A View from the Back of the Envelope top

A Pinocchio estimation game
Fermi Questions
On Being Approximate
Counting by powers of ten
"What order of magnitude is ...?" game
detecting implausible approximations

Is Pinocchio lying?

How to play

  1. Players take turns being Pinocchio.
  2. The Pinocchio player makes up a statement. It may be true, or a lie.
    Examples: "The average life span in the US is two billion seconds."
    "The total number of miles driven in the US each year is greater than the national debt in pennies."
  3. The other players each guess/estimate whether the statement is accurate, within a factor of 10.
  4. The Pinocchio gets one point for each player who guesses wrong.   :)

Details and Variations

Making up statements
      You can use any source of numbers. Stuff you already know. This site, government web pages, and any other stuff on the web or off.

You can use some fact directly. Or combine it with others. Or describe it in a bizarre way (average life span in seconds, cost of a slice of pizza in lifetime salary). Or the Pinocchio can just make up a question, and estimate hir own answer.

You may allow the Pinocchio to choose how many factors of ten accuracy the statement has. Or you can just use one factor of ten. Or you can all decide together, maybe ahead of time.

      You can use stuff you know.

You may decide to permit using some other reference material, perhaps even the web.

Deciding what is "right"
      The players decide together.

With statements based on reference numbers, you can just check the numbers and any math.
With statements which are Pinocchio estimates, all the players persuade each other of the validity of their estimates. If agreement cannot be reached, then the statement may be discarded, or the players may vote, or ...?

      It can be fun to have "players" which are teams of more than one person.

You may wish to treat numbers from unreliable sources, such as television news, politicians, and even newspapers, as Pinocchio estimates. If the number seems really wrong... it may well be.


Game credited to George Lukas (UMass Boston).

Pinocchio is a wooden boy whose nose grows when he lies. Here is The Adventures of Pinocchio, a translation of the Italian children's book by Carlo Collodi/Lorenzini (1826-1890). Here are other Project Guetenberg mirrors.

The Pinocchio Game. We also plan to implement interactive games expressly designed to develop QR skills. One computer-mediated game enables students to exercise their mathematical skills and become familiar with the dimensional calculator and computer almanac while experiencing the flavor of QR problem work. Each player in turn becomes Pinocchio or the "proposer" and-using the information in the computer almanac-makes a supposedly "factual" statement. This statement might be based directly on an entry in the data base combined with a bizarre scaling, e.g., The average life span in the US is two billion seconds. It might be based on a combination of data-base entries, e.g., The total number of miles driven in the US each year is greater than the national debt in pennies. Each of the other players has to decide whether the statement is true or a lie, i.e., inaccurate by a factor of 10 or more (or by an amount chosen by the players.) The proposer gets one point for each incorrect choice made by a player. In an alternate version, the computer proposes the statements (based on the almanac data.) In one variant of this version the players may use the almanac to respond; in another, their responses must be based on their own estimates. In either case, the computer can offer hints and "explain" the process used in developing its "factual statements". This mode of play is particularly effective when used with teams. The software for the computer-generated version will contain a complexity measure that can be set to provide statements suitable for students at different age and skill levels.
- Quote from a personal communication from Wally Feurzeig.
- Game credited to George Lukas (UMass Boston).

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

  I'm not sure "Pinocchio" ideally characterizes the game.
  Additional statement examples.
  Collect pointers to "number" resources on another page.
  Cleanup draft.
  I'm not sure about the tactical dynamics of the accuracy choosing.
  I'd be nice to better integrate the error bars into the weave of the game.
  And perhaps a variant with confidence level rather than binary estimates.

  2003-Feb-03  Repaired links - 2 replaced.
  2001-Mar-15  Changed "Pinnochio" to "Pinocchio".  Ouch.
               Thanks to a reader for catching it!
  2001-Feb-18  Created.  First draft.