ZENO'S COFFEEHOUSE Results #11
The Eleventh Coffeehouse Challenge
The challenge of Charles' Choice, which is repeated below, prompted much debate over what Zeno patrons considered to be Charles' most rational choice, given the situation. And the debate still seems to rage on, but I had to call it to a halt sooner or later. I have listed two representative responses, one for each option considered most likely to maximize Charles' interests. Read on.
Charles can't believe it. It seems that he really hit it lucky at Zeno's. As a true lover of Zeno's outstanding coffee (he prefers the Stadium Brand), Charles has been given quite an offer---sort of reminiscent of the old T.V. game show Let's Make a Deal---which might just set him and Maggie up for the new year!
Charles has been presented with three envelopes---A, B, and C---one of which contains a coupon for Free Zeno's Coffee for Two for One Entire Year (worth many hundreds of dollars, given their love of the java), and the two others which each contain a coupon for a free glass of water on May 6, 1997! Nervously, Charles has selected envelope A, which was set aside, as his anxiety increased. "Coffee or water?," he was heard to whisper under his breath.
Zeno's manager Rob Prob then reached over and unsealed envelope B, and revealed its contents: a coupon for water in May. Rob then proposed the following to Charles:
"Either keep envelope A, along with a free $50, or switch to envelope C---yours is the choice, Charles..."
Wow! After a moment's reflection, Charles decided to leave it to Zeno's patrons as to what choice he should make! And awaiting the results of your input, Charles has put on hold the big decision. QUESTION: What should Charles do to maximize his chance for the free Zeno's coffee? (There is a correct answer, by the way)
Keep Envelope A (with the extra $50), or Switch to Envelope C?
First, here's a comment regarding the preference for choice A:
comments: Charles should keep his envelope and take the fifty bucks for it is a fifty-fifty chance that his envelope will have
the coupon or it won't. Plus hey fifty bucks isn't bad for coffee money.
And here's a comment regarding the preference for switching to C:
comments: Charles would best maximize his chances of getting the coffee if he were to switch to Envelope C. The reason for this is quite straight-forward. In his original choice, his odds for success were 1 in 3, meaning that his odds for failure were 2 in 3. There is a much higher probability that the coffee coupon is in either envelopes B or C. Since envelope B has been revealed as a non-winner, it can be eliminated as a cntender. This is now the situation: The original choice still has a 1 in 3 chance of success. But, that means all other likely contenders have a 2 in 3 chance, and, since B has beem eliminated, THERE IS ONLY ONE OTHER LIKELY CONTENDER: C.
So, which position is correct?
Robert Martin wrote Zeno's to say that he covered this type of puzzle in his book ,There Are Two Errors In The The Title Of This Book (Broadview Press, 1992)---a wealth of information for logicians, I might add---and is now parked prominently in the Coffeehouse. Sure enough, Martin went over the very details facing Charles' choice, on pp. 42-43. His conclusion: Switch to C, so he will have a 2/3 chance of winning!
I don't know where you patrons might want to go with this debate, if anywhere, but if you want to pursue it, drop me a line at firstname.lastname@example.org
Click here to review all the responses, which are mixed indeed!