Lottery matrix, in full
Read 6/49 as six numbers chosen from a pool of 1 to 49. Games with a second pool add a term: Powerball is 5/69 + 1/26, meaning five white balls from 69 plus one red ball from a separate 26, and EuroMillions is 5/50 + 2/12. Order never matters in these games, so the count of possible tickets is a combination rather than a permutation.
The matrix fixes the jackpot odds completely, with nothing else involved. C(49,6) = 13,983,816, so a 6/49 game has that many distinct tickets and exactly one of them matches. Small changes to either number move the total a long way. When the UK widened its main Lotto pool from 49 to 59 in October 2015, the ticket count went from 13,983,816 to 45,057,474, which is why jackpots there began rolling over and growing more often.
The matrix says nothing about prize money. Two games can share a format and pay wildly different amounts, because payouts come from ticket sales, the operator's payout percentage and the prize table. The matrix also does not tell you the overall odds of winning anything, since that depends on how many match levels the game pays and how low the smallest one goes.
- Lottery mechanics
- Game format, Number matrix
A worked example
Powerball's matrix is 5/69 + 1/26. The white balls give C(69,5) = 11,238,513 possible sets, and each of those pairs with any of the 26 red balls, so 11,238,513 × 26 = 292,201,338 tickets. Mega Millions is 5/70 + 1/24: C(70,5) = 12,103,014, times 24 gives 290,472,336. Almost identical odds from two different-looking matrices.
Sources
Powerball's format gives 292,201,338 possible tickets, which is the published jackpot chance of 1 in 292,201,338.
Powerball — Prizes and odds chartMega Millions asks for five numbers from 1 to 70 plus one Mega Ball from 1 to 24, giving jackpot odds of 1 in 290,472,336.
Texas Lottery — Mega Millions game informationThe UK Lotto main pool went from 49 to 59 balls on 10 October 2015, moving the jackpot odds to 1 in 45,057,474.
Wikipedia — National Lottery (United Kingdom)
See also
Where it comes up on this site
Lottery matrix: frequently asked
Six numbers picked from a pool running 1 to 49. That gives C(49,6) = 13,983,816 distinct sets, all equally likely.
Widening the pool always lengthens them, but asking for more picks does too, and the two are not interchangeable. A 6/49 game has 13,983,816 tickets. Widening it to 6/59 gives 45,057,474. Keeping the pool at 49 and asking for seven picks gives 85,900,584, a bigger jump than the wider pool produced.
No. Prizes come from ticket sales and the prize table, not from the format.