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Math

Winning the Lottery

For those of you who play the Lotto regularly, you might benefit from realizing this. I'm not suggesting that you quit (altho' that might be smart too), but there's a better way to play:

For those of you who aren't interested in the theory part of it, skip down to my conclusion.

Let the following variables indicate values as follows:
a = how many tickets bought per game.
b = number of possible combinations
c = chance of winning jackpot
d = number of drawings

Now let's consider the probability of you hitting the jackpot if you enter one drawing:

c1 = a1 / b

That's pretty straightforward, tho' notice than c1 is much less than 1. (1 would mean that you'd win for sure.) Indeed it is much closer to 0. (0 would mean that you have LESS THAN a snowball's chance in Hell; a snowball's chance in Hell is what you currently have.) Now let's calculate your chances of hitting the jackpot at least once if you enter two drawings:

c' = c1 + c2 - c1c2

You may have guessed that you would add the chances of hitting the jackpot on either draw. However, perhaps if you are not a mathematician, you might be wondering whence the minus sign came. It's there because in adding your chances together, you counted the possibility of winning both drawings twice: once when you considered c1 and then once again when you added c2. Thus, if you subtract the chance of hitting both jackpots, you get your actually probability, which still includes the chances of you hitting both jackpots ONCE (instead of twice). It would be impossible to hit both jackpots twice (four jackpots total) in two drawings. If you are concerned because you don't follow this logic, consider how you would find the total area that is inside the circles of a Venn diagram.

Now let's consider your chances if you enter a third drawing:

c'' = c' + c3 - c'c3

Note that you make the same subtraction, AGAIN! This pattern is continued for each drawing you enter. Each time, you must subtract this amount. Wouldn't it be nice if there was a way to avoid subtracting this amount and thus increase your chances of hitting the jackpot? Guess what: That's right: THERE IS!!!

Consider if you saved up all of the money that you would have spent in buying tickets for each drawing, and just spent all that money on buying a lot of tickets for one drawing:

c = (a1 + a2 + a3 + … + ad) / b = c1 + c2 + c3 + … + cd

Look at that! No subtraction! You simply add up the chances you would have had in each separate drawing and subtract nothing! This is because you don't over count your chances of hitting multiple jackpots. Admittedly, you don't count any such chance because none exists if you only enter one drawing. But let's be real: what are the chances that YOU are going to hit multiple jackpots anyway? (Hint: it's much closer to LESS THAN the chance a snowball has in Hell.)

If you had trouble following all of that, consider this: What if one had enough money to buy a ticket for every possible combination of numbers that could be drawn, and for some strange reason, even tho' he already had more money than he might win (and more than he could ever need), he still wanted to play the Lotto. Which method would guarantee that he would hit the jackpot? If he bought several tickets for each drawing over the next few centuries, it's still possible that he might never hit the jackpot, but if he played every single combination possible in one drawing, then no matter what combination of numbers was drawn, he would win.

Conclusion: Your overall chances of hitting the jackpot in the Lotto are greater if you save up all the money that you would have paid to play in separate drawings, and used all of it to play in one drawing. (All or nothing!)

Now, if you're saving up all the money that you would have used to play the Lotto, when do you know to finally play it? Theoretically, you would never play because you'd always save the money 'til the next drawing. However, this isn't practical, so let's consider what is:

When you do actually win something, just remember you told you about this method! And if someone remembers that you told them about this method, remember the person who told you!

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Last Updated: 2009-05-02