Lottery mathematics Lottery mathematics Lottery mathematics is used to calculate probabilities of winning or losing a lottery game. It is based heavily on combinatorics, particularly the twelvefold way and combinations without replacement. In a typical 6/49 game, each player chooses six distinct numbers from a range of 1-49. If the six numbers on a ticket match the numbers drawn by the lottery, the ticket holder is a jackpot winner—regardless of the order of the numbers. The probability of this happening is 1 in 13,983,816. The chance of winning can be demonstrated as follows: The first number drawn has a 1 in 49
Lottery on the player's ticket match those produced in the official drawing (regardless of the order in which the numbers are drawn), then the player is a jackpot winner. For such a lottery, the chance of being a jackpot winner is 1 in 13,983,816. In bonusball lotteries where the bonus ball is compulsory, the odds are often even lower. In the Mega Millions multi-state lottery in the United States, 5 numbers are drawn from a group of 75 and 1 number is drawn from a group of 15, and a player must match all 6 balls to win the jackpot prize.