More lottery nonsense
From Stuff, on this week’s Lotto
The winner chose the six lucky numbers they played regularly but, in a clever move, chose to play the same numbers on 10 different lines with each Powerball number. That way they were ensured to win Powerball if their lucky numbers came up.
This strategy doesn’t increase the chance of winning Powerball, because you can’t increase the chance except by cheating or magic. If they match the six numbers they are certain to win Powerball, rather than having only a 10% chance, but this is exactly compensated by their ten-fold lower chance of having a ticket that matches all six numbers.
The strategy does reduce the chance of winning the first division, by a factor of ten, but increases the fraction of the first-division prize that they snag (in this particular win, from 1/4 to 10/13). Over all, the strategy reduces expected winnings compared to ten random picks. On the other hand, if you cared primarily about average expected return you wouldn’t be playing Lotto.
Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. See all posts by Thomas Lumley »