Lotto, PowerBall and Daily Lotto odds: the maths behind every division

The game matrices at the time of writing

Lottery odds depend on just two things: how many balls are in the drum and how many of them you must match. Sizekhaya Holdings has run the National Lottery since 1 June 2026, and the handover from Ithuba brought renamed games and new number ranges, as this summary of the lottery changes sets out. Lotto Plus 2 is now Lotto 5 Max and PowerBall Plus is now PowerBall Xtra. Matrices can change again, so check the game rules on the official National Lottery site before you rely on the figures below.

Lotto Plus 1 and Lotto 5 Max are separate draws on the same matrix as Lotto, so each one has exactly the same odds as the main game. PowerBall Xtra works the same way next to PowerBall. An add-on gives you a second, independent chance with the same numbers. It does nothing to your odds in the main draw.

How the combinations are counted

The number of ways to choose k balls from n, ignoring order, is C(n,k) = n! ÷ (k! × (n − k)!). In practice you multiply k numbers counting down from n, then divide by k!:

• Lotto: C(52,6) = (52 × 51 × 50 × 49 × 48 × 47) ÷ 720 = 14,658,134,400 ÷ 720 = 20,358,520.
• PowerBall main balls: C(50,5) = (50 × 49 × 48 × 47 × 46) ÷ 120 = 2,118,760. Multiply by the 16 possible PowerBalls: 2,118,760 × 16 = 33,900,160.
• Daily Lotto: C(36,5) = (36 × 35 × 34 × 33 × 32) ÷ 120 = 45,239,040 ÷ 120 = 376,992.

Lower divisions are counted the same way. To match exactly m of the drawn balls, you choose m numbers from the winning set and the rest of your board from the losing balls, then multiply the two counts. The odds are the total number of combinations divided by the number of winning ways. Every figure in the tables below matches the division odds published by Lottochecker, an independent results site. The official rules page could not be reached for this article.

Lotto, Lotto Plus 1 and Lotto 5 Max

Six numbers are drawn from 52, then a bonus ball from the 46 left in the drum. A “+ bonus” division needs one of your non-matching numbers to be the bonus ball. Of the 46 balls not drawn as main numbers, one is the bonus and 45 are plain losers, which is why 45 shows up in every line. In the table, 6, 15 and 20 are C(6,5), C(6,4) and C(6,3); 990 is C(45,2) and 14,190 is C(45,3).

Add up the winning ways and you get 532,252 out of 20,358,520. So a single board wins something about once in 38.2 tries, or 2.6% of the time. Division 7 is the most common win, because you only need three numbers and no bonus ball.

PowerBall and PowerBall Xtra

The PowerBall comes from a separate drum, so the maths splits in two. The main-ball part is C(5,k) × C(45,5 − k): k of the five winning numbers and the rest from the 45 losing ones. The PowerBall either matches (1 way out of 16) or it doesn’t (15 ways out of 16).

In total 2,270,650 of the 33,900,160 combinations win something, which is 6.7% of boards, or about 1 in 14.9. Most of those wins are small. The last two divisions alone account for 1,966,734 of the winning ways, close to 87% of them. Before the PowerBall range was cut from 1–20 to 1–16, the jackpot stood at 2,118,760 × 20 = 42,375,200 to one. The smaller drum removed a fifth of the combinations.

Daily Lotto

Daily Lotto has no bonus ball, so there is only one formula: C(5,m) × C(31,5 − m), where 31 is the number of balls you can pick that are not drawn.

That gives 49,756 winning ways out of 376,992, or 13.2% of boards. The small matrix explains why Daily Lotto’s top prize is hit far more often than the Lotto or PowerBall jackpots, and also why it is much smaller.

Worked example: R100 on PowerBall

At the time of writing a PowerBall board costs R10 including VAT, and PowerBall Xtra adds R5 a board, according to Sizekhaya figures reported by The Citizen. R100 therefore buys 10 PowerBall boards. Here is what those 10 boards give you:

• Jackpot chance: 10 ÷ 33,900,160, or 1 in 3,390,016.
• Expected number of winning boards: 10 × 0.06698 = 0.67.
• Chance that at least one board wins anything: 1 − 0.93302 to the power of 10 ≈ 1 − 0.50, so roughly a coin toss. This treats the boards as independent, which is a close approximation.

Spread over time, the picture is starker. If you put R100 into one draw every week, that is 520 boards a year. Dividing 33,900,160 by 520 gives about 65,193, so on average you would wait around 65,000 years for a jackpot. Doubling your spend halves the wait. It does not make a jackpot likely.

What the numbers mean for you

Every combination is equally likely in every draw. “Hot” and “cold” numbers, past results and quick picks have no effect on the odds above. What your choice of numbers can change is how many people you share a prize with if you win, never whether you win. Our lottery games guide compares draw formats, and if you do land a prize, the claiming guide explains where to take your ticket.

Treat a ticket as the cost of entertainment, not as a plan. You must be 18 or older to play. If spending on draws is getting out of hand, the South African Responsible Gambling Foundation runs a free 24/7 helpline on 0800 006 008, and our responsible gambling page lists the tools available to you.