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How To Win the Lottery

March 30, 2012

Know the Odds

Before you can successfully play any game of chance you need to know the odds of winning. Knowing the odds of winning will tell you exactly what you need to do in order to guarantee a win. It is how a successful poker player appears to win all the time, by knowing the odds.

How do you know the odds of winning any given lottery? Well, you could find out the parameters for playing the lottery, that is, how many numbers you pick within what ranges of numbers, and whether or not there is an extra number, and then you could do the math to calculate the odds of any given set of numbers being a winner.

As an example, let’s assume that we have a lottery where we pick 5 numbers in the range of 1-56 and there is a “bonus” ball in the range of 1-46. (These happen to be the parameters of a popular American lottery.) Given these constraints, we need to calculate the number of ways that 5 balls out of 56 balls can be combined and what effect adding another 46 balls has on the outcome. Thanks to our good friend, combinatorial algebra, we know that we can calculate the number of ways that X items can be selected from a set of Y items using the following formula:

X! / (Y! * (X-Y)!)

So, for our first 5 balls from a set of 56 balls, we plug in our values for X and Y, 56 and 5 respectively, and get the following result:

56! / (5! * (56-5)!)

We calculate the effect of the bonus ball in a similar manner, this time using 46 and 1 for our X and Y:

46! / (1! * (46-1)!)
46 (Neat, huh?)

The final probability of hitting the jackpot is the product of those two values. As we know, we determine a product by using multiplication:

3,819,816 * 46 = 175,711,536

So, our odds of winning this lottery with a single ticket are 1 in 175,711,536. Of course, we didn’t have to go to all this trouble to determine our odds of winning. Since the good people who run the lottery have already done that math for us, the easier solution is to find the web site of the lottery in question and look up the odds of winning. If we visit the web site for the unnamed lottery described above, we find that they list the odds of winning the jackpot as 1 in 175,711,536, showing that they are just as good at math as we are.

Buy the Tickets

So you know the odds of winning…. Now what? Well, now you have to buy the tickets, and you have to buy them with a winning strategy in mind. Simple math will tell us that if buying 1 ticket gives a 1 in 175,711,536 chance of winning, then buying two tickets will double the odds to an amazing 2 in 175,711,536, or 1 in 87,855,768. In order to guarantee a win, you want to get the odds down to 1:1, or 1 in 1 if you don’t like me changing notation on you midstream. In order to do that, you need to buy … You guessed it! … 175,711,536 tickets.

Not only do you have to buy that many tickets, these tickets have to be unique. That is, they have to cover the entire range of possible winning numbers with no duplications. This means that you can’t simply walk in to your local lottery retailer and say, “Give me 175,711,536 quick picks, please.” The quick picks will ge generated by a computer using a pseudo-random number generation algorithm. (Note the presence of “pseudo” in that phrase.) While these numbers might give the appearance of being random, they are in no way, shape or form actually random, and you will be guaranteed of having some duplicate tickets. This is the main reason that most lotteries use mechanical devices (typically involving balls and jets of air) to gather their winning results. Mechanical devices are far closer to actually random than a computer running deterministic algorithms.

Besides, even if you had a truly random number generator, you wouldn’t want randomly generated tickets because you’re still very likely to have some duplicate tickets, and you don’t want any duplicate tickets. You want a definitive set of tickets. In fact, you want them all, the set of all possible tickets. So, you should enter your local lottery retailer’s shop and say, “I’ll take one of each, please.” Of course, the sales persion is not going to understand what you mean, so you’ll have to explain.

“Hold on a minute!” I hear you protest. “These lottery tickets aren’t free. They cost $1.00 each. How am I supposed to pay for all of these tickets? My local lottery retailer won’t give them to me for nothing, you know.”

That is a fair question, and I have a fair answer.

You go to the local branch of your bank, walk right up to the assistant branch manager, and say, “Bob…” (The assistant branch manager is always named Bob, whether a man or a woman.) You say, “Bob, I want to borrow 175,711,536 dollars, please.”

Bob will not even blink.

You continue, “I want the 175,711,536 dollars to buy 175,711,536 lottery tickets. You see, the lottery jackpot has hit record levels, and the cash pay out right now is $360 million. After deducting forty percent for state and federal taxes, that leaves about $216 million. That’s more than enough to pay back the 175,711,536 dollar loan and leaves about forty million in winnings for me. — Statistically, it’s a sure thing!”

Of course, you have neglected to mention the 45 tickets that also match the first 5 winning numbers, but don’t match the bonus ball. These are worth $250,000 each, for a total of another $7 million or so after taxes. You would also possess several thousands of other tickets that matched various other prize levels, and you would collect all of that additional money. You neglect to mention this because you haven’t thought of it, and I am too lazy to figure out the amount of those winnings. — Whose story is this, anyway?

Bob inhales and exhales slowly. He stares at you as he seems to be thinking. Finally, he says, “There are at least two problems with your idea. One, we could never get 175,711,536 dollars for you by the Friday ticket purchasing deadline. Two, the bank would never approve a loan of 175,711,536 dollars for you even if we could get the 175,711,536 dollars on time.”

“But, why wouldn’t the bank approve such a loan?” You complain. “It is a sure thing. The winning ticket is guaranteed. The jackpot is the amount that I’ve stated or more. The bank is guaranteed to get its money back, and at the current interest rates to make a few million dollars just for loaning some money out for a few days. — It’s a win-win.”

Bob smiles as if you have just provided him with the out that he needs. “You see, sir…” (You are always addressed as “sir” whether you are a man or a woman.) “You see, sir,” he explains, “the bank does not loan money for the purposes of gambling.”

“But … but … the bank loans money so that people can speculate on the stock market.”

“Only against good collateral, and investing in stocks is not really gambling in the same sense as buying lottery tickets.”

“But, it is,” you insist.

“Be that as it may, sir,” he goes on, “I doubt you have any collateral of sufficent value to secure a 175,711,536 dollar loan and as you said, it could very well be a ‘win-win.’ After all, what happens if someone else also has a jackpot winning ticket? You would receive only half of the prize money, and after handing all of your winnings over the bank as payment, you’d still owe the bank $60 million that you have no hope of repaying. — No, sir, I cannot in good conscience allow you to take such a loan.”

“That’s novel…” you think, “a banker with a conscience.”


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  1. Sam's Branch permalink

    I enjoyed that. didn’t try to follow all the math, figured I would trust your genius. Your have an amazing mind! Much love to you and April and Meghan. Did I spell Megan right?

    • Thanks. I’m glad you liked it.

      You know you’re partly responsible for that “genius,” don’t you? When I was a kid and I’d ask “why,” you always turned the question into “how” and helped me answer it. Along the way I learned some science and how to figure things out for myself.

      And, yes, you did spell Meghan correctly.

      • Sam's Branch permalink

        You were an easy student, interested in everything. I remember that we had some great times thumping around Charleston.

      • Sam's Branch permalink

        I am happy to know that I was a positive influence on you. You made me very happy.

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