Is 1-2-3-4-5-6 less likely to win? No — but please don't play it

This is the question that best separates how lotteries feel from how they work. Ask anyone: could 1-2-3-4-5-6 really come up? Almost everyone says no — it's "too neat". And yet the same people will happily play 4-13-19-27-34-45, which is precisely, exactly, to-the-last-decimal equally likely.

The two-sentence proof

A 6/49 draw selects one 6-number set out of C(49,6) = 13,983,816 possible sets, and a fair draw selects each set with equal probability — that's what the mixing, the certified machines and the randomness testing are for. So:

P(1-2-3-4-5-6) = P(4-13-19-27-34-45) = P(your numbers) = 1 / 13,983,816

There is no clause in probability theory about neatness. "1,2,3,4,5,6" is only special in our notation — the balls don't come out in order, and the machine has no idea that our counting system makes those six glyphs adjacent. If you relabelled the balls with 49 random animal pictures, the draw "ant, bee, cat, dog, eel, fox" would strike nobody as suspicious.

If you want it even more concrete: the draw happens one ball at a time. P(first ball is one of your six) = 6/49. Then 5/48, 4/47, 3/46, 2/45, 1/44. Multiply:

(6 × 5 × 4 × 3 × 2 × 1) / (49 × 48 × 47 × 46 × 45 × 44) = 720 / 10,068,347,520 = 1/13,983,816

That calculation never asked which six numbers you hold. It can't — the arithmetic has nowhere to put the information.

So why do mathematicians still say "don't play it"?

Because winning the lottery has two parts: matching the draw, and not sharing the jackpot with a crowd. Lotto jackpots are parimutuel — split equally among all winning tickets. Your six numbers being drawn is chance; how many people you split with is entirely determined by other players' psychology. And 1-2-3-4-5-6 is the most psychologically magnetic line in existence — it's the first thing that occurs to everyone who has the "all lines are equal, so I'll prove I get it" epiphany. Cleverness this common stops being clever.

The scale is reported, not hypothetical: it is widely reported that over 10,000 people play 1, 2, 3, 4, 5, 6 every week in the UK National Lottery alone. Treat the exact figure as journalism rather than an audited statistic — operators only occasionally publish pick data — but even the order of magnitude is devastating. Run the division on a £10,000,000 jackpot:

£10,000,000 / 10,001 winners ≈ £1,000 each

You'd have beaten odds of 13,983,816-to-1 — a genuine miracle — and collected roughly the price of a used piano. Meanwhile the match-5 players below you on the prize table might out-earn you. It is the worst possible outcome in all of lottery: maximum luck, minimum payout.

This has actually happened (with a subtler pattern)

If mass coincidence on one line sounds theoretical, the UK provided a controlled experiment in its ninth-ever draw. On 14 January 1995, UK National Lottery draw 9 came up 7-17-23-32-38-42 — and 133 tickets matched all six, so the £16 million jackpot paid each winner just £122,510. Why 133? As mathematician Kit Yates has written, the winning numbers happened to sit in the central columns of the printed playslip in a visually pleasing arrangement — a pattern thousands of players had independently "invented". Nobody colluded. Human brains just run on shared hardware.

And that was an accidental Schelling point. 1-2-3-4-5-6 is the deliberate one — the single most famous line in lotto. The 133-way split would look generous.

The actually-useful takeaway

The right lesson isn't "avoid 1-2-3-4-5-6" — that line will almost certainly never be drawn in your lifetime anyway (at one draw per week, expect to wait on the order of 269,000 years for any specific line). The lesson is the principle it makes vivid:

1. You cannot change your odds. Every line: 1/13,983,816. Full stop.
2. You can change your expected share. Avoid anything a human brain finds satisfying: famous sequences, dates (numbers 1–31 are massively over-played), playslip geometry, arithmetic progressions, last week's winning numbers, numbers from TV shows.
3. Random picks dodge the crowd for free. A machine-generated line has no psychological gravity. Our number generator gives you uniform random lines, and the number-sharing risk tool scores how "human" any line you're considering looks.

For the deeper dive into why unpopular numbers genuinely raise expected returns — one of the few peer-reviewed "edges" in lottery play, documented by Haigh in JRSS Series A — see our articles on consecutive numbers and lucky number 7.

So: is 1-2-3-4-5-6 less likely? No. Not by a hair, not by rounding, not at all. It is merely the world's most efficient machine for converting a 14-million-to-1 miracle into a four-figure cheque.