So, the Massachusetts State Lottery tried an interesting new product over the last couple months, which was more of a raffle format than the format the lottery usually uses. Tickets cost $20 and were available over the past couple months, and the winning ticket numbers will be chosen tomorrow. There’s a $20 million prize, as well as ten $1 million prizes and forty (40) $250,000 prizes. They were planning on selling 4 million tickets. However, they’ve only sold 32% of that amount so far, and are still planning on giving out the same prize distribution.

I *think* that means that the expected value of a ticket purchase is actually *positive*, or pretty close. It’s almost tempting me to buy one. I may run some numbers later this evening.

The expectation may be positive, but the variance is so high that you’d have to buy millions of tickets to get a reasonable probability of making money. Your utility function is probably concave down (the first $10k/year is worth a lot more than going from $1m to $1.01m), so the expected gain in utility could be negative even if the expected money gain is positive. (This so-called risk-aversion is why people buy insurance.)

A rich person operates in a smoother part of their utility function and therefore might reasonably buy tickets. Consider buying 10% of the outstanding tickets (around 150k?) to get about 4 $250k prizes, about 1 $1m and a 10% chance at the $20 million.

You’d be very likely to get about $2 million back for your $3 million investment, and the extra 10% chance at the big one would make it worth while in expectation.

That was me.