The following puzzle appeared (worded differently) in John Derbyshire's May diary .
Can you label the faces of 3 cubical dice with the numbers 1,2,3 ... 18 (using each number exactly once) so that if someone else picks any one of the three dice you can then pick another so that if you both roll your chosen dies with the high roller winning you will win more than half the time? How big an edge can you achieve by an appropriate labeling? Can you prove optimality?
Derbyshire follows up here .