Crack the Game Show
You’re on a game show. One door hides a car, two hide goats. How do you maximize your chance of winning?
Concept
Three doors. One car, two goats. You pick a door, the host opens a different one to reveal a goat, and offers you the choice to switch. Kid discovers that switching wins two times out of three — and that the reason is almost more surprising than the result.
The Experience
Kid picks one of three doors, knowing only one hides a car. The host — who always knows what's behind every door — opens one of the other two to reveal a goat, then asks: stick with the first pick, or switch?
The kid tries this many times, first choosing to always stay, then always switch, and tracks the win rate for each strategy across many rounds — watching "switch" pull ahead to roughly 2 out of every 3 wins.
The reasoning is then unpacked directly: the first pick only had a 1/3 chance of being right, which means there was always a 2/3 chance the car was behind one of the other two doors. When the host removes a goat from those two, that entire 2/3 chance collapses onto the one remaining door.
A second way to see it: staying only wins on the rounds where the first guess happened to be right (1/3 of the time), while switching wins on every round where the first guess was wrong (2/3 of the time) — and a wrong first guess is the more likely outcome.
What Math Does The Kid Do?
- Runs and tracks the outcomes of a repeated probability experiment.
- Compares the win rate of two different strategies (stay vs. switch) across many trials.
- Reasons about how eliminating one known-wrong option changes the probability of the remaining options.
- Applies conditional probability — updating a belief after new information arrives.
Why This Matters
You can explain why switching doors is the better strategy — not because you memorized the answer, but because you watched new information change the odds with your own eyes.
Frequently asked questions
Crack the Game Show is tagged for Grades 7-12.
No — Crack the Game Show plays directly in the browser, right on this page. No login, no download.
Fact-check a real-world claim — is it true, or does it just look true?
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