cs-122 — The Game Show Switch
| Field | Value |
|---|---|
| id | cs-122 |
| difficulty | Foundational |
| topics | probability, strategy |
| lecture | lecture-31 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | lectures 1-2 (problem framing, precise pseudocode) |
| objective | recognise the pattern, translate it into precise steps, and trace it correctly |
| solution | held by the instructor; discussed after the attempt |
Problem
The three-door switch-or-stay problem, argued with an outcome table and then by simulation. Updating on new information.
Your deliverable is the stated assumptions, the two expected values computed for the worked instance, the host-knowledge assumption named, and one contested case. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: 3 doors, car behind one; host opens a goat door; switch or stay
- Output: stay wins 1/3; switch wins 2/3 - the host's knowledge is the hidden assumption
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- Count the worlds: car behind door 1/2/3. In two of three, switching wins. A 900-line outcome table convinces everyone.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which assumption would you attack first if you had to argue the other side?"
Constraints and assumptions
- Difficulty: Foundational (early-semester techniques assumed: precise statements, traces, simple loops).
- Topics: probability, strategy.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes; naming the pattern and stating the assumption is already a pass, completing the calculation is the stretch.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Compute the flip point where the decision changes and defend the threshold.