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A made-up dice game costs 1.5 tokens to play…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up dice game costs tokens to play. You roll one fair die. A six wins tokens, a five wins tokens and any other number wins nothing. Find the expected prize and the expected gain per play. Give four decimal places. Is the game fair?
Need a reminder? The key ideaShow
Expected value: , the long-run average. Expected gain is the expected prize minus the cost. A fair game has an expected gain of .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The expected prize. tokens.
Step 2. The expected gain. tokens.
Answer: about tokens and tokens. The game is not fair: the player loses about a sixth of a token a play on average.
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