with a progression condition.

Another mistake is changing the display and the rule together, then claiming that the display caused the unlock. Change one relevant value at a time so the source of the behavior remains observable. To identify separate dependencies, test both directions: vary the run count while holding the multiplier constant, and vary the multiplier while holding the run count constant.

398. Guided practice

Use this case and do not change multiple assumptions at once:

Displayed Survival reward: ×8
baseReward: 6
payoutMultiplier: 8
survivalRunsCompleted: 7
unlock rule: survivalRunsCompleted >= 8

1. Calculate the reward amount.
2. Decide whether the unlock succeeds.
3. State what the 8 in ×8 means.
4. State what the 8 in >= 8 means.
5. Change only survivalRunsCompleted to 8. Confirm that the payout remains 6 × 8 = 48 while the unlock becomes available.
6. Keep survivalRunsCompleted fixed at 8 and change only payoutMultiplier from 8 to 10. Predict and verify that the payout changes from 48 to 60 while the unlock remains available.
7. Keep payoutMultiplier fixed at 10 and return survivalRunsCompleted to 7. Predict and verify that the payout remains 60 while the unlock becomes locked.

Your required decision is this: based on the two controlled comparisons, does the unlock depend on the reward multiplier or on the completed-run count? Justify your answer by naming what changed and what remained constant in each comparison.

399. Validation / evidence

Produce a short rule trace for the initial state and each controlled comparison using these fields:

Displayed value:
Authoritative economy values:
Authoritative progression value:
Operation:
Threshold comparison:
Reward result:
Unlock result:
Changed value:
Values held constant:

A valid trace records all three observations:

• At payoutMultiplier = 8 and survivalRunsCompleted = 7, the payout is 6 × 8 = 48 and 7 >= 8 is false.
• With the multiplier still at 8, changing the count to 8 leaves the payout at 48 and makes 8 >= 8 true.
• With the count held at 8, changing the multiplier to 10 changes the payout to 60 while the unlock remains available.

The trace must explain that changing the run count across the threshold changes the unlock result, whereas changing only the multiplier at the boundary changes the payout but not the unlock result.

You have met the objective when you can inspect a mismatch between a display and an unlock result and name the relevant economy value, progression value, operation, and comparison without relying on the label alone.

400. Key takeaways

• A displayed multiplier communicates an economy calculation; it is not automatically a progression threshold.
• A multiplier transforms an amount, while a threshold is the value or condition used for comparison.
• The same numeral can appear in two different meanings, such as ×8 and >= 8.
• Keep economy flows and costs distinct from progression advancement and unlocks.
• Test each suspected dependency independently by changing one value while holding the other constant.
• Use ACT → RESPOND → CHANGE → AGAIN to compare observable results.

401. Next lesson

Continue to 1.9 L3 — Write one economy invariant.

402. Knowledge check