In many competitions the host, moderator, or emcee wishes all the contestants good luck, yet one contestant’s good luck in winning could only come at the expense of the other contestants’ not having similar good luck.
Interesting question, Karl! In many competitions (e.g athletic, academic), the winner may be so from a combination of luck and ability. In such cases, wishing all the contestants good luck may make some sense but not mean much, as when we wish our students good luck on an exam (I used to tell my students 'may the force be with you!'). This may especially be the case on multiple-choice exams where equally good students may guess differently to some difficult questions and only some get the right answer (by luck). Indeed, with true-false questions students can get high scores just by this kind of luck (can be checked out using the binomial distribution with discrete outcomes). But with TV shows where an outcome is entirely dependent on luck, or in a casino the 'good luck' phrase might function as a kind of joke or stress easier.
Thanks Ivan. However, the luck aspect is a red herring, since the statement can be rephrased without reference to luck and the problem remains. If an emcee says to the contestants, "I wish you all success" and the contest is such that only one contestant can be successful, then the wish is impossible to satisfy.
No, I don't think wishing all the contestants good luck makes sense. It reminds me that very few people think logically all the time!
You could wish all students good luck before they start writing a test, but it is silly to do that before a beauty pageant for example, when you know all but one will have a bad luck.
Very good point!
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