An ice-token store

Provenance: Constructed RS Learning Lab teaching walkthrough, authored with AI assistance on 2026-09-11. The prediction, correction, and calculations are prepared examples, not a recorded learner or chatbot exchange. The numeric result is a prepared worked construction, not measured evidence.

📎 Resource · Return to the Gallery · 📎 Resource · Required Model cards

Choose and predict before calculating

This extends 📎 Resource · How did people keep food cool before refrigerators? with an invented token exercise. Open the original walkthrough for real research and attributed sources. The store is not a reconstruction of any historical icehouse.

Question: after four turns, how does increasing a fixed loss from 2 to 3 change the tokens remaining?

Constructed prediction to inspect: “The changed loss is one token larger, so I think the final store will be one token smaller.” Make your own prediction before looking at the table. Does the loss happen once or on every turn?

Inspect the rules

Copy the ice-token block from the 📎 Resource · Model cards. Start with 12 tokens. Each turn, next store = max(0, current store - loss). Use that result for the following turn. There is no replenishment. Run four turns with loss = 2; reset to 12 and run four with loss = 3. Only loss changes, and it stays fixed within each run.

Tokens and turns are arbitrary, not kilograms or hours. Before the live exchange, consult 🧩 Module · Safety if considering anything beyond these invented values.

Ask for one live check

Here is my invented model: [paste the ice-token rule block]. I will compare loss = 2 and loss = 3 for four turns, resetting to 12 tokens. Audit the rules or propose one hand check. Do not change assumptions, add weather or insulation effects, or calculate both runs for me.

Inspect the actual response against the card. Reject an invented changing melt rate, replenishment, or a claim that tokens establish a safe storage period. The response is not evidence that the rules work. Use 🧩 Module · Reality Check and do your own arithmetic check.

Prepared worked result

Baseline turn 1: max(0, 12 - 2) = 10. Turn 2 uses 10, so max(0, 10 - 2) = 8. Continue the rule, then reset to 12 before the changed run.

Scroll sideways to see all columns.

Turn	Baseline store, loss = 2	Changed store, loss = 3
0	12	12
1	10	9
2	8	6
3	6	3
4	4	0

Hand-check changed turn 4: max(0, 3 - 3) = 0. Check zero loss separately: max(0, 12 - 0) = 12 each turn. Check the floor with a separate test state of 1 token and loss = 3: max(0, 1 - 3) = 0. This test state is a rule check, not a changed starting state in the comparison.

Correct and interpret

After four turns the baseline has 4 tokens and the changed run has 0, a difference of 4 tokens.

Constructed correction: “I treated the extra loss as if it happened once. Here it happens on each of four turns, so the changed run ends four tokens lower. I checked the rule instead of keeping my first prediction.”

Do not extend that difference formula to every possible run without checking the zero floor. Once a store is empty it stays empty under these rules. Both runs keep the same starting tokens, turn count, and update rule.

The model assumes a fixed loss and omits temperature, insulation, and changing melt rates. It provides no real refrigeration rate, historical finding, or food-safety advice. Explaining its arithmetic does not establish how long actual ice or food lasts.

Your unworked variation

Compare loss = 1 with loss = 2, starting with 12 tokens and running four turns. Predict before calculating, choose a live AI request, reset between runs, and hand-check the result. Explain what AI contributed and what you checked yourself. Choose to stop or return to the original research inquiry for a question requiring sources.