The birthday problem in lottery numbers

The claim

Players pick dates. Birthdays, anniversaries, the day a child was born — which means the numbers 1 to 31 are chosen far more often than 32 and above. If a winning line happens to sit entirely inside that range, more tickets match it, and the jackpot is split more ways.

Avoid 1 to 31 and you have not made yourself more likely to win. You have made it more likely that if you do, you win alone.

What the arithmetic says, with no data at all

This part needs no archive. It follows from the matrix. For a game drawing 6 numbers from 59, the chance that all six land inside 1 to 31 is the number of ways to choose 6 from 31, divided by the number of ways to choose 6 from 59 — about 1 in 61.

So roughly one draw in sixty-one produces an all-calendar line. It is not rare enough to ignore. Over a few years of a twice-weekly game it happens repeatedly, and each time it does, the prize is split among a crowd.

How often an all-calendar line comes up, by game
Game	Matrix	Chance of an all-calendar line
Bonoloto	6 from 49	1 in 19
US Powerball	5 from 69	1 in 66
La Primitiva	6 from 49	1 in 19
Mega Millions	5 from 70	1 in 71
El Gordo	5 from 54	1 in 19
Mega-Sena	6 from 60	1 in 68

What our archive shows

Across 7,873 draws in the games where we hold enough history, an all-calendar line came up 317 times. The matrix says it should have come up about 320 times.

That is the expected result and it is worth stating plainly: the draws are fair. Low lines are not drawn unusually often. The bias is in what players choose, not in what the machine does.

What our archive honestly cannot show

Whether players really do over-pick those numbers. No operator publishes ticket data. Nobody outside a lottery knows how many people played a given line, so nothing on this page — or on any site — can measure player choice directly.

There is one indirect trace: the number of jackpot winners. If low lines are over-picked, a jackpot won on a low line should be shared more often than one won on any other. That is measurable from data we hold, so we measured it.

Average jackpot winners, low lines against all others
Game	Low-line jackpots	Shared by	Other jackpots	Shared by
Loto 6	6	2.33	51	1.84
Loto 7	9	1.33	17	1.41

Our data does not settle it. Only 2 of our games have enough won jackpots on both sides to compare at all, the samples run to single figures, and they point in opposite directions. One shows low-line jackpots shared more often, the other slightly less.

On numbers that small, that is what noise looks like. We are not going to present it as a finding, and we will report it again when the archive is deep enough to mean something.

The underlying effect is well established in published research on lottery ticket choice, which has access to data we do not. What we can tell you is that our own archive cannot yet demonstrate it, and we would rather say that than borrow someone else's number and present it as ours.

So what should you actually do?

If you play, and you would rather not share: spread your line beyond 31. That is the whole of the practical advice, and notice how small it is. It does not make you more likely to win. It changes what winning would be worth if it happened.

Anything more than that — a system, a set of due numbers, a pattern to follow — is someone selling you a coin they have already flipped.

Generate a line, and if you want one that avoids the calendar, simply discard any line where every number is 31 or below. About one in sixty will be.

Method

Every figure here is computed by scripts/birthday-bias.mjs from the draw archive published on our data page, partitioned by the number matrix in force on each draw date so that a pool change never moves a denominator. The probability figures come from the matrix itself, not from counting.

Last computed Sunday 20 September 2026 across 17 format windows.