Two separate questions
When a lottery jackpot is won, two different things matter: whether your ticket matches the winning numbers, and how many other tickets match them too. The first is a matter of probability. The second is a matter of how other players choose their numbers. Mixing the two up leads to a lot of confusion about “lucky” or “smart” picks.
In many draw games, if more than one ticket holds the winning combination, the top prize is divided between them. Rules vary, so check the specific game, but equal shares are a common arrangement.
The odds are the same for every combination
In a hypothetical game where you pick 6 numbers from 49, there are 13,983,816 possible tickets, and every one of them is equally likely to be drawn. A popular-looking combination has exactly the same 1 in 13,983,816 chance as an unpopular one. The way those odds are counted is the subject of lottery odds, and the argument that individual combinations are not special is made in more detail under lottery patterns.
What differs between combinations is not the chance that they win but the number of players who chose them.
How sharing divides the prize
Suppose, as an illustration, that a jackpot is 10,000,000 and it is split equally. The amount per winning ticket is:
| Winning tickets | Share each |
|---|---|
| 1 | 10,000,000 |
| 2 | 5,000,000 |
| 3 | about 3,333,333 |
| 4 | 2,500,000 |
The chance that the draw produces your numbers does not depend on the table. But the table shows that if the winning combination also happens to be a popular choice, a winner receives a smaller share. Winning alone and winning with three others are the same event as far as the draw is concerned. They differ only in the payout.
Why some numbers are chosen more often
Players do not choose numbers at random. Some tendencies are widely observed:
- Birthdays and dates. Many people use birthdays or anniversaries, which limits them to numbers from 1 to 31. In the 6-from-49 illustration, the number of tickets using only numbers up to 31 is 736,281, about 5.3 percent of all possible combinations. If a large fraction of players uses dates, those combinations will be chosen by far more people than their share of the total suggests.
- Visible patterns. Sequences such as 1-2-3-4-5-6 or neat lines on the playslip are chosen by a noticeable number of players.
- “Lucky” numbers. Numbers like 7 and other personal favourites tend to be popular, although this varies by culture and place.
The exact proportions are different for every game and are rarely published, so treat these as general tendencies rather than measured facts.
A rough picture of the split
Imagine 14 million tickets are sold in the 6-from-49 illustration, which is close to the number of possible combinations. If tickets were chosen entirely at random, the average combination would be held by about one ticket. If the draw produced a combination that players choose ten times as often as average, you would expect it to be held by roughly ten tickets.
This is a case of conditional probability: given that the draw matched your numbers, how many others also match depends on how popular those numbers are. When the jackpot is won, it is more likely to be shared if the winning combination is a popular one, and the bigger the sales, the more tickets there are to share with. That is why jackpot rollovers, which tend to bring more buyers, also make splits more likely.
Does that make unpopular numbers a good choice?
Choosing a less common combination does not make you any more likely to win, because all combinations have the same probability. At best it might reduce the expected size of a split in the event that your numbers do come up. The effect on the average return per ticket is limited by how tiny the chance of winning is in the first place, since sharing only matters if you win.
The simple expected value calculation therefore stays roughly where it was: with a negative expectation, each ticket costs more than it returns on average, regardless of the numbers you pick. Quick-pick tickets, which are generated at random, avoid human tendencies, and they are no better or worse in terms of the chance of matching.
It is also worth being careful about claims that a particular set of numbers is “safe” or “ahead of the crowd”. Nobody can predict which numbers will be drawn, and no choice of numbers makes the jackpot likely. The draw is governed by random chance and has no memory of previous results.
Other ways prizes get divided
Sharing is not limited to the top prize. In many games, lower prize tiers are paid from a pool that is divided among all the winners in that tier, so the payout in those tiers varies from draw to draw. In other games, those prizes are fixed amounts. Which system applies is written in the game’s rules, and it affects how much risk the operator takes versus how much the players share among themselves.
Keeping it in proportion
Sharing arithmetic is interesting, but it does not turn a ticket into an investment. Set a limit on what you spend, treat any ticket as entertainment, and never buy more to recover earlier losses. If gambling is causing you difficulty, a local support service can help.