The Lottery Is a Tax On People Who Are Bad at Math

This topic recently came up in discussion, so I thought I would comment on it. Here is a longer more mathematical explanation.  This same reasoning applies to casinos and many other forms of gambling.

Let's consider a hypothetical example.  Suppose there is a simple lottery for $20 million.  Any given ticket has a probability of 1 out of 80 million of winning.  Suppose each ticket costs $1.  If 80 million people play this lottery, one would expect on average one person to win the jackpot.  In such an average case the lottery gains $80 million in ticket sales and pays out $20 million to the winner for a net of $60 million.  The average payout for each player is therefore $20 million divided by 80 million people, or $0.25.  This $0.25 is considered the expected payout of this lottery based on the probability.  Therefore each player loses an average of -$0.75.

Here is the Wikipedia page on Powerball.  It calculates that the expected payout per dollar spent is less than a dollar for jackpots less than $322.274.  Therefore, when the jackpot is less than this number, on average one loses money by playing.  When the jackpot rises above $322.274, one could argue that money is made by playing the lottery.  It seems to me, however, that this is not the case.  If multiple people win the jackpot, then the prize is divided among the winners.  In theory such a situation would present a prisoner's dilemma, causing so many tickets to be sold that on average the pot is likely to be split.


In my view, one would be wiser taking the money he or she spends on the lottery and investing it.