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A Good Gamble for Investors

I occasionally go to Casinos and sometimes play the state lottery. The whole marketing effort tied to gambling, particularly for low end gambling, conflicts with my sense of logic. I understand that this is business and they go to great lengths to determine how to cater to different customers. Just go to any slot machine parlor, each one is branded differently to appeal to a small slice of customers. They are too noisy and complicated for my taste.

Most everyone knows that gambling is a losing game over the long term, the odds are in the house’s favor. If you look at it as entertainment, without any expectation of winning, it helps to justify the spending.

Some games are better than others. For example, some slot machines payout over 98% of the take, which is a very small house advantage. These higher payout machines, though, require bets of many dollars instead of dimes. Better odds require larger bets. But what if you could make a bet that pays better than odds? This would be like the slot machine paying out 102% of the take. You would think that no one would offer such a bet, but you can in fact buy a better than odds bet in the multi-state lotteries. You just need to know when to buy.

A better than odds bet occurs when the payout exceeds the odds of a payoff. The odds of the multi-state lotteries are as follows:

So, when the prize exceeds the payout (175 million or 195 million), you are getting this over odds bet, right? Well, not exactly. The lotteries are playing a marketing trick to inflate the size of the prize. The big prize quoted for these games is an annuity, not a cash prize you can collect now. The cash prize is significantly less. In order for the cash prize to pay at odds, the annuity prize needs to be much higher. I ran a calculation on recent cash prizes to determine the discount applied to the payments. Here are the results:

Big Prize Odds Annuity Interest Rate Payout Years ‘At-Odds’ Cash Prize
Mega Millions 1 in 175M 4% 26 years $300M
Powerball 1 in 195M 6% 29 years $400M

So, there you go. If you want to get a better than odds bet, buy a Mega-Millions ticket when the prize exceeds $175M. Or, $300M if you want to see this payout in cash today. Good luck, the $300M prize has occurred only about 4 times for Mega-Millions, and a $400M prize has never occurred (yet) for the Powerball!

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