Jan Hvizdak

Karpatska 3

Kosice 04001

Slovakia

One of many techniques used in betting lotteries is picking numbers from the latest draw. Although it may look weird, because as we know, it is very unlikely to draw the same numbers as day before (assume that only one draw is performed per day), this betting system is not as bad as one could think. In fact, in most number lotteries draws sometimes contain up to 70% same numbers as in a previous draw. Of course, there are moments when only 10% of numbers repeat and sometimes this can be even lower.

Analysing lotteries brings the knowledge of repetitive numbers in time periods. Say that there are 100 draws where numbers 1, 2, 3, 4, 5 are being drawn more often than average. In the next time period, numbers 6, 7, 8, 9, 10 are being drawn more often too. And so on. This process is well known and the only problem is answering the question “When will the period start and when will the period end for a particular number?” This is a problem, of course.

So if we know that this behaviour exists, we can assume that in the time period A (where A has it's known start and end) the number X will be drawn more often than the average value given by theoretical probability. An example:

Our lottery contains numbers from 1 to 40. The number 20 is going to be drawn more often during the next 20 draws. Each draw consists of 10 numbers. The probability of any number to be drawn is 0.25 (which is 25%). During 20 draws, each number should be drawn 5 times. Just theoretically, this is how the number 20 should be drawn if all was as average:

**drawn**-break-break-break-**drawn**-break-break-break...

If the number 20 is going to be drawn more often, it will look like this for example:

**drawn**-break-**drawn**-break-break-**drawn**-break-break...

**drawn**-**drawn**-break-break-break-**drawn**-**drawn**-break...

As you can see, there are different scenarios and no-one can predict how the number is going to be drawn. However, if we know that “the period” is now, it is very likely that the number 20 will be drawn in two or three consecutive draws.

In most lotteries, there are balls which represent drawn numbers. Even in computer-based lotteries, the drawing process is a function of something (unless it's a true random numbers generator). The balls have some weight, physical structure, dimensions, and there can be plenty of aspects that determine the draw. Take balls as an example... Since a ball is made of some material, it doesn't last for ever. There are scratches, deformities, the machine itself contains deformities too. Many factors affect the result, and if some variable (in balls) is out of standard value, a ball is replaced with a new one.

All factors that have influence on a draw vary as time goes by. However, in a short time period they're not balanced. This is the reason why betting repetitive numbers can be beneficial.

Below are draws using the *rand()* PHP function which is very similar to most lotteries.

365 draws, 20 numbers per draw, 1..80 is the range

Of these 365 draws,

- in 1 consecutive draws (0.274% out of all) 0 numbers were same which means 0% success rate
- in 5 consecutive draws (1.37% out of all) 1 numbers were same which means 5% success rate
- in 17 consecutive draws (4.658% out of all) 2 numbers were same which means 10% success rate
- in 44 consecutive draws (12.055% out of all) 3 numbers were same which means 15% success rate
- in 54 consecutive draws (14.795% out of all) 4 numbers were same which means 20% success rate
- in 91 consecutive draws (24.932% out of all) 5 numbers were same which means 25% success rate
- in 81 consecutive draws (22.192% out of all) 6 numbers were same which means 30% success rate
- in 48 consecutive draws (13.151% out of all) 7 numbers were same which means 35% success rate
- in 15 consecutive draws (4.11% out of all) 8 numbers were same which means 40% success rate
- in 7 consecutive draws (1.918% out of all) 9 numbers were same which means 45% success rate
- in 2 consecutive draws (0.548% out of all) 10 numbers were same which means 50% success rate
- in 0 consecutive draws (0% out of all) 11 numbers were same which means 55% success rate
- in 0 consecutive draws (0% out of all) 12 numbers were same which means 60% success rate
- in 0 consecutive draws (0% out of all) 13 numbers were same which means 65% success rate
- in 0 consecutive draws (0% out of all) 14 numbers were same which means 70% success rate
- in 0 consecutive draws (0% out of all) 15 numbers were same which means 75% success rate
- in 0 consecutive draws (0% out of all) 16 numbers were same which means 80% success rate
- in 0 consecutive draws (0% out of all) 17 numbers were same which means 85% success rate
- in 0 consecutive draws (0% out of all) 18 numbers were same which means 90% success rate
- in 0 consecutive draws (0% out of all) 19 numbers were same which means 95% success rate
- in 0 consecutive draws (0% out of all) 20 numbers were same which means 100% success rate