Statistics and Lotteries

Let's take a look at lotteries such as Lotto, or in general any other game where one has to pick numbers.

From the statistical point of view, any combination of numbers carries the same weight and so the probability of the combination 1,2,3,4,5,6 is the same like the probability of the combination 41,42,43,44,45,46. However, lotteries aren't usually true random numbers generators. A true random numbers generator is completely unpredictable, but a lottery machine can be predictable.

The break

In order to simplify things, don't think about combinations, but about single numbers only. If there are say 50 numbers in the draw and if you let it run 50 times, each number should be present in one draw in average. Naturally, it doesn't work this way and for example the result will be :

number 0 – drawn 0 times
number 1 – drawn 5 times
number 2 – drawn 2 times
and so on...

Now, if you repeat draws 1000000 times, the aberrance should lead to zero and each number has to be drawn 1000000/50 times which is 20000. However, this is just a theory and the actual numbers will vary. No matter that the results may vary for each number, the aberrance shouldn't be too high. In 1000000 draws, any number shouldn't be drawn more than 26% and less than 24%. If it's so, then the lottery isn't using a true random numbers generator for sure.

Generally if a number hasn't been drawn in the last 100 draws, and if there are only 50 numbers to choose from, the probability of being drawn raises as one could consider. In fact, the probability raises only in statistical point of view.

Practically a number doesn't have to be drawn even a one time during 1000000 draws, but a true random numbers generator or a pseudo-random numbers generator MUST generate the same result for each number in a long time interval. In this term, if a number hasn't been drawn for too long, the time when it's going to be drawn is close. Because the probability is still the same!

The problem with breaks

No-one can tell when a number is going to make a break-through and when it's break ends as long as the algorithm of our random numbers generator is not known.

From one number to a set of numbers

The same principle as above applies to sets of numbers; No matter if you're going to bet on 2 numbers or 6 ones. The break is just a variable that depends on how many numbers we have and how many are going to be drawn.

10 numbers to choose, 20 numbers to be drawn, 80 numbers in the machine

One number's average break is 4.

Two numbers' average break is roughly 17.

Three numbers' average break is approximately 72.

Ten numbers' average break is 8911711.

As you can see above, one number's average break is only 4 while 10 numbers' average break is almost 10M.

Betting on numbers that haven't been drawn for too long

It's possible to bet on a single number with currently long break. In most games you'll win 2x if you pick one number correctly. If you don't pick the right number, you lose. So the example:

Our lottery contains 40 numbers, each draw consists of 13 numbers.

Your chance to pick 1 number correctly is 32.5% which is 1:3. 3 is also the average theoretical break for each number. One could think that it's not so likely to find a number with a break of 60 (say) days. If such a person decides to bet on a number that hasn't been drawn for the last 55 days, statistically it shouldn't be hard to win. On the other hand, betting each day $5 on one number won't bring you any profit if there are next 20 days without that number and it's finally drawn on 21th day. You'll lose 20*$5 ($100) and win only $5 ($10-$5). That's why it's necessary to increase the bet according to your total investments.

Day 1$5
Day 2$10
Day 3$20
Day 4$40
Day 5$80
Day 6$160
Day 7$320
Day 8$640
Day 9$1280
Day 10$2560
Day 21$5242880

There are two problems; Firstly, it's necessary to have plenty of money available for this scenario. No-one can guarantee that on 21th day you're going to win. The break can last 30 or 40 days! In addition, your total earnings will be $5 anyway! I wouldn't risk over $500000 for some $5!

This strategy can be effective if only you're aiming at more than 1 number and if the potential income is much higher than potential loss.

©2009-2010 How to Win a Lottery created by Jan Hvizdak, best viewed on Opera