Here at Knewton we decided to purchase Mega Millions lottery tickets collectively. Here are some musings from our data science team on our chances of hitting it big.
The upcoming Mega Millions jackpot is around $540 million per $1 ticket, or a payoff of 540 million to one. The odds of winning are (according to the lottery web site) about 1 in 176 million. Neglecting the chances that the jackpot will split, this appears to be very favorable odds. An “investment” in the jackpot will provide 5.4/1.76 = 3.1 factor of return, so clearly this is worthy of investment. On average, every dollar we invest will give us a return of $3.10!
But how much should we invest? If I have $50,000 to invest in 50,000 tickets, my odds of winning are only around 1 in 3,500. So 99.97% of the people who “invest” $50,000 in this system will lose everything. How much of our money might we need invest in such endeavors such that we are unlikely to go broke before we get rich?
The answer comes from the Kelly Criterion. Here, it reduces to roughly what one’s odds of winning are: we should invest only around 1/88,000,000 of our net worth. Anything less, and we will likely go broke before we get rich. Knewton’s 70 or so employees should only invest $1 collectively (with each of us contributing an average of $0.014) if all of us together have a net worth of $88 million that we’re prepared to risk. Such an investment would earn us an average of $3.00 to split up, or 4.3 cents each.
Anything more than that, anything that takes up more than 1/88,000,000 of our net worth, and even with an infinite number of favorable lotteries to play, all of us would almost certainly go broke before we ever got rich.
In conclusion, everyone at the company who put up $1 for a ticket in the pool is a fool.
And for the record, I totally bought in.