Hot and cold numbers are a myth: here is the proof
· Every figure is worked out from the game's rules.
Tables of numbers that "come up often" and numbers that are "overdue" look as if they say something. To see what they say, we built a machine we know is perfectly fair, and let it draw.
A fair machine, 1,000 draws
The machine draws 6 numbers from 49, as Greek Lotto does, and every number has exactly the same chance in every draw. Over 1,000 draws each number is expected to come out about 122.4 times. Here is what happened:
| "Hot" | Times | "Cold" | Times |
|---|---|---|---|
| 16 | 142 | 1 | 103 |
| 12 | 138 | 46 | 105 |
| 18 | 136 | 31 | 105 |
Number 16 came out 39 times more than number 1, for no reason at all: the machine is fair. Gaps like that are the rule. Over 1,000 draws, by chance alone, the "hottest" number usually comes out about 146 times, well above 122.4. The statistical test (χ²) says a fair machine spreads its results at least this unevenly 98% of the time: nothing unusual.
The proof: what happened next
If hot numbers meant anything, they would keep coming out more often. We split the 1,000 draws in two. The 5 numbers drawn most often in the first 500 came out on average 58.6 times in the next 500. The 5 drawn least often came out 61 times. Each number was expected to come out 61.2 times. The hot ones did not stay hot, and the cold ones did not catch up.
"Overdue" numbers
Every number has a 12.2% chance in every draw, however long it has been missing. In any 30 draws, a given number is absent from all of them 2% of the time, and on average 0.97 of the 49 numbers are missing from all 30. A number that is "overdue" is what a fair machine is expected to produce, not a sign that it is coming.
Check it yourself
The simulation uses a fixed seed ("trainyourodds-hot-cold"), so it always gives the same draws and the results can be repeated. The Greek Lotto odds table shows that a line's chance does not depend on which numbers came out lately.