The Mathematics of Lotto - What Do the Numbers Say?

Where does the number 13,983,816 come from

In Lotto, you mark 6 numbers out of 49. The order of the draw doesn't matter, so the number of possible outcomes is described by the binomial coefficient „49 choose 6”: 49! / (6! × 43!). After simplification, this gives 13,983,816 different six-number sets. Exactly one of them matches the drawn numbers, so the probability of hitting six numbers with a single bet is 1/13,983,816, or about 0.0000072%.

This number is not an estimate or the result of observation. It's a value calculated from the rules of the game, identical for every draw since the pool of numbers was set at 49. It doesn't depend on how many coupons were sold, how many draws have passed without a jackpot winner, or how high the jackpot currently is.

Probability of individual prize tiers

Lotto rewards four prize tiers. The table below shows how many sets correspond to each one and how that translates into the odds of a single bet. The numbers in the „Number of combinations” column are the product of choosing the matched numbers among the six drawn and the missed numbers among the remaining forty-three.

Odds for individual prize tiers in Lotto (6 of 49), single bet

Tier	Matches	Number of combinations	Odds
I	6	1	1 : 13,983,816
II	5	258	1 : 54,201
III	4	13,545	1 : 1,032
IV	3	246,820	1 : 57
—	0, 1 or 2	13,723,192	approx. 98.1% of bets

The sum of all rows gives 13,983,816 — the complete set of possible combinations. The „1 : n” values are rounded to whole units.

It's worth noting the proportion in the last row: in almost 98 out of 100 bets, no rewarded tier is hit. Matching three numbers, which seems common to many players, occurs on average once every 57 bets — statistically rarer than once every two months with a single bet per draw.

System bets: more bets, not a higher chance

On a system coupon, you mark more than six numbers, and the lottery operator generates the full set of single bets from them. With seven numbers, this creates 7 bets; with eight — 28; with ten — 210; with twelve — 924. The cost is the price per bet multiplied by the number of bets.

This is where a common misunderstanding needs clearing up. A system bet does not change the probability of a single bet — it's still 1/13,983,816. What changes is only the number of bets you pay for. Twelve numbers give a chance of hitting six equal to 924/13,983,816, or about 1 : 15,134 — but the same result would be achieved by anyone who buys 924 different single bets for the same money. The advantage of a system bet is convenience, and the fact that a matched six within the system triggers an entire series of lower tiers from the same coupon. It is not a mathematical advantage.

The same rule works both ways: since the chance grows linearly with the number of bets, so does the cost. The ratio between the two remains constant and is fixed in the game's rules, not in the way you mark the coupon.

Frequent and rare numbers — what the statistics actually show

Tallies of how often individual numbers have been drawn have been kept since the first draw in 1957 and do indeed show differences: some numbers have come up more times than others. This, however, is not proof of an unfair machine, but a natural property of randomness. Given a finite number of draws, a perfectly even distribution would be a far more suspicious phenomenon than the fluctuations actually observed.

The balls and machines are subject to inspection, and draws are carried out using interchangeable sets of equipment, which further disperses any potential micro-differences. Even if some ball had a slightly different weight, its effect would be lost across the scale of many thousands of draws.

What matters most, however, is something else: the balls have no memory. The result of the previous draw has no effect on the next one. The belief that an „overdue” number must come up soon is a classic gambler's fallacy. Every draw starts with the same distribution, regardless of history.

What the numbers don't tell you, and what many players assume

Mathematics lets you calculate the odds and the cost. It doesn't let you calculate the size of the prize — that depends on the prize pool and the number of people who matched the same tier. This is the source of the only decision that has any influence on the future outcome at all, and it's not on the odds, but on the amount to be divided.

Players rarely mark sequences like 1-2-3-4-5-6, and also avoid numbers above 31, since many people bet on birth dates. A set made up of high or „unattractive” numbers appears less often on other coupons, so in the event of a win, there would be fewer people to share the pool with. The probability of hitting stays exactly the same, though — 1 in 13,983,816 for every set without exception. The growing popularity of quick-pick style bets further weakens this effect, since randomly generated coupons are distributed evenly across the entire pool.

There is no number pattern, marking method, or analysis of draw history that would raise the odds of a single bet above this value. Any offer claiming otherwise contradicts the arithmetic of the game.

When Lotto draws take place

Lotto draws are conducted by the national lottery operator. The current schedule, betting deadlines, and the price of a basic bet can be found in the operator's official materials — these details are updated from time to time, so it's worth checking the source rather than relying on older publications.

We publish current results for all draws on our site, on the pages dedicated to each game, together with frequency statistics and a draw archive.