Keno & Lottery Odds: Among the Worst Bets in Gambling

Keno and lotteries sell the biggest dreams in gambling at the worst prices. Keno house edges commonly run 25% to 30% or more, and lotteries typically pay back around half of what they take in. A 6/49 jackpot is 1 in 13,983,816; a two-drum 5/69 + 1/26 jackpot is 1 in 292,201,338. Here's the exact math, and why the numbers are so lopsided.

How keno works

1. Pick your spots. You choose a set of numbers from 1 to 80, typically 1 to 10 of them (some games allow more).
2. The draw. The game draws 20 numbers at random.
3. Count your catches. Each of your numbers that's drawn is a "catch" or "hit."
4. Get paid. The pay table for your number of spots says what each count of hits returns.

Twenty of 80 numbers are drawn, so any single number has a 20 ÷ 80 = 25% chance. A pick-1 ticket would need to return $4 for $1 to be fair. If it returns $3, you get back 75% on average: a 25% house edge.

The keno math, exactly

With more spots, the chance of catching exactly k of your n numbers is a hypergeometric probability:

C(20, k) counts ways your hits come from the 20 drawn numbers, and C(60, n − k) counts ways your misses come from the 60 undrawn ones. Here's a pick-6 ticket with an illustrative pay table, not any particular game's:

Bigger tickets make the top prize much rarer. Catching all 10 on a pick-10 ticket is C(20, 10) ÷ C(80, 10), or about 1 in 8,911,711.

Why the keno edge is so big

Table games compete on thin edges because the bets are simple and anyone can check them. Keno pay tables are long, differ by game and spot count, and rarely state their return. When a price is that hard to compare, it can stay high.

At a 30% edge, $100 of keno tickets costs about $30 on average. The same $100 bet on red at a single-zero wheel costs about $2.70. For how any edge turns into dollars over time, see house edge explained.

Lottery odds, derived

In a 6/49 lottery you choose 6 numbers from 49. The number of possible tickets is:

Exactly one of those combinations wins the jackpot. The smaller prizes follow the same counting logic:

Lotteries often advertise the "overall odds" of winning any prize. In this plain 6/49 example that's 260,624 winning combinations out of 13,983,816, about 1 in 53.7. It sounds encouraging, but nearly all of those wins are the smallest prize tier.

Two-drum jackpot games stack two drums. You pick 5 white balls from 69, which can be done C(69, 5) = 11,238,513 ways, and 1 red ball from 26. The jackpot needs both: 11,238,513 × 26 = 292,201,338.

That single extra ball is what turns a roughly 1-in-11-million game into a 1-in-292-million one. Each additional drum or number in the pool multiplies the combinations, which is how lotteries build jackpots big enough to make headlines.

Putting 1 in 292 million in perspective

Imagine buying 100 different tickets every week for 50 years: 2,600 draws and 260,000 tickets.

• 6/49 lottery: your chance of ever hitting the jackpot is about 1.8%. On average you'd wait around 2,700 years.
• 5/69 + 1/26 jackpot: your chance is about 0.09%, or roughly 1 in 1,124. The average wait is over 56,000 years.

Check scenarios like this with the probability calculator, which works out the chance of at least one hit in any number of tries.

Small, regular spending adds up. Spend $5 a week for 10 years and you've put in $2,600. At a return of around 50%, your expected loss is roughly $1,300, and the most likely outcome is a scattering of small prizes and no jackpot.

Big jackpots and the expected value question

When a jackpot rolls over and grows, the expected value of a ticket rises. People sometimes argue that a big enough jackpot makes a ticket a "good bet." Three things work against that:

• Taxes can take a large share of a prize, depending on where you live.
• Lump sum versus annuity. The advertised jackpot is often the annuity total; the cash option is smaller.
• Sharing. Bigger jackpots tend to attract more ticket buyers, which raises the chance that you'd have to split the prize.

The odds of winning never change with jackpot size. A ticket is 1 in 292,201,338 whether the prize is modest or record-breaking.

Number myths

• Hot and cold numbers. Balls have no memory. A number drawn often recently is no more likely next time; that's the gambler's fallacy.
• Patterns look unlikely. 1-2-3-4-5-6 is exactly as likely as any other combination. It feels rarer only because random-looking sets are so much more numerous as a group.
• Lucky numbers and birthdays. They don't help you win. Because birthdays cap at 31, they may raise the chance that you'd share a jackpot with others who chose them.
• Wheeling systems. Covering more combinations raises your chance in exact proportion to the extra money spent. The edge per dollar doesn't move.

The bottom line

Keno and lotteries are honest about one thing: anyone can calculate the odds. Do the math and they're among the most expensive bets available, with keno edges commonly 25% to 30% or more and lotteries returning around half of what they take in.

If you buy a ticket, treat it as the price of a daydream, not an investment, and keep it to money you'd happily spend on entertainment. If lottery or keno spending is getting out of hand, start with our help resources.