You've probably seen the infomercials for lottery boxing systems. You send off your money, and you get back some templates and some rules for using them to select and play numbers. You pick more numbers than are necessary for one ticket, and then play combinations of those numbers.
For example, if you're playing a lottery which requires you to pick 6 numbers, you could pick 7 numbers and then play every six-number combination out of those seven. If your numbers were 8, 10, 15, 18, 31, 34, and 47, you would play the following seven lines:
Line 1: 10,15,18,31,34,47 Line 2: 8,15,18,31,34,47 Line 3: 8,10,18,31,34,47 Line 4: 8,10,15,31,34,47 Line 5: 8,10,15,18,34,47 Line 6: 8,10,15,18,31,47 Line 7: 8,10,15,18,31,34
One big advantage that this method is supposed to offer you is that you will often have multiple winning tickets. For example, if the winning numbers are 3, 9, 15, 18, 27, and 47, you have four lines (lines 1, 2, 5, and 6) with three of the winning numbers. If the prize for three numbers is $10, you win 40 bucks.
What they don't mention is that your increased chances of having multiple winners are exactly balanced by the increased chance that you will have no winner at all. We can see how this works by looking at a very simple example of this strategy - buying multiple tickets with exactly the same numbers.
For example, if you buy three tickets with exactly the same numbers, and three of the numbers come up, you have three winners. However, you'll have fewer weeks with winners than someone who buys three tickets each with completely different numbers. While the other person will never have three winning tickets on the same draw, he or she will have three times as many weeks with winners. In the long run, the two of you have the same chances of making money.
The other supposed big advantage is that you improve your odds. This claim will usually be true, but only in an unimportant way. If the boxing system gets you to buy more tickets, then your odds will improve. The more tickets you have, the better your odds are. To buy more tickets, though, you don't have to send away for all those plastic sheets. All you have to do is walk to the store and ask for more tickets.
The boxing of numbers does not by itself increase your chances of winning. You can only improve your odds by buying more tickets. You do not, though, improve your odds very much by buying more tickets. A little simple work with a calculator will show you that even when you buy a hundred Lotto 649 tickets a week you still can't reasonably expect to win the jackpot in the average lifetime.
There's Nothing in the Box
© John FitzGerald, 1997