Lottery Math · 2026-10-12
Mega Millions: The Mathematics of a Basic Ticket
A theoretical explanation of how Mega Millions basic-ticket combinations and jackpot odds are calculated under the current published rules.
Mega Millions uses a basic ticket with five main numbers selected from 1 through 70 and one Mega Ball selected from 1 through 25. This page explains the combination math behind that ticket structure; it does not describe which numbers to choose.
This is a theoretical calculation based on the current published rules; it is not historical draw data.
The basic-ticket structure
The order of the five main numbers does not matter. The number of possible five-number main-ball sets is therefore a combination:
C(70, 5) = 12,103,014
The Mega Ball is a separate selection with 25 possible values. Each main-ball set can be paired with each Mega Ball value:
Basic-ticket outcomes: 12,103,014 × 25 = 302,575,350
So the basic-ticket outcome space contains 302,575,350 distinct combinations. A jackpot requires matching all five main numbers and the Mega Ball, so the theoretical jackpot probability for one basic ticket is:
Theoretical jackpot probability: P(jackpot) = 1 / 302,575,350 = 0.000000003305
Equivalently, the published jackpot odds are 1 in 302,575,350 for a basic ticket.
Why a random draw is not a recommendation
Every valid basic-ticket combination is one possible outcome in the same theoretical outcome space. A random draw is a process for selecting one valid combination; it is not a recommended number set, a ranking of future combinations, or evidence that a historical pattern changes the draw mechanism.
The formulas above describe the rules of the game. They do not use prior winning-number history, and they do not imply a forecast for a future draw.
Prize levels
Mega Millions prize levels are determined by matching the published main-number and Mega Ball criteria. The jackpot is the top prize level and requires all five main numbers plus the Mega Ball. Other prize levels correspond to the published match combinations and prize rules; this article does not estimate prize values or provide winning-number recommendations.
Sources
Always refer to the official Mega Millions materials for the current rules, prize chart, and game notices.