Keno Balls

1. Superball Keno is my ultimate favorite keno game of all time. I don't know what it is about it.I think it's the bouncing ball on the final number on a line.
2. Mass Lottery To Go Games Return to full site. My Recent Tickets.
3. Keno ball is a highly popular gambling game, and it attracts lots of players because of how simple the game is. But unlike blackjack, slots, or roulette, the keno game moves at a slow pace. That means there’s more chance for you to win a progressive jackpot, while other players get the same opportunity. Keno is not a recent game.
4. Keno is a game of eighty numbers drawn at random from a lottery like tumbler machine. Almost every live casino offers Keno gambling to its patrons. The game is played via keno boards throughout the casino. A player marks a Keno ticket with a crayon and turns it in with his bet.

Keno / kiːnoʊ / is a lottery -like gambling game often played at modern casinos, and also offered as a game by some state lotteries. Players wager by choosing numbers ranging from 1.

The probability of n numbers drawn in the first 40, last 40, or any given 40 is combin(40,n)*combin(40,20-n)/combin(80,20). So the probability of exactly 10 in the first 40 (and 10 in the last 40) is combin(40,10)*combin(40,10)/combin(80,20) = 0.203243. The probability of one half having more than the other is 1-.203243= 0.796757. The probability of a specific half having more is half this number, or 0.398378. If this bet paid even money the house edge would be 20.32%. If the even bet paid 3 to 1 then the house edge on that bet would be 18.70%. If it paid 4 to 1 the player would have a 1.62% edge. About positive expectation blackjack online the more the player plays the greater the probability of a net profit. The best game is currently Unified Gaming’s single deck, with a player edge of 0.16%. If the player flat bet one millions hands the probability of being down would still be about 8.6%. At Boss Media’s single player game with a player edge of 0.07% the probability of a loss after a million hands is about 27.5%.

I doubt certain numbers are more likely than others. My advice is to pick anything, it doesn’t make any difference.

Your overall expected return is the same regardless of how many games you play. Of course it is more likely to hit a number the more machines you play, but if they all miss you lose more money.

'Anonymous' .

Pai gow poker is the least volatile and on average keno is the most.

In Nevada, and I think other major gambling markets in the United States, the balls truly are random and the outcome determined by the balls. However in class II slots, sometimes found in Indian casinos, anything goes.

HEADS - bet that eleven to twenty numbers in the top half appear - even money
TAILS - bet that zero to nine numbers in the top half appear - even money
EVENS - bet that exactly ten numbers in the top half appear - pays 3 to 1

The probability of the tie bet winning is combin(40,10)*combin(40,10)/combin(80,20) = 0.203243. Paying 3 to 1 the house edge is 18.703%. The probability of the heads (or tails) bet winning is (1-0.20343)/2 = 0.398378. Paying even money the house edge is 20.324%.

Compliments will get you everywhere. The number of combinations for n heads is combin(40,n)*combin(40,20-n). This is the number of ways to choose n numbers out of the top 40 and 20-n out of the bottom 40. The following table shows the probability of 0 to 20 heads.

Probability of 0 to 20 Heads

The probability of hitting all 20 is 1 in combin(80,20) = 3,535,316,142,212,180,000. So the odds are more like 3.5 quintillion to one. Assuming 5 billion people on earth, and they all played once a week, there would be one winner every 13.56 million years on average. Most casinos pay the same amount for hitting close to 20. For example the Las Vegas Hilton pays $20,000 for hitting 17 or more out of 20. I have never heard of anyone every hitting 20 out of 20, and doubt very much that it has ever happened.

I disagree. I can’t think of a single major Strip casino without a keno lounge. In general the only casinos without keno are the locals casinos in the suburbs of Vegas, because most of us locals know that keno is a sucker game.

P.S. A reader later wrote in to correct me, stating that the New York New York casino in Las Vegas removed their keno lounge.

I hope you’re happy, I spent all day on this. After writing and running a simulation I find that the probability that any 3 lines will contain 11 or more marks is 86.96%! That isn’t even giving the other side a fighting chance. You can go up to 12 marks and still have a probability of 53.68% of winning, or an advantage of 7.36%. However, I think you have the wrong side of the empty row bet. The probability of at least one empty row is only 33.39%, better to take the other side of no empty rows. While I was at this I did lots of other probabilities and put them in a new page of keno props. Here is a list from that page of these and other good even-money bets. The good side is listed.

Even Money Keno Props

Much like live keno the odds are the same regardless of what you pick, but they are independent of the balls the game draws.

That is actually a pretty hard problem. It is easy to get the probability of the number of times any of your four balls are drawn, including repeats. The tricky part is determining the probability that x distinct picks will be chosen, given that any pick was chosen y times. I indicate the answer and solution on my MathProblems.info page, problem 205.

1/2.

Keno Balls Generator

If we used keno as a comparison, everybody would have 40 genes, each represented by a keno ball. However, each ball would have unique number. When two people, who are not related, mate it is like combining 80 balls between the two of them into a hopper, and randomly choosing 40 genes for the offspring of the mating.

So when you were conceived, you got half the balls in the hopper, and the other half were wasted. When your brother or sister was conceived he/she got half from the balls drawn when you were born, and half that were not drawn. So you are 50% genetically identical. Much for the same reason that if 40 numbers were drawn in keno, two consecutive draws would average 20 balls in common.

This question was raised and discussed in the forum of my companion site Wizard of Vegas.

Romes

As a reminder to our other readers, Cleopatra Keno plays like conventional keno, except if the last ball drawn matches one of the player's picks AND results in a win, then the player will also win 12 free games with a 2x multiplier. Free games do not earn more free games.

You didn't specify the number of picks or pay table, so let's use the 3-10-56-180-1000 pick-8 pay table, as an example. First, let calculate the return.

The number of ways to catch x balls out of y in keno is the number of ways to pick x balls out of 20 and y-x out of 60. This equals combin(20,x)*combin(60,y-x), to put it in Excel terms. As a further reminder, combin(x,y) = x!/(y!*(x-y)!). Finally x! = 1*2*3*...*x.

With that review out of the way, here is the return table for that pay table. The right column shows the expected square of the win, which we'll need later.

Pick 8 Keno

Next, let's calculate the average bonus. We can see from the table above that the average win, not counting the bonus, is 0.593301. In the bonus, the player gets 12 doubled free spins. Thus, the expected win from the bonus is 2×12×0.593301 = 14.239212.

Next, let's calculate the probability of winning the bonus. If the player catches four numbers, the probability the 20th ball is one of those 4 is 4/20. In general, if the player catches c, then the probability that the 20th ball contributed to the win is c/20.

The formula for winning the bonus is prob(catch 4)*(4/20) + prob(catch 5)*(5/20) + prob(catch 6)*(6/20) + prob(catch 7)*(7/20) + prob(catch 8)*(8/20). We know the probability of any given win from the return table above. So, the probability of winning the bonus is:

0.081504*(4/20) + 0.018303*(5/20) + 0.002367*(6/20) + 0.000160*(7/20) + 0.000004*(8/20) = 0.021644.

With the probability of winning the bonus and the average bonus win, we can calculate the return from the bonus as 0.021644 × 14.239212 = 0.308198.

Not that we need to know, but the overall return for the game is the return from the base game plus the return from the bonus, which equals 0.593301 + 0.308198 = 0.901498.

Now, let's start getting into the actual variance. As a reminder, a general formula about variance is:

var(x + y) = var(x) + var(y) + 2*cov(x,y), where var stands for variance and cov stands for covariance. In this case of this game:

Total variance = var(base game) + var(bonus) + 2*cov(base game and bonus).

The fundamental formula for the variance is the E(x^2) - [E(x)]^2. In other words, the expected square of the win less the expected win squared.

That said, let's start with the variance of the base game. Remember when I said before when we would need that expected win squared from the first table. The lower right cell of that first table shows us the expected win squared is 19.530214. We already know the expected win is 0.593301. Thus, the variance of the base game is 19.530214 - 0.593301² = 19.178208.

Next, let's calculate the variance of the bonus (assuming it was already hit). For that, recall that:

var(ax) = a²x, where a is a constant.

Also recall that the variance of n random variables x is nx.

That said, if x is the base win in a bonus game, then the variance of the whole bonus is 2² × 12 × x. We know from above the variance of a single spin in the base game, not counting the bonus, equals 19.178208. So, the variance of the bonus, given a bonus was already hit, is 2² × 12 × 19.178208 = 920.554000.

However, what we need to know is the variance of the bonus before the first ball is drawn, including the possibility the bonus won't be won at all. No, we can't just multiply the variance of the bonus by the probability of winning it. Instead, recall that var(x) = E(x^2) - [E(x)]^2. Let's rearrange that to:

E(x^2) = var(x) + [E(x)]^2

We know the mean and variance of the bonus, so the expected win squared in the bonus is 920.554000 + 19.178208² = 1123.309169.

So, the expected square of the win from the bonus, before the first ball is drawn is the prob(bonus) × E(x^2) = 0.021644 × 1123.309169 = 24.313239.

We already calculated the expected win from the bonus, before the first ball, is 0.308198. So, the overall variance of the bonus, before the first ball, is 24.313239 - 0.308198² = 24.218253.

The next step is to calculate the covariance. 'Why is there a correlation between the base win and the bonus win?', you might ask. It's because the last ball drawn must contribute to a win to trigger the bonus. Given that the last ball contributed towards a win, the average win goes up. As a reminder, Bayes' formula of condition probability says:

P(A given B) = P(A and B)/P(B).

Let's then redo our return table for the base game, given that the last ball was a hit:

Free Red Ball Keno

Pick 8 Keno given Last Ball Hit

The bottom right cell shows that assuming the last ball was a hit, the average win is 6.757734.

Next, recall from your college statistics class that:

cov(x,y) = exp(xy) - exp(x)*exp(y) .

In our case, let x = base game win and y=bonus win. Let's work on exp(xy) first.

Exp(xy) = prob(bonus won)*(average base game win given bonus won)*average(bonus win) + prob(bonus not won)*(average base game win given bonus not won)*average(bonus win given bonus not won). It's easy to say that average(bonus win given bonus not won) = 0, so we can rewrite as:

Exp(xy) = prob(bonus won)*(average base game win given bonus won)*average(bonus win) =

We already solved for E(x) and E(y), so the covariance is:

cov(x,y) = exp(xy) - exp(x)*exp(y) = 2.082719 - 0.593301 × 0.308198 = 1.899865.

Let's go back to the overall equation for the variance when covariance is involved:

Total variance = var(base game) + var(bonus) + 2*cov(base game and bonus) = 19.178208 + 24.218253 + 2×1.899865 = 47.196191. The standard deviation is the square root of that, which is 6.869948.

So, there you go. That one took me hours, so I hope you're happy.

This question is asked and discussed in my forum at Wizard of Vegas.

Upon doing some research, I found this isn't a side bet, but what the pick-20 ticket pays for catching zero. The following is my complete analysis of the Station Casinos pick 20 ticket.

Station Casinos Pick 20 Keno

The lower right cell shows the overall return of the ticket is 69.70%, which is typical for live keno.

To answer the question about catching 0, the probability column shows the probability of that is 0.001186 and at a win of 200 for 1, it returns 23.71% towards the return.

Introduction

Note: The page addresses the conventional keno game, known as Spot Keno, where the player picks 1 to 20 numbers from 1 to 80 and the game draws 20 balls. There are links to keno variants towards the bottom of the page.

Keno is a simple game of luck, much like most lottery games, where the player chooses numbers and hope as many as possible match those randomly drawn by a hopper or machine. The simple form with no multipliers or extra balls is called Spot Keno and is addressed on this page. See the Internal Links section below for many keno variants.

There are two formats for playing keno: live and video. In live keno, the player uses a crayon and paper to indicate his picks. Every few minutes numbers will be a live draw from a hopper filled with numbered balls. In video keno, the player touches a screen, sometimes using a wand, to pick numbers and the machine does the draw randomly.

Like most games of pure luck, the odds in keno are pretty poor. Keep reading to learn more about the rules and how much you can expect to lose on the game.

Rules

Following are the rules for basic keno:

1. The player makes a wager and indicates which numbers he wishes to pick. The picks are made on a slip of paper in live keno and by touching the screen in video keno. The range of numbers the player may pick from is 1 to 80.
2. The number of picks the player may make depends on the game itself. Usually the range is 2 to 10 or 1 to 15.
3. The game will randomly choose 20 out of 80 balls.
4. If the game chooses a number the player chose that is known as a 'catch.' The player is paid according to the number of balls he catchs.

Examples

Following are some common video keno pay tables found mostly on Game Maker machines. The bottom row shows the expected return.

Pay Table 1

Pay Table 2

Pay Table 3

Pay Table 4

Pay Table 5

Pay Table 6

Pay Table 7

The following Pay Table 8 I saw on a 25¢ Aristocrat video poker game at Binion's Las Vegas on October 13, 2019.

Pay Table 8

Surveys

In 2001 I did a survey of every live keno casino game in Las Vegas. The returns ranged from 65% to 80%. In other words, the house edge was 20% to 35%, making live keno among the worst bets you can make in Las Vegas.

In 2012 I did a similar survey of live keno in Laughlin, which showed a range of return of 50% to 74%.

In 2008 I did a survey of video keno in San Diego. The returns ranged from 84% to 95%.

In 2017 I redid my Las Vegas video keno survey, which can be found at Wizard of Vegas.

Advice

If you must play keno, the only skill is choosing where to play to play and then how many numbers to choose. It makes no difference which numbers you choose. Contrary to popular myth, legitimate keno games, like those in Las Vegas, are fair and every ball has a 1 in 80 chance of being drawn each game. To determine the odds of any keno game you can use my keno calculator. Just put in the pay table and you will see how much you can expect to get back every bet.

However, I tend to think anybody who would take the trouble to analyze the game is probably not playing it in the first place. The odds in video keno are about as bad as slot machines. If you want to lose a lot less money gambling I would highly recommend converting to video poker. For live keno players, I would suggest converting to bingo.

Practice Game

Get your keno fix right here on my practice game.

Calculators

We have calculators to determine the payback for any pay table for the following keno games:

• Keno.
• Power Keno/Super Keno.
• Cleopatra Keno.
• Caveman Keno.
• Caveman Keno Plus.
• Triple Power Keno.
• Extra Draw.

Scouting Guide

When you're in the casino it would take a long time to put in every pay table through my many calculators above to determine the best game to play. That is why I created two printer-friendly guides you can print out and take with you:

• My Keno Scouting Guide is a short reference to the best available game for any pay table for all the most popular forms of keno. Each game has a table showing the possible pick-10 pay tables available and the best number of picks for that game and its return. See the last page of the guide for a full explanation how to use it.
• My Full Pay Table Report is a longer guide showing every known pay table for all the major keno games and their associated return. For those who want to know the return for any number of picks, not just the best number (which the Keno Scouting Guide provides).

For a printer-friendly document showing keno pay tables and returns for several major keno games please see my Keno Scouting Guide (PDF). Perfect for printing and taking to the casino to find the best game and pay table available.

Popular Keno Variants

• Caveman Keno.
• Triple Trouble Keno.
• Power Keno.
• Super Keno.
• Extra Draw Keno (three extra balls).
• Ultimate X Keno.
• Book of Keno.
• Alien Attack Keno.

Internal Links

• Las Vegas Hilton keno games.
• Atlantic City Tropicana keno.
• Jumbo Keno Progressive/Mega 10 — Progressive keno games found at Station Casinos of Las Vegas.
• Progressive keno games at the Boyd and Station casinos.
• Nevada numbers — a progressive lottery game.
• High/Low/Middle Keno — keno game seen at the Lisboa in Macau.
• Extra Draw Keno (two extra balls).
• Jumbo Keno Progressive — kenogame at the Station Casinos.
• Laughlin keno survey.
• Keno sums — Math behind the sum of all 20 balls drawn

Keno games by U1 Gaming

Following are keno games by U1 Gaming.

External Links

• German translation of this keno page.