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Assume I have two tickets to tonight's PowerBall:

  1. Chosen by me: 1, 2, 3, 4, 5
  2. A randomly selected "QuickPick" ticket

Are the odds that both tickets win exactly the same?

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  • $\begingroup$ Yes, think of each number as a unique shape, rather than a symbol that represents a quantity. Each shape is equally likely to appear. $\endgroup$ Jan 13, 2016 at 18:52

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Yes the odds to win are exactly the same, but the expectation value is different, given that other people choose popular numbers, as pointed out by User @morgan-rodgers.

To maximize the expectation value, simply bet on the least popular numbers you can think of.

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    $\begingroup$ But if everyone thinks of the least popular numbers... :) $\endgroup$
    – fosho
    Jan 13, 2016 at 18:59
  • $\begingroup$ The advice of "bet on the least popular numbers" is good. It's just that, if left to your own devices, you won't think of them. (A random number generator on the other hand probably will fare better) $\endgroup$ Jan 13, 2016 at 19:00
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    $\begingroup$ If the jacpot should carry over once again, you will soon know at least one combination that was not popular this time;) $\endgroup$ Jan 13, 2016 at 19:06
  • $\begingroup$ I don't think so, since random number generators will also generate popular numbers. the best numbers would be randomly generated and filtered against a heuristics, containing the most popular numbers, like birthdates, series, symetrical series... $\endgroup$
    – Gewure
    Jan 13, 2016 at 19:10
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    $\begingroup$ I suspect that picking numbers sparingly from $17$ through $31$ and not at all from $0$ through $16$ will work fairly well. Fortunately, we are in the early $21$st century, and most anniversary or birth years are out of range or covered by the above. $\endgroup$
    – Brian Tung
    Jan 13, 2016 at 19:24

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