You can win a free galley proof copy of his forthcoming book if you can correctly guess the dollar value of the change in his loose change box.
Details of his contest and a better picture are here.
Professor Orzel's contest reminded me of the famous coin-jar auction experiments that a psychologist and an economist conducted with their MBA students to illustrate the winner's curse phenomenon, an important concept in game theory, a branch of applied mathematics.
Robert Frank's Behavioral Economics text describes those experiments as follows:
[When] psychologist Max Bazerman was teaching at Boston University some years back, he and his colleague William Samuelson performed the following experiment in their microeconomics classes. First they placed $8 worth of coins in a clear jar. After giving their students a chance to examine the jar carefully, they then auctioned it off--coins and all--to the highest bidder. They also asked each student to submit a written estimate of the value of the coins in the jar.
On the average, students behaved conservatively, both with respect to their bids and to the estimates they submitted. Indeed, the average estimate was only $5.13, about one-third less than the actual value of the coins. Similarly, most students dropped out of the bidding well before the auction price reached $8.
Yet the size of the winning bid in any auction depends not on the behavior of the average bidder, but on the behavior of the highest bidder. In 48 repetitions of this experiment, the top bid averaged $10.01, more than 20 percent more than the coins were worth.
Professor Frank goes on to note that: "Bazerman and Samuelson thus made almost $100 profit at the collective expense of their winning bidders. At that price, the winners may consider it an important lesson learned cheaply." Why? Because the winner's curse phenomenon can occur in real world situations with far greater stakes, for example, in oil lease auctions and corporate takeovers. For more information, see here and here.
However, as I noted above, Professor Orzel teaches physics, not psychology or economics, so there's no "winner's curse" risk in his contest, but you can still have fun thinking about your strategy for coming up with a guess.