Lottery tickets graph

As a child, I was fascinated with lottery odds. I recall that the odds of winning the Florida lottery jackpot at that time were about 1 in 14 million, and that scratch-off tickets displayed the odds of winning a prize on the back, which was usually around 1 in 4.

The above graph (drawn by me) is actually far too optimistic. The odds of overall gains are lower than 1 in 4 because a typical scratch-off or instant-win ticket counts a prize of the same amount as the purchase price as “winning,” even though this is actually breaking even. Of course, buying a $2 ticket and “winning” $2 is the second commonest outcome, behind the most common outcome of losing $2. Further, the overall odds of making money decline precipitously as additional tickets are purchased. Although the “1 in X” odds of winning X fantastic prize increase with the purchase of additional tickets, the value of the improved odds is always far below the ticket price.

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