1. “Guess How Many” Game
Camp Calcium
Summer 2005

2. Game Description
This sack contains numbered tokens. The numbers begin at 1 and there are no duplications and no omissions. The total number of tokens is less than 1000.
The object of the game is to use a small sample of tokens to estimate how many tokens are in the bag.

3. Historical Anecdote (possibly apocryphal)
Background
Historical Anecdote (possibly apocryphal)
German tanks were captured in WW II. The
tanks were found to be numbered starting
with #1. It would be very useful to know how
many tanks the Germans have at their
disposal. What would be the best guess
using the numbers of the tanks that have
been captured?

4. On a 1-10 scale, how confident are you that your guess is good? ___
First Round
Draw five numbered tokens from the sack. Do not return the tokens after drawing them.
Use the numbers that you drew to guess how many tokens are in the bag.
Round 1 Guess ___
On a 1-10 scale, how confident are you that your guess is good? ___

5. On a 1-10 scale, how confident are you that your guess is good? ___
Second Round
You have been assigned randomly into a group of three players. You may share your numbers and discuss your guess within your group.
Round 2 Guess ___
On a 1-10 scale, how confident are you that your guess is good? ___

6. On a 1-10 scale, how confident are you that your guess is good? ___
Third Round
You can now share information with any other player. It is up to you to determine the best way of doing this.
Round 3 Guess ____
On a 1-10 scale, how confident are you that your guess is good? ___

7. Results and Follow-up Questions
The actual number of tokens was ___ (to be given by instructor.)
How did your guesses (and confidence) change as you received more information?
At what point is getting more data “not worth it”? (Data collection is not free.)
Can you think of a systematic way of guessing?

8. For More Information Links
Wikipedia Entry
Random Sampling applet