What a bonus ball actually does to your odds

"Bonus ball" covers two completely different machines wearing the same name. One kind multiplies the difficulty of the entire game; the other kind doesn't move the jackpot odds by a single combination. Knowing which is which tells you more about a lottery's design than anything else on the ticket.

Kind 1: the separate drum — a straight multiplier

US Powerball draws 5 white balls from a drum of 69, then 1 red ball from a separate drum of 26. The drums know nothing about each other, so the count of possible tickets is a product:

Without the red ball: C(69,5) = 11,238,513 → 1 in 11,238,513

With it: 11,238,513 × 26 = 292,201,338 → 1 in 292,201,338

One extra ball, drawn from its own machine, makes the game 26 times harder — figures matching the official prize chart.

Here's the elegant design trick. Suppose Powerball instead asked you to pick 6 numbers from 69 in one drum:

C(69,6) = C(69,5) × 64 ÷ 6 = 11,238,513 × 64 ÷ 6 = 119,877,472

That's a 1 in 119.9 million game. The 5+1 format with the same 70 numbers printed on the slip yields 292.2 million — nearly two and a half times longer odds, while feeling easier ("I only have to pick five, then one little ball"). Australia's Powerball works the same way: the 7-from-35 main game is C(35,7) = 6,724,520, and the 1-from-20 Powerball stretches it to 6,724,520 × 20 = 134,490,400 (The Lott). A tiny second drum, a 20-fold stretch.

The separate drum has a second effect: it manufactures prize tiers. Every main-ball outcome now splits into "with" and "without" the bonus, which is how Powerball fields nine divisions from ten drawn balls — and how the friendly "overall odds 1 in 24.87" figure gets built, as unpacked in jackpot odds vs any-prize odds.

How sensitive is the multiplier? Ask Mega Millions

Because a separate drum multiplies the whole space, changing its size by a single ball moves the jackpot odds by millions. Mega Millions demonstrated this live in April 2025, when its redesign removed one gold Mega Ball, going from 25 to 24 (megamillions.com):

Before: C(70,5) × 25 = 12,103,014 × 25 = 302,575,350

After: C(70,5) × 24 = 12,103,014 × 24 = 290,472,336

One ball out of the little drum: 12.1 million combinations gone, jackpot odds "improved" by exactly one twenty-fifth. (The same announcement raised the ticket from $2 to $5 — the odds got 4% shorter while the price went up 150%, a trade cost per chance can referee.) Operators tune games this way precisely because the second drum is such a fine-grained lever: adjusting the main pool by one ball changes odds in big lumpy steps, but the bonus drum moves them in neat slices of C(main pool, picks).

Kind 2: the same-machine bonus — invisible at the top

UK Lotto draws 6 main balls from 59, then a 7th ball — the Bonus Ball — from the same machine. Your jackpot odds:

C(59,6) = 45,057,474 → 1 in 45,057,474

The bonus ball appears nowhere in that calculation, because the jackpot requires matching the 6 main balls and nothing else. The bonus ball's only job is one prize tier: Match 5 + Bonus. Derive its odds:

Ways to match exactly 5 of the 6 winners: C(6,5) × C(53,1) = 6 × 53 = 318

Of those 318 tickets, the sixth (non-matching) number is one specific ball among the 53 still in the machine — and the bonus is drawn from those 53. So exactly 1 in 53 of them scores the bonus:

318 ÷ 53 = 6 winning combinations

45,057,474 ÷ 6 = 7,509,579 → 1 in 7,509,579 for Match 5 + Bonus

which is precisely the figure the National Lottery publishes. Same machine, zero effect on the jackpot, one extra rung on the prize ladder.

Kind 2 at scale: Australian supplementaries

Saturday Lotto draws 6 winning numbers plus two supplementaries from its barrel of 45. Division 1 is still plain C(45,6) = 8,145,060. The supplementaries exist to build Divisions 2, 5 and 6 — for example Division 2 (5 winners + a supplementary) at 1 in 678,755 (The Lott). Oz Lotto goes further with three supplementaries propping up four of its seven divisions.

Why operators bother

Both kinds of bonus ball earn their keep, just differently:

• More divisions. Extra balls create extra "match patterns", which become extra prize tiers. More tiers means more frequent small wins, which means a much friendlier "overall odds of winning" line on the marketing.
• Longer jackpot odds without scaring anyone (separate drum only). Jackpots grow by rolling over; rollovers happen when nobody wins; nobody wins when odds are long. A second drum lengthens the odds dramatically while the slip still looks like a modest pick-5 or pick-7. Long odds → more rollovers → bigger advertised jackpots → more tickets. The red ball is, functionally, a jackpot-inflation device.
• Cheap near-misses (same machine only). A same-barrel bonus turns some heartbreaking "5 of 6" tickets into slightly-paid "5 + bonus" tickets at no cost to the jackpot column.

The one-line summary

Before you compare two games, ask where the bonus ball lives. Same machine: decoration below the jackpot. Separate machine: a multiplier on everything. Then check the numbers yourself with the odds calculator — every figure above is three lines of C(n,k).