Tuesday, March 27, 2012

Mega Millions Mega Ball Frequency

A good investor looks for any opportunity in which capital can be deployed into a situation in which a contract can be purchased for $1 that has an expected value greater than $1.  With the mega millions jackpot at $356M tonight, this is one of those special times that the expected value of one lottery ticket is actually greater than the dollar it's purchased for (excluding the possibility of a split jackpot).  This is because the lump sum after tax value of tonight's jackpot is $191m in the state of California, but the odds of winning are 1:171m.  This implies that each ticket is worth roughly $1.12, a statistical arbitrage!

If you live in a mega millions state and are going to try your luck tonight, below is a frequency chart for just the mega ball, showing the all time frequency (in red) and the frequency in the last 50 draws (in blue).  In 705 drawings, each number should have been drawn about 15 times.  In the last 50, each number should have been drawn about once.

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