A Rational Choice to be Irrational?

Everyone knows the odds of winning the lottery are infinitesimal (1 in 8 million for Lotto 6/45). Yet, millions play every week. Are they stupid?

The Cold Math: Expected Value (EV)

Expected Value is the average outcome if you played the game infinite times. $$ EV = (Probability of Win \times Reward) - Cost $$

If the jackpot is $2 million and odds are 1 in 8 million: $$ EV = (\frac{1}{8,000,000} \times 2,000,000) - 1 = 0.25 - 1 = -0.75 $$

Every time you buy a $1 ticket, you strictly lose 75 cents. Mathematically, it is a terrible investment.

The Utility of Hope

However, humans are not calculators. We buy Utility.

• For $1, you buy the right to fantasize about quitting your job for 3 days until the draw.
• That "cheap dopamine" and stress relief might be worth more than 75 cents to you.

Conclusion

If you play for fun, you are buying entertainment. If you play to get rich, you are paying a "tax on hope." Know the difference.