Keno Basics

I was asked to write a column about Keno. I’m familiar with the game and the math of the game. What I didn’t have handy were current paytables. So, I went to three local casinos – Red Rock, Suncoast and Rampart. It turns out that only Red Rock plays live Keno. I remember the days when I would come here in the late 1980’s and you would sit at the buffet, the Keno runners would come into take your sheets and money and then you would watch the numbers be drawn on the boards that hung in multiple places. Ironically, you didn’t know which games you were actually playing because there was a delay between when you handed the numbers to the runner and when she put them in. It was not a high-tech era relative to today.

Keno has diminished greatly in popularity through the decades. Fortunately, the rise of video machines has allowed Players who want to partake in this game a chance to do so. Many of the multi-game slot/video poker machines also have Keno options. Also fortunate for the Player is that the video Keno versions tend to have higher paybacks than live Keno. This is for two significant reasons. The first is that the overhead on video Keno is much lower and the second is that you can play far more Keno hands on a video Keno machine, so the casino can make the same (or higher) profits because the amount wagered per hour is much higher.

Unfortunately for the Player, the paybacks on any type of Keno is pretty low relative to most other games in the casino. The paybacks are likely to be rather comparable to slots with one noticeable difference. You can at least calculate the payback of Keno with absolute certainty once you know paytable. The probability of hitting any combination is a known quantity. So, we just multiply the payout of each winning combination by the probability of that combination and sum up these values arrive at our payback.

I’m limited in space here to describe the way the probabilities are calculated. In short, the math is sort of done backwards. Keno involves the game picking 20 out of 80 possible numbers. The Player may select two or more numbers that will be picked from that 20. He is paid if at least a minimum number of his numbers are picked out of the 20. There are a few variations in which the Player is paid for picking very few or a large number of numbers, but loses if it is in the middle. The math is still the same. I use combinatorial math to calculate the probability that 4 out of the Player’s five numbers will be in the 20 numbers picked while 1 is in the numbers not picked. This is repeated for 5 out of 5 and 3 out of 5 – which are the usual paying combination for picking five numbers.

The table below has the probabilities for picking x out of 5 numbers:

Numbers Probability

5 0.0645%

4 1.2092%

3 8.3935%

I found a variety of paytables at live Keno just at the Red Rock. One paytable paid 750, 10 and 1. Following the formulate I stated earlier, this provides a payback of 68.85 percent. Yes, you read that right. The paytable for video Keno was 810, 12 and 3 which gives the Player a 91.93 percent payback. It can’t compare to even the worst video poker machines, but at least it competes with the slot machines. If you are wondering, the probability of hitting 10 out of 10 is 0.0000112 percent or 1 in 8.9+ million. So, getting paid $50,000 for this doesn’t add much to the overall contribution.

For those who are interested, I have a Keno sheet that lists out all the probabilities for picking up to 15 numbers. You just need to plug in the payouts and do some multiplication and addition to get the payback of whatever paytable/number of pick combinations that interests you. Head on over to the Catalog page if you would like to order one of these sheets. If you do order one, you are free to make as many copies as you would like for your own personal use.

The Sum of Its Parts

The Sum of Its Parts

The purpose of the last several columns has been to show that math drives everything in the casino. While the casinos have a macro approach, the Player has a more micro approach, generally looking at things in shorter sessions. Also, the Player doesn’t really care how any other Player does, only himself. When you are looking at it this way, it all begins with each hand. In the end, the total experience is nothing more than the sum of its parts.

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National Video Poker Day

National Video Poker Day

Back in March, I wrote about National Blackjack Day.  March 2 was selected for this day because it is written as 3/2 and an major push for this day was to get casinos to go back to paying 3 to 2 on blackjacks.  When I did a little bit of research on that day, I found that there is no organization that officially assigns ‘National’ anything day.  Essentially, anyone can pick any day to be anything they want.  There may be significance regarding which day is picked as in National Blackjack Day or with May 4th being Star Wars day.  In some cases, it might be more random like ‘Talk Like a Pirate Day’.

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Not My House

Have you ever been tempted to throw away a Full House and go for the Four of a Kind? In a Jacks or Better machine this is essentially a suicidal move. The Full House is obviously worth the full 9 EV. The Trips is worth only 4.3. Further, it is not like the Quads will pay some significant amount of money. Quads paying only 25 doesn’t seem like enough of a payday to even contemplate giving up that Full House.

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The Timeless Razgu

           By now, hopefully we all know that once something is posted on the internet, it never disappears completely.  Nonetheless, it was quite a shock when I received an e-mail this past week from a reader who came across a column I wrote in 2004!  I knew the site still existed, but I'm still amazed that a column I wrote nearly 13 years ago can so easily be referenced.  You'd think that they might archive the articles or during some redesign of the site would remove the older articles.  I guess the good news is that more than a decade later, the column is still as relevant today.

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Never Surrender

            This week's column is again in response to an e-mail I received this past week.  It's good to see that after nearly 15 years of writing for Gaming Today that my readers finally seem comfortable to shoot me an e-mail!  This one asked how come I never talk about Surrender in blackjack.  I gave it some thought and realized that I don't think I have written a single word about the Surrender option in blackjack through those 15 years!  As I thought about it some more, I'm not sure I've talked about Insurance either.  So, this week, I'm going to talk about both.

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Pocket Hand Win Frequency

Pocket Hand Win Frequency

            The inspiration for this week's column comes from a reader this week who e-mailed me and had a question regarding a column I recently wrote about Ultimate Texas Hold'em.   In that column I was describing a hand I saw actually played at the Wynn a while back.  The Player was dealt a K-8 offsuit and did NOT wager 4x at that point, instead opting to wait for the Flop.  I had said that this hand was a marginal 4x wager and that the Player could expect to win the hand 54%, while losing it 42+% of the time. 

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Math vs. ESP

            You're playing blackjack and you're dealt a 16 looking into a Dealer 7.  What do you do and why?  I've watched a lot of Player with this hand and it is almost fun watching them.  Sure, there are some blackjack counters who spend a few seconds thinking about it, thinking about the count and working out what to do in this situation.  Then there are the good Player who aren't really counting but trying to figure out what is left in the shoe - big or small cards?  Next up are the Players who haven't been paying attention to the shoe but are trying to do some form of math to figure out the probability that they will bust (8 out of 13!) and if they are better off hoping the Dealer will bust.  Last, but not least, we have the majority of Players who are simply trying to 'guess' what the next card will be using more ESP than math.

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Not All Props Are Created Equal

Not All Props Are Created Equal

As I write this column, the world is getting all excited about the Big Game, this Sunday.  Oodles of money will be wagered on the game.  Here in Vegas, most of it will be legally wagered!  Some of the people might have a clue what they are wagering on.  For those that remember last year's column at this time, I had the pleasure of watching a man plunk hundreds of dollars on the game and then ask the man behind the betting desk what the +110 and +3 meant!  Nothing like betting first and then figuring out what you actually wagered on.

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Running Hot and Cold

            Through the years, a number of betting schemes have been created that are supposed to increase the chances of winning by the Player.  To the best of my knowledge not a single one of them has ever been shown to actually work.  I'm sure I could spend my time giving a detailed math proof as to why not, but there is actually simpler methods to use to prove it doesn't work.  The first is the most obvious one - no casino will stop you from trying to use one. 

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Video Poker Beginnings

Video Poker Beginnings

            This past week, with my son in town, I found myself sitting at a blackjack table.  When I was in my 20's that is what I played when I went in to the casino.  It had a good payback (99%+) and it required a fair amount of skill in the form of strategy to earn this payback.  When video poker came along, I slowly found myself playing more of that and less blackjack.  Nowadays, I almost never sit at the blackjack table except when my son is in town and drags me over.  My experience this past week only reinforced why this is so. 

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            I never know if my explanation of how an expected value is calculated is really being understood by my readers.  It seems obvious enough to me, but I've been working on casino games for nearly 30 years.  In my writings, I've generally tried to explain by using an example which I think explains it clearly enough.  I usually use one of a couple of examples that my father originally used in his Expert Video Poker for Las Vegas book.  This book starts by using a Three of a Kind and follows up with a 4-Card Straight that is also a Low Pair.   

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The Magic of Video Poker

            A few months ago, I volunteered at my son's school at their book fair.  During slow periods, the parents shoot the breeze while getting to know one another.  My job is relatively unique, so it tends to get a lot of attention.  This inevitably leads to me telling the story about how my dad got started analyzing casino games.  It started one day when he walked into a casino and saw a video poker machine.  This was the late 1980's (maybe early 1990's?).  A short time later he walked into a different casino and saw a similar video poker machine.  The two machines advertised very different paybacks.  My dad didn't understand how two machines with identical paytables could have different paybacks.

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Don't Deviate!

Don't Deviate!

            This past week, I ventured over to Red Rock Station and had what was possibly the worst video poker session I have had in years.  I was playing Double Double Bonus on a Multi-Strike machine and I just had no luck from beginning to end.   To win at Double Double, you have to get the Bonus Quads.  To win at Multi-Strike, you need your Four of a Kinds to appear at the higher levels.  Well, I certainly didn't get many of the Bonus Four of a Kinds and what little I got in Quads were at the bottom two levels for the most part.

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Don't Be a Turkey!

Don't Be a Turkey!

By the time you read this, Black Friday will be done.  Cyber Monday will be done.  Never mind that neither is quite what they once were.  I picked up some Black Friday items the Monday before Black Friday.  It’s only Thursday as I write this and my son and I have been going back and forth about some on-line sales.  The point of this column is NOT about how the retailers have completely destroyed their own marketing tool.  It is about how everyone gets so hyped up to save a few bucks even if it means getting up at 3 a.m. or leaving the Thanksgiving table to go wait on line for a few hours.

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          Successful game inventors know that they cannot fall in love with their game idea.  Just because you like it, doesn't mean everyone else (or anyone else) will.  Of course, one of the issues with this is that even if you are willing to be flexible, you generally don't get endless chances.  Some have suggested that you get only one, maybe two changes at tinkering with your game before you're likely going to have to abandon it.  This applies to a game that has been placed in a casino and not necessarily one in the process of being showcased.

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How to Beat the Casinos?

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