A Keno "Ask the Wizard" question.

I have a question for the Wizard. I apologize in advance if this has been answered somewhere else, and if it has, please point me to that answer.

I've seen an electronic Keno game where if you pick 10 numbers and don't match any of them you get paid 1:1. You also get paid 1:1 if you match 4 out of the 10 numbers.

Since the payoff is the same I have to assume the probability of matching 4 or matching 0 must be the same, but how is this possible?

Quote: tsmith

I have a question for the Wizard. I apologize in advance if this has been answered somewhere else, and if it has, please point me to that answer.

I've seen an electronic Keno game where if you pick 10 numbers and don't match any of them you get paid 1:1. You also get paid 1:1 if you match 4 out of the 10 numbers.

Since the payoff is the same I have to assume the probability of matching 4 or matching 0 must be the same, but how is this possible?

You'll match 0 of 10 about 4.5% of the time.
You'll match 4 of 10 about 14.7% of the time.
A good resource for calculating the return of your favorite keno game is http://www.reviewpokerrooms.com/casino-games/keno/odds-calculator.html

Thank you for your answer and that link, miplet.

If it's less likely to match 0 than it is to match 4, and matching 0 is almost as likely as matching 5, I should think the payoff amounts should reflect that.

Gee, it couldn't be that this gambling machine isn't set up to pay true odds, could it? :)

Quote: tsmith

Gee, it couldn't be that this gambling machine isn't set up to pay true odds, could it? :)

No. And that's why the payoffs are the same even though the odds are significantly different.

In most games (all games?) where there are multiple ways to win on a single wager, the payoffs do not accurately reflect the odds. Sure, when the odds go up, so does the payoff, but not proportionally.

What they did was alter ALL of the payouts so they can afford to pay the 4 out of 10 something, while still having money left for the bigest prizes.


Take a look at a Video Poker machine. A typical Jacks or better paytable pays even money for a pair of Jacks, and 800 for a Royal. But the Royal is 8,500 times harder to hit.

It's the same thing.

Oh, okay. That makes sense.

tsmith- the casino will set rules/payoffs to maximize their profits. They balance how much of a house edge they can build into a game while still having people willing to play. The 'pay for 0 out of 10' concept may increase player participation, as many will 'remember the time' when I couldn't get a number....

Quote: tsmith

Thank you for your answer and that link, miplet.

If it's less likely to match 0 than it is to match 4, and matching 0 is almost as likely as matching 5, I should think the payoff amounts should reflect that.

Gee, it couldn't be that this gambling machine isn't set up to pay true odds, could it? :)

Payoffs CANNOT match the individual odds against possible occurences, otherwise the game couldn't exist---in a game where any of those occurences is possible.

Consider a game where a number is drawn, between 1 and 10. You get payoffs based on which number is drawn. Now, the odds against any given number being drawn are 9 to 1, but how long do you think the game would last if you got paid 9 to 1, no matter which number was drawn?

Right, that's only for win/loss propositions. Slot games, keno, VP, most side bets - they have multiple winning outcomes. Anything where there are multiple winning outcomes requires multiple winning amounts. If there's an edge, none of them can be the true-odds payouts.

For what its worth, usually the pays in a paytable are inversely correlated to the frequency of winning. But not always (as this keno example demonstrates). Moreover, sometimes pays are based more on perception than actual odds. For example, the standard poker hierarchy changes as you move from 5 cards to 3 cards. But lots of people don't know that, and I've seen paytables for 3-card variants which still pay flushes higher than straights even though they're easier to achieve.