Posted by Dr Fro 2:52 PM
A bit of maths

Your odds of winning Saturday's Lotto Texas is 1 in 48 million. People always assume that this is a bad bet. They are not always correct.

The expected prize is $145 million. The last prize was $120 million. That tells me that your expected value of a ticket is $145m/48m, or roughly $3 for a $1 ticket. What gives? Well it is because the pot is built by a lot of people that have bought tickets for previous drawings that rolled over into this pot.

For simplicity's sake, I have ignored the possibility of a split pot, but with 45m people vying for a 1 in 48m shot, this does not materially mess up the math. Take a very simple case of a 50% chance of splitting two way yields $3 * 50% + $1.50 * 50% or $2.25, which is well over the $1 you paid. The chances of splitting with more and more people is even less remote.

There are a lot of assumptions above to make the math simple, but the most important point is that the "dead money" in the pot can, at times, make an otherwise negative EV play in the Lotto a positive EV play.

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