Powerball great if you know the risks

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The Consumer Electronics Show is going on in Las Vegas this week, but all anyone is talking about is the Powerball Jackpot. It is up to $700 million with the potential to become the first $1 billion lottery jackpot. (Editor’s note: As of deadline Monday, the estimated jackpot was $1.4 billion.)

A few friends of mine were discussing it before this past Wednesday’s winnerless drawing and wondering why someone doesn’t come along and buy every possible combination. At 292 million combinations and a $700 million jackpot, this would seem to be a good proposition. I had to explain the multiple flaws in their conclusions.

There are about 259,200 seconds between the draw on Wednesday and the draw on Saturday. This would mean you’d need to find a way to print out 1,126 tickets PER SECOND to print all 292 million combinations. You would probably need a large van (at least) to haul away all those tickets.

With Powerball, there are 69 white balls and 26 red. Five white balls are selected and one red is selected. To win the jackpot, you have to have all six. This works out to exactly 1 in 292,201,338. Each ticket costs $2. So buying every ticket will cost nearly $585 million.

The argument for buying all of them is that besides the jackpot, you’ll win all those secondary prizes. But “all” is a relative term in this case. There are eight secondary prizes the player can win. In all states but California, they are fixed dollar payouts. The table at right shows the winning combinations, the prize and the probability of winning that prize:

To calculate the payback of these combinations, we multiply the payout (on a FOR 1 basis) by the probability and sum up these values. Remember, the ticket costs $2, so when you hit “1 White + Red,” you’re only winning 2-for-1 or $4 for your original $2 wager.

These combinations add up to 16%. If you don’t eventually hit the jackpot, you’re playing a game with a 16% payback. The hit frequency is just over 4%. Hitting the jackpot here is not the same as hitting a Royal in video poker. You will NOT eventually get your fair share – unless you live to be several million years old!

So, video poker pays back about 96% without the Royal and the Royal contributes the final 2-3% in the case of a progressive. Here it is 16% plus some unknown quantity.

Combination Prize Probability
5 White $1,000,000 0.00000856%
4 White + Red $50,000 0.00010951%
4 White $100 0.00273784%
3 White + Red $100 0.00689935%
3 White $7 0.17248381%
2 White + Red $7 0.14258662%
1 White + Red $4 1.08722295%
Red $4 2.60933507%

Progressives have two paybacks – one for the casinos, which is fixed, and one for the player, which changes as the progressive meter changes. The same is true of lotteries. I don’t know the exact payback of the lottery from the lottery side of things, but I’m going to guess and say it is about 70%.

That is really meaningless for the player. We calculate the payback by plugging in the actual jackpot meter. As of this moment, that is about $700 million. This amounts to a 350 million-for-1 payback and when we plug this into our formula we find the lottery now has a payback of 135%. Sounds like a dream come true. Not so fast. Time to check the fine print.

The $700 million is an annuity. If you want all the money at once, it gets cut to $420 million. Immediately, the payback is cut to only 88%, BUT when you buy $585 million in tickets the jackpot will go up.

One problem is we don’t know by exactly how much. The lottery has to keep its share, it has to pay the sellers of the tickets and it has to allocate 16% for the secondary winners. If we use the 70% payback, it is possible the jackpot could increase by as much as $340 million.

Let’s assume it is the current amount that increases by that $340 million. This takes us to $760 million, which puts us back up to 146%. This is a best case scenario. You could be looking at a $267 million dollar profit.

If any of the assumptions about how much of your $585M goes to the jackpot is off, you could be looking at significantly less. But the real issue happens if more than one person hits the jackpot.

Sure, it is easy to think it won’t happen because for the past several drawings no one has hit it. But, one rule of lottery is that as the jackpot goes up, more and more tickets are purchased. As more tickets are purchased, the odds of more than one ticket hitting it go up.

Without knowing how many tickets are sold, there is no way to calculate the probability. If someone else shares the jackpot, you are now looking at a loss of $111 million. If two other people hit it, you are looking at a loss of $238 million. It just gets uglier from there.

If playing all the tickets was a guarantee of winning a lot of money, someone with a lot of money would do it. But it isn’t a guarantee and probably not a likelihood. If you don’t play all the numbers, you’re playing a game with a 16% payback and a 4% hit frequency unless you’re one of the guys to hit the big winner.

Buy his book now!

Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Email: [email protected].

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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