Risk and reward
Try point games and discover when a big prize, a better average and a better chance mean different things.
Compare long-run averages
1 question · No time limit
Example
Example
Which game has the greater expected net points per play in the long run?
Each game uses a fair six-sided die. Every listed face is equally likely and shows net points after all costs; negative numbers are losses. Plays are independent.
1. Predict
| Die face | Net points |
|---|---|
| 1 | 6 |
| 2 | 6 |
| 3 | 6 |
| 4 | 6 |
| 5 | 6 |
| 6 | 6 |
| Die face | Net points |
|---|---|
| 1 | 10 |
| 2 | 4 |
| 3 | 6 |
| 4 | 9 |
| 5 | 8 |
| 6 | 5 |
Plays per run: 1
Make a prediction first. It is not scored.
2. Test your idea
Run the experiment to compare the outcomes.
These are random trials, not exact probabilities.
Try the controls, then check your solution.
Why?
Game A totals 36 points across its six faces, for a mean of 6. Game B totals 42, for a mean of 7. Compare the averages. The largest single reward does not decide which game is better on average.
Revisit your prediction
Keep exploring the experiment.
3. Change the rules
A linked challenge. This answer is not scored.
Continue your unfinished round
Your answers are saved in this tab. Continue from where you left off.
Continuing uses no additional practice start.
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Starting the new round uses one practice start.
- Answered
- 0 / 1
- Active time
- 0:00
Round complete.
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Try the controls, then check your solution.
Your first checked solution is recorded. You can keep experimenting afterwards.
About this practice
Learn a method
Compare expected rewardsTry point games and discover when a big prize, a better average and a better chance mean different things.
For a broader mix of practices, explore the probability practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used