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Ponder This

February 2006

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Ponder This Challenge:

Puzzle for February 2006.

This month's puzzle is about a simple 2 player poker like gambling game. The two players each ante 1 unit to a pot. Then each player receives a random number uniformly distributed between 0 and 1. Each player knows the value of his number but not the value of his opponent's number. The first player is then given an opportunity to bet one additional unit. If the first player doesn't bet there is a showdown and the player with the highest number collects the antes. If the first player bets the second player may call by matching the bet or drop out (giving the antes to the first player). If the second player calls there is again a showdown and the player with the highest number collects the pot (consisting of 4 units, the bets and the antes). If both players follow their optimal strategy what is the value of the game? In other words if they play (optimally) a large number of games how much is the first player expected to win (or lose if the value is negative) per game?

The first 100 people who answer correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the

If you have any problems you think we might enjoy, please send them in. All replies should be sent to:


Challenge: 02/01/2006 @ 09:00 AM EST
Solution: 03/01/2006 @ 09:00 AM EST
List Updated: 02/01/2006 @ 09:00 AM EST

People who answered correctly:

Eugene Vasilchenko (02.02.2006 @12:06:30 PM EDT)
Joe BGI SF Fendel (02.02.2006 @01:14:05 PM EDT)
Claudio Bartolini (02.03.2006 @07:38:45 PM EDT)
Joseph DeVincentis (02.03.2006 @08:16:12 PM EDT)
Daniel Bitin (02.04.2006 @06:13:41 PM EDT)
Patrick J. LoPresti (02.05.2006 @03:28:10 PM EDT)
Joe Schauder (02.06.2006 @07:23:52 AM EDT)
Giorgio Antonelli (02.06.2006 @03:12:12 PM EDT)
Adrian Groves (02.06.2006 @07:04:44 PM EDT)
Yizhou Liu (02.07.2006 @12:49:47 AM EDT)
James Dow Allen (02.07.2006 @01:09:58 AM EDT)
Don Coppersmith (02.08.2006 @08:55:56 AM EDT)
Frank Yang (02.08.2006 @11:23:19 AM EDT)
Deron Stewart (02.08.2006 @01:46:07 PM EDT)
David McQuillan (02.08.2006 @03:08:50 PM EDT)
John Hart (02.09.2006 @03:29:16 AM EDT)
Dave Parashar (02.09.2006 @04:39:22 AM EDT)
Mark Pilloff (02.10.2006 @09:14:08 PM EDT)
Phil Muhm (02.12.2006 @08:08:47 PM EDT)
Dmitry Litvinenko (02.13.2006 @03:49:29 AM EDT)
James Boyce (02.13.2006 @05:19:42 PM EDT)
Adel El-Atawy (02.14.2006 @01:06:48 PM EDT)
Dave Biggar (02.14.2006 @01:41:44 PM EDT)
Malcolm J. Powell (02.16.2006 @12:43:32 PM EDT)
Immanuel Litzroth (02.16.2006 @05:38:33 AM EDT)
Chris Messer (02.18.2006 @05:40:07 PM EDT)
Wolf Mosle (02.22.2006 @08:42:00 PM EDT)
Ed Sheppard (02.23.2006 @04:45:01 PM EDT)
Christopher Quayle (02.24.2006 @08:59:59 AM EDT)
Frank Mullin (02.24.2006 @11:19:59 AM EDT)
Kerry M. Soileau (02.24.2006 @05:44:32 PM EDT)
Dharmadeep Muppalla (02.25.2006 @09:05:37 AM EDT)
Mike Szydlo (02.26.2006 @01:28:31 AM EDT)
Wei Wu (02.26.2006 @08:33:55 PM EDT)
John G. Fletcher (02.26.2006 @11:08:09 PM EDT)
Du Yang (02.27.2006 @05:12:54 AM EDT)
Forest C Deal (02.27.2006 @12:41:34 PM EDT)
Shmuel Menachem Spiegel (02.27.2006 @11:34:46 PM EDT)

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