Even and Odd Numbers in Lotto — Historical Distribution

The question of the proportion of even and odd numbers comes up in every analysis of Lotto results. The answer is simpler than the results tables suggest: the distribution is not a historical phenomenon, but a consequence of how many sets of a given type can even be arranged from 49 numbers. History merely confirms what follows from counting combinations — and it does so more precisely the longer the time period considered.

How many even numbers are in the Lotto pool

The range 1-49 does not split evenly. There are 24 even numbers — from 2 to 48. There are 25 odd numbers — from 1 to 49. This single-number difference is enough for sets with a majority of odd numbers to be slightly more numerous than their mirror counterparts: there are slightly fewer 4:2 sets than 2:4 sets, and fewer 6:0 sets than 0:6 sets.

The total number of possible six-number sets from 49 is 13,983,816. Each one has exactly the same probability of being drawn. The differences discussed below concern only how many sets of a given type exist in that pool — not any bias toward a particular set.

How many sets fall into each combination — table

The table below is the core of this article. The numbers in the middle column are the result of multiplying combinations: the number of ways to choose k numbers from 24 even ones times the number of ways to choose the remaining numbers from 25 odd ones. The last column shows the share of the pool of 13,983,816 sets.

Combination (even:odd)	Number of sets	Share of pool
0:6	177,100	1.27%
1:5	1,275,120	9.12%
2:4	3,450,600	24.68%
3:3	4,600,800	32.90%
4:2	3,190,200	22.81%
5:1	1,063,400	7.60%
6:0	134,596	0.96%

Combinatorial calculations for the 1-49 pool when choosing six numbers: 24 even, 25 odd, 13,983,816 sets in total. Shares are rounded to two decimal places, so their sum may not equal exactly 100 percent.

The three middle rows — 2:4, 3:3 and 4:2 — together give 11,241,600 sets, or about 80.4 percent of the pool. This is the whole answer to why draw results "look balanced": there are simply the most sets of that kind. The extremes of 6:0 and 0:6 together give 311,696 sets, or about 2.2 percent — statistically they will appear roughly once every forty-five draws, but they can turn up twice in a row or not appear for several years.

Why the 6:0 combination is rare

Not because the drawing machine "prefers" anything. For six even numbers to come up, all six balls must come from the subset of 24 numbers, not from the full pool of 49. The number of such sets is 134,596 out of 13,983,816 total — hence under one percent. The same arithmetic governs every other split of the pool: six numbers from a single decade, six numbers below 25, or six numbers ending in the same digit.

It is worth stressing what does not follow from this. A single set of 2, 8, 14, 22, 36, 44 has exactly the same probability as 3, 11, 24, 31, 38, 49 — one in 13,983,816. Rarity applies to the category, not to a specific ticket. Marking six even numbers is neither a worse nor a better choice than any other; it is simply a choice from a less numerous category.

What the draw history shows

Over a sufficiently long series of draws, the observed frequencies of combinations approach the shares in the table above. This is not a discovery, just the law of large numbers at work — the more trials, the smaller the deviation from the expected value. Over a short span, say fifty draws, deviations can be large and mean nothing beyond the fact that the sample was small.

Current frequency breakdowns for individual numbers and the full draw history can be found in the Lotto statistics. Visual distributions, including hit-density heatmaps, are collected on the Lotto heatmaps page.

Do other games have the same distribution

No. Each game has its own pool and its own number of picks, so the combination shares differ. In Mini Lotto you pick 5 numbers from 42, where even and odd numbers number 21 each — the pool splits perfectly in half, and with an odd number of picks a perfectly balanced combination does not exist. In Eurojackpot you pick 5 from 50 plus 2 from 12, so two distributions have to be calculated separately. In Multi Multi we have 20 numbers from 80, which shifts the weight of the distribution even further toward proportions close to ten and ten.

The conclusion is common to all six games: the more numbers are picked and the more evenly the pool splits, the more strongly the distribution concentrates around the middle. Data for the other games is collected in the Eurojackpot statistics and on the analogous pages for each game.

The most common misunderstandings

The first: that after a series of draws with a majority of odd numbers, "it will be even numbers' turn." It will not — the balls have no memory, and every draw starts from the full pool of 49 numbers. The second: that the 3:3 combination is "better to play." There are the most sets of this type, so they come up most often — but the chance of hitting a specific 3:3 ticket is identical to any other. The third: that choosing a particular proportion of even and odd numbers increases the chance of winning. Nothing increases it, because the probability of every individual set is fixed and equal.

The only practical application of these calculations concerns splitting the prize. Unusual sets — for example, numbers only up to 31, popular because of birth dates — tend to be picked by more people at once. Choosing a set from a rarer category does not raise the chance of winning, but if you do win, it reduces the risk of splitting the prize with a dozen or so other players. This is an argument about the amount, not about the odds.

If you want to compare your own set against the draw history, the coupon checker will be useful. A random set with no preferences of your own can instead be generated by the random pick generator.