Gaming Gurus: Strategy Expert Article Archive - Page 838

Here's something different you can do for VALENTINE'S DAY

Here's something different you can do for VALENTINE'S DAY ... get married at GOLD STRIKE CASINO RESORT. The casino is running a special Valentine's weekend special and that will let you and your significant other say "I DO" in their Golden Hearts Chapel...read more

Best-Case Money Management Scenario - Part 1

Last time I mentioned that we talk about money management in losing situations more frequently than in winning situations because the house edge against us makes it more likely that we'll be behind than ahead. This time let's look at some money management ideas for when we're ahead. As I've said before, money management to me has two goals: to ensure that your bankroll lasts as long as your visit and to make your visit more fun by removing some of the stress involved in dealing with money...read more

Online Casino Job Posting Resources

In recent years new legislation has opened the door for thousands of new jobs within the casino gaming industry, including everything from dealers and cashiers to waiters and security personnel. In addition the casino industry provides a large number of employment opportunities for individuals with many years of business, regulatory or community experience...read more

Slot Machines Worth Their Weight in Gold

Slot machines have had a profound impact on the value of horse racing properties nationwide. One industry insider told me: “It is remarkable to me that within the last three years, Gulfstream Park, Santa Anita and Hollywood Park (three of America’s most prestigious thoroughbred tracks) have all sold...read more

New Slots from IGT

It was the last day of the Global Gaming Expo in Las Vegas, and I was taking advantage of the thinning crowds to get a good look at new games in the IGT booth. IGT is the world's largest manufacturer of slot machines, always has the biggest, most varied collection at the fall gaming industry show and also draws crowds so big that I can't always get near the games on the first couple of days. At the booth, I spotted a familiar face...read more

The Enduring Effect of Match Play Coupons on House Edge

"Match play" coupons are common casino promotional incentives. The idea is to combine chips and coupons of equal face value into a bet worth twice the real money actually set out. Losing costs both the chips and coupons. Winning pays according to the total of the two parts, returning the chip portion but not the coupons. Monetarily, a coupon is worth somewhat under half its denominated value...read more

Hell's Kitchen

Dear Mark,Hell broke out at our kitchen table poker game last Friday night. Quite an argument ignited over the following hand in pai gow poker. Does the five card straight of 9-10-J-Q-K beat an A-2-3-4-5 straight? Scooter T...read more

Popular Fallacies That Aren't - Part 2

Some notions gamblers have about gambling are both common and completely misguided. These ideas often have a basis in truth, however, though the connection between the idea and the reality is often tenuous. Lets look at idea of quitting while ahead. The reasoning is: You are certain to be ahead at some point during a session...read more

City Picks, Euler, and the Ditsy Coat Check Girl

One of the interesting things about doing gaming analysis is that every now and then I discover a clever piece of mathematics that is just the thing I need to complete a job.  Unfortunately, I don't always discover the mathematics I need.  A year or so ago I was asked to look at a video game that was based on both geometry and Poker hands.  Try as I did, I just couldn't see a way to analyze the game nor did I recall any mathematics that I felt would help me out.  To this day I'm baffled by this game and occasionally I go back and take another look at it -- frustrating.  Happily, this doesn't happen that often, usually things work out.  Here is just such a story.    I am writing a book about state lotteries which should be published sometime this spring.  The title is The Lottery Book, The Truth Behind the Numbers and it is being published by Bonus Books of Chicago.  The Foreword to the book is by Frank Scoblete.  In it I analyze just about every state lottery game in the country and explain to the reader just how such analyses are carried out.  As you might imagine, I ran into some unusual games whose analyses required some serious thought.  To my mind, the most notable of these was provided by the state of Wisconsin.    Wisconsin has a lottery game called City Picks.  Here is how it is played.  The player is provided with nine Wisconsin cities: Chippewa Falls, Dodgeville, Green Bay, Kenosha, Madison, Milwaukee, Superior, Two Rivers, and Wisconsin Rapids.  To play City Picks the bettor simply arranges these nine cities in order 1 through 9.  The Wisconsin State Lottery then randomly arranges these same cities in a different order, again 1 through 9.  The player is paid according to how many of his numbered choices match the lottery's numbered choices.  Since I cover the game in detail in my book, I'm not going to repeat the complete analysis here.  Suffice it to say, however, that in order to carry out such an analysis one must determine how many of the 9! or 362,880 permutations of these cities occur as no matches, one match, two matches, and so on.  Let me show you an example.    Suppose for a given lottery ordering we want to determine how many ways we can produce an ordering of ours that has exactly 5 matches.  Well, we first have to choose which 5 of the 9 numbers will be our matches.  This is old stuff to us by now; it is just the number of way of picking 5 things from a set of 9 and is the number 9!/(4!5!) or 126.  Now for each such choice the remaining 4 numbers have to not match those of the same remaining 4 lottery choices.  In mathematical jargon, they have to be a derangement of the lottery's choices.  Let's take a closer look at this.    Consider the integers 1 2 3 4 in that order.  How many ways can we rearrange these numbers so that there are no matches in the rearrangement?  For a small number like 4 this is relatively easy, we can just list them.  The derangements are:                    2 3 4 1                3 4 2 1                2 1 4 3                    2 4 1 3                4 1 2 3                3 1 4 2                    3 4 1 2                4 3 1 2                4 3 2 1 There are 9 of them.  Thus the number of ways of getting exactly 5 matches in the City Picks game is 126 x 9 or 1,134.        For larger numbers it is not feasible to list all of the derangements.  For example, if we consider the derangements of 1 2 3 4 5 6, there are 265 of them and these derangements increase rapidly as the number of integers increases.  So, in general,  how do we determine derangements?  The answer goes all the way back to the Swiss mathematician Leonhard Euler (1707 - 1783).  Euler gave a simple recursion relation for generating the number of derangements.  Here's how it works.    Let dn denote the number of derangements of the integers 1, 2, 3, ..., n.  Clearly if n = 1 then d1 = 0.  If n = 2 then the only derangement of 1 2  is 2 1 so d2= 1.  Euler's recursion relation is dn = (n - 1)(dn - 1 +  dn - 2) (1) If we let n = 3 in (1) then we have d3 =  (3 - 1)(d2 +  d 1) = 2(1 + 0) = 2 (2) Since we now have d3and d2we can let n = 4 in (1) and obtain d4 =  (4 - 1)(d3 +  d 2) = 3(2 + 1) = 9 (3) which, as we saw in our example, is exactly right.  One can continue with this "bootstrap" operation as long as one wants.  I won't prove to you that (1) is correct, but you can contact me by email (just click on Technigame at the end of this article) if you would like to see a proof.    By doing a bit of algebra using (1) and recalling some calculus, one can show that the expression dn / n! gets arbitrarily close to the number 1/e as n gets large, e being the ubiquitous base of the natural logarithms...read more

Paradise Is a Pretty Nice Place

I’ve been to Paradise recently, and I have to say that Paradise is a pretty nice place. Wondering how to find this Paradise? Look no further than the Atlantis Casino Resort in Reno. I decided to drop in the other evening before dinner (mistake) and decided to hang out for a bit up in the Skywalk, between the Pillars of Hercules, where there is a wonderfully elegant Oyster Bar, with displays of oysters and King Crab legs that get that old saliva flowing...read more