Statistics
What hot and cold numbers really mean
· Updated: Dariusz Ostrowski
In short
„Hot" and „cold" are simply labels that sort the frequency table: the first marks the number with the highest hit counter over the chosen period, the second — the lowest. Both describe results that have already happened. The next draw is an independent event, so neither label changes the probability of a number being drawn — not even by a fraction of a percent.
The question about hot and cold numbers lands in our inbox more often than any other. The answer is short but inconvenient: these two words describe history, not a forecast. Below we show why the differences in counters look large without being statistically significant, and how to read Lotto statistics without drawing conclusions they don't contain.
How we calculate frequency
The mechanism is plain and holds no secret. We take all draws of a given game from the chosen date range, go through each one, and for every number drawn we increase its counter by one. At the end we sort the pool in descending order. Numbers at the top of the list we call hot, those at the bottom — cold. That's the only operation our statistics script performs.
This exposes the first trap: the result depends on the chosen period. A number that tops the ranking over the last fifty draws may sit in the middle of the table across a five-year range, and in the bottom third across the game's entire history. Same number, same data, three different labels. If someone calls a number „hot" without stating the range, they're saying nothing.
The second trap concerns the additional number. In Eurojackpot, numbers from the main pool (1–50) and the additional numbers (1–12) are drawn from separate sets, so their counters must never be compared against each other. Multi Multi works similarly: the „plus" number has its own mechanics. In our tables these two groups are always kept separate, and that's how they should be read.
Why the counters aren't equal
The most common question is: if every number has equal odds, why did one come up 800 times and another only 700? The answer: because equal odds don't mean equal results. They mean each number has the same chance in every single draw — nothing more. Natural spread is built into randomness itself and would appear even if the machine were perfectly fair.
A simple thought experiment anyone can run at home. Flip a coin a hundred times and count the heads. A 50:50 result is the single most likely outcome, but it comes up less often than you'd think — far more frequently you get 47:53, 44:56, or 55:45. No one would call heads „hot" afterward, because everyone knows where the difference comes from. With 49 numbers and thousands of draws, exactly the same mechanism is at work — it's just that the spread feels less intuitive.
A key property: the spread grows in absolute numbers but shrinks as a percentage. After a hundred draws, the gap between the most and least frequent number can amount to dozens of percent. After several thousand draws, the counters still differ by dozens of units, but that same difference is now just a few percent of the pool. The longer the history, the more the proportions even out — and that is the only pattern frequency actually shows.
What hot and cold numbers don't tell you
The table below compares four common beliefs with what the mechanics of drawing actually show. It's worth reading in full, because each row describes a different way the same mistake returns under a new name.
| Belief | How it actually works |
|---|---|
| A hot number is „on a streak" and will come up again | Balls have no memory. A high counter doesn't change the mechanics of the next draw. |
| A cold number „has to come up eventually" | It doesn't. There's no mechanism that evens out absences — that's the gambler's fallacy. |
| If 7 has come up 800 times and 38 only 700, then 7 is better | Both have an identical chance in the next draw. The difference in counters is natural spread. |
| Mixing hot and cold numbers gives you an edge | Every set of six numbers has the same odds. The choice doesn't change the probability. |
The figures in the third row are illustrative and serve only to show the scale of the difference. We publish current counters for all six games in the statistics section.
The gambler's fallacy — why intuition fails
The belief that after a streak of absences a number is „due" has its own name: the gambler's fallacy. It comes from confusing two different things — a long-term pattern and a single event. It's true that over a very long series of draws, the proportions of occurrences tend to even out. It's not true that this happens through a specific number „making up" for its absence in a specific draw.
The evening-out happens through dilution, not correction. If after a thousand draws a number has twenty fewer hits than average, then after another ten thousand draws that same gap of twenty hits is already a negligible fraction of the total. Nothing makes it up — it simply stops mattering against the growing pool. That's why the gap you see in the column showing draws since the last hit isn't a hint or a warning.
How to read our tables
The frequency table has four columns, and each answers a different question. The hit counter tells you how many times a number came up over the chosen range. The date of the last hit points to the most recent draw in which it appeared. The gap shows how many draws have passed since then. The percentage share shows what portion of all occurrences in the pool this single number accounts for.
All four are a record of history, and none of them is a forecast. If you want to see how hits are distributed across the whole pool at once, heat maps are often more useful — colour intensity corresponds to frequency there, and the differences between neighbouring fields become visible at once, usually turning out smaller than a plain ranking sorted in descending order would suggest.
A practical tip when reading these tables: before treating a difference as meaningful, check how many draws the range covers. Over fifty draws, the top and bottom of the table change every week and carry no information. Over several thousand draws, the ranking is more stable, but precisely because the gaps between numbers have become small as a percentage.
What statistics are actually good for
If they don't predict results, why do we publish them? For three reasons. First, they're a complete and searchable record of the game's history — that has value on its own, whether or not someone plays, or simply checks what came up on their birthday. Second, they show, with actual numbers, what randomness looks like: no one who looks at the distribution of hits from five thousand draws will still claim that a perfectly even split is the norm.
Third, for some players they're a way to choose a set — not a better one, but their own. If you're looking for a set with no criteria at all, it's simpler to use the random pick generator, which draws numbers without reaching for history. The outcome in the next draw is exactly the same as with the most carefully chosen mix of hot and cold numbers — and that is precisely the point of this whole article.
Every combination has the same chance — the calculation
This is easy to check with numbers. There are C(49, 6) = 13,983,816 sets of six numbers out of 49. How many of them contain a particular number, say 7? The other five numbers are chosen from 48, so C(48, 5) = 1,712,304. The chance that 7 is among the drawn numbers is therefore:
1,712,304 ÷ 13,983,816 = 6/49 ≈ 12.24%
There is not a single piece of information about the past in this calculation — which is why the result is the same for a hot number, a cold one and any other, in every draw. In the same way the set 1-2-3-4-5-6 has exactly the same chance as any “nicely mixed” set: 1 in 13,983,816. It does not look random, but that is only our impression — the machine does not tell pretty sets from ugly ones.
How big a difference in the counts is normal
Since every number has a 6/49 chance in every draw, after many draws its count should be roughly the number of draws × 6/49. Roughly, because chance alone creates spread. An example for 7,000 draws:
- Expected number of appearances of one number: 7,000 × 6/49 ≈ 857.
- Typical deviation: √(7,000 × 6/49 × 43/49) ≈ 27.4.
- About 95% of numbers should have a count in the range 857 ± 2 × 27.4, i.e. roughly from 802 to 912.
A difference of a hundred appearances between the most and the least frequent number looks impressive, yet it is within ordinary spread. It would rather be suspicious if all 49 counts were almost equal — real randomness always produces unevenness. The counts of different numbers are slightly linked, because exactly six numbers come up in every draw, but for an estimate like this the approximation is good enough.
The gambler's fallacy in numbers
The probability that a particular number does not come up in one draw is 43/49. That it does not come up in 20 draws in a row — (43/49)²⁰ ≈ 7.3%. So at any moment a few of the 49 numbers (about 3.6 on average) are on a run of 20 draws without appearing. Such “overdue” numbers are a normal sight, not a signal. In the next draw each of them again has a 6/49 chance — not a bit more.
What historical statistics are good for
- Checking that draws behave randomly — counts spread within the expected range are a good sign.
- Describing the history of the game: which numbers came up most often, what the sums, pairs and gaps were.
- Learning statistics on real data — comparing the results with theory.
They are not good for one thing: predicting the next draw. You will find the current counts on the Lotto statistics page. How the total chance changes with more tickets or more draws is shown by the multiple tickets calculator, and the C(49, 6) calculation step by step is in How Are Lottery Odds Calculated?. All the tools are gathered in the Probability Academy.
Exercises
Level: secondary school. Try to work it out yourself first, then open the solution.
Exercise 1. An overdue thirteen
Number 13 has not come up in the last 15 Lotto draws. What is the probability that it comes up in the next one?
Show solution
- The balls have no memory: the previous 15 draws do not change what is in the machine.
- The chance that a particular number is among the 6 drawn out of 49: C(48, 5) ÷ C(49, 6) = 6/49.
Answer: 6/49 ≈ 12.24% — the same as for every other number.
Exercise 2. Ten draws without a number
What is the probability that a particular number does not appear in 10 consecutive Lotto draws?
Show solution
- In one draw the number fails to come up with probability 43/49.
- Draws are independent, so the probabilities multiply: (43/49)¹⁰ ≈ 0.2708.
Answer: about 27.1%. The complement — the number comes up at least once — is about 72.9%.
Exercise 3. The expected count
How many times on average should one number come up in 1,000 Lotto draws, and what spread is typical?
Show solution
- Expected value: 1,000 × 6/49 ≈ 122.4.
- Standard deviation: √(1,000 × 6/49 × 43/49) ≈ 10.4.
- Typical range (± 2 standard deviations): roughly from 102 to 143.
Answer: about 122 times on average; a result between 102 and 143 is ordinary chance.
Games of chance are intended solely for adults (18+). Every draw is an independent event with a completely random outcome — no method of choosing numbers or analysing history increases your chance of winning. The statistics published here describe only results that have already happened. Play responsibly and only with amounts whose loss won't affect your financial situation.
Tags: statistics hot numbers cold numbers frequency lotto