I am trying to find the complete rules to a numbers game I recall
learning and playing in 1982/1983 timeframe. I thought it was called
"underwhelm", but that could be wrong. In general it took two players,
and each would state their number, taking turns, and at a certain
point, a player lost that round if something happened. As I remember,
each successive number had to be lower than the previous number. Again
not so sure.

What I do know, it was quick, and easy to play, required plenty of
strategy, and did not require any paper/pencil to write down - it was
simply a fast paced oral numbers game.

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Request for Question Clarification by pinkfreud-ga on 17 Mar 2004 21:58 PST

Does this sound like your game?

"In his book Metamagical Themas, computer scientist Douglas Hofstadter
introduced a simple two-player game called Undercut... The game is
played as follows: Each player secretly picks an integer between 1 and
5 (inclusive). Once both players have chosen, they reveal their
numbers. If they both chose the same number, they each receive that
number of points (so if both players pick 4, they each get 4 points).
Otherwise, the player who selected the lower number gets the sum of
their choice (so if I choose 4 and you choose 1, you get 5 points).
This is repeated until one player earns 40 points."

http://www.sci.brooklyn.cuny.edu/~sdexter/cis15/HW/Program1.html

If this is the game you remember, I'll be glad to find more information about it.

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Clarification of Question by mkguru-ga on 17 Mar 2004 22:09 PST

I think you have found it, since I did read that book around that
time. Bet it from that book. Go ahead and comlete the answer!

The game of "Undercut," created by Douglas Hofstadter and Robert
Boeninger, is a great way to pass some time while waiting in line with
friends, or in other circumstances where one wishes to keep the mind
alive for brief periods. The game appears in the chapter "Undercut,
Flaunt, Pounce, and Mediocrity: Psychological Games with Numbers" in
Hofstadter's book "Metamagical Themas." I believe the material was
also published in "Scientific American" in the early 1980s.

I've gathered a few good links for you.

If you are a registered user of Amazon.com, you can "Look Inside the
Book" to read about "Undercut" in Hofstadter's own words:

Amazon.com
http://www.amazon.com/gp/reader/0465045669/ref=sib_vae_pg_700/102-7310719-0732914?%5Fencoding=UTF8&keywords=game%20of%20undercut&p=S0KA&twc=18&checkSum=zPQ0Fz8d5U%2B823vRgTMTX720jvMOLqNByWb9POSbvB0%3D#reader-link

If the link above doesn't function, please try this one:

http://tinyurl.com/2nzfs

Here's an interesting essay that discusses strategy in playing
"Undercut" (starting about halfway down the page):

Urticator: Game Theory
http://www.urticator.net/essay/2/218.html

A computer version of "Undercut":

Math Forum: Computer Undercut
http://mathforum.org/mam/96/undercut/

Google Web Search: "douglas hofstadter" + "game" + "undercut"
://www.google.com/search?hl=en&ie=UTF-8&oe=UTF-8&q=%22douglas+hofstadter%22+game+undercut

Thanks for an enjoyable question! I hadn't thought about "Undercut"
for years. If anything is unclear, or if a link doesn't work for you,
please request clarification; I'll cheerfully offer further assistance
as needed.

Best regards,
pinkfreud

Wow, what fast turnaround, and completely what I was thinking of. Great job.

I love prisoner dilemma type strategy games, but I'm wondering if
someone can explain this one to me.  Why would a player pick a number
other than 1? The worst you can do is tie using this method.  Could
someone explain what aspect of the game I am missing?

I believe the instructions to the game were not stated quite
accurately.  A player receives the sum of both players' scores only
when selecting a value that is EXACTLY ONE LESS than the opponent's
choice.

Example:  Player A chooses 5, Player B chooses 2.  Result: A gets 5, B gets 2.
A picks 4, B picks 4, result: both get 4
A picks 4, B picks 3, result: A gets 0, B gets 7.

That's why choosing 1 everytime would not work.  Try those rules.