Expected Bonus Point Payoff Maximization

Here goes the economist in me. For High
Schoolers, if you have a 5-10-15 with the 15 point clue
being very hard and the other two proportionally
"getable" consider this distribution: 5pts (w/ p=0.8) 10pts
(w/ p= 0.65) and 15 pts (w/ p= 0.2). With these
probabilities somewhat reasonable you have an expected payoff
of 13.5. Now consider a 10-10-10 where the 10 pt
clue is just as difficult (that is, p=0.65 for each)
then your expected payoff is 19.5. If the goal in the
tournament is to have the players score more points and you
can switch your 5-10-15 to a 10-10-10 then it's
probably a good idea. Even if that 5pt clue becomes a 10pt
clue and still p=0.8 then not only will they of course
earn that 10pts with some degree of certainty, but
also be more encouraged. Discouraging High School
players by having tough questions, at least in the Bay
Area circuit is certainly something that needs to be
avoided in orderto induce further participation.

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