New Casino Bonus

Automated Roulette Winning System

2009-06-08T05:43:00.000-07:00

There is a new winning system in the commercial Roulette Software game, and in this review, you are going to learn all about it. The new AUTOMATED software is called Roulette Assault, and it has become worthy of this review because of its stunning new features that no other roulette software can compare to.

Over the last few months, I have seen several new roulette software products crop up in to the scene. The newest feature that most of them are boasting is automation. The software basically does all the work for you, no mouse required. In this case, that is a good thing, but it doesn't really make the software any more unique than the traditional manual method of playing, simply because these other products don't offer anything unique about the actual strategies they implement.

The developers at Roulette Assault stepped up and not only created a completely automated roulette betting robot, but it looks like they did things a little differently as well.

The biggest difference that I noticed about the Roulette Assault software is that it doesn't utilize the sleeper system like the vast majority of its competitors. This system waits for several "misses" of a section of the roulette board, and then starts placing bets using a progression. Although Roulette Assault offers the sleeper system as one of the systems the player can use, it also has 3 additional systems the player can implement, such as the Six Point Divisor system, the Double Dozens system, and the Progressive Singles system.

When it comes to using a roulette system, there should be a way to test it without having to place a single dime on the roulette table. Roulette Assault has a feature called "foreplay mode" that does this. You can set the robot up to spin the roulette wheel and collect numbers and play them against a fictitious game. In other words, it plays the game inside itself while keeping track of the balance and settings you have set.

Roulette Assault can also store the previous numbers using the History feature. Recording the history will save the player a lot of time because it can take several hours to record 30,000 or more "real money" spins to test a system. The best part is that when you are satisfied with the number of spins you have recorded, you can then tweak whatever system and settings you want to use and run it against the analyzer. The analyzer is another great feature.

Although there are several more features that Roulette Assault offers, I will not go over them here because they are very "nice-to-have", but are explained in great detail on the Roulette Assault website, and also on my review website. The above mentioned features are totally unique to Roulette Assault, and the rest are common amongst various commercial roulette systems.

Click Here for Roulette Assault

Hollywood Poker Bonus

2009-06-04T07:59:00.000-07:00

With Hollywood Poker you can get up to 1000% BONUS (calculated at your deposit).

The maximum amount paid for bonus is $5000, so if you deposit $500 you will get $5000 as a bonus.

Play Poker With The Stars
HollywoodPoker lets you go all-in with your favorite celebrities.

Private Holding Investment

2009-04-02T12:51:00.000-07:00

Genius Funds is a program that continues to pay me every time.

I joined new interesting HYIP. It’s called Private Holding Investment and it looks like a long term program.

I deposited $50 in Private Holding Investment. They offers 1.6% - 3.5% Daily For 40 Days and the minimum deposit is just $5. For more information you can call them at the phone number from their website 520-461-9418.

Invest Online Or Play Online Lottery

2009-03-25T05:34:00.000-07:00

Here are some High Yield Investing Programs that paid me a lot of profits: Private Holding Investment and Genius Funds.

You can make lot of profits by playing online lottery with Virtual World Direct for three online lotteries: UK Lotto, Euro Millions and Spanish Lottery.The best feature is that you can play UK Lotto and Euro Millions in a syndicate, increasing your chances of success by almost 1000%I play Euro Millions Lottery from 2007 and I recommend it to you because they are very serious in paying your earnings.Personally I used Moneybookers to play the e-Lottery. For more information please read e-Lottery Review.

If you want to trade forex using Moneybookers or E-bullion then BetOnMarkets is your best choice to make big profits investing in ForEx Market.BetOnMarkets offers fixed odds financial bets; i.e. financial bets that pay a fixed amount (or nothing) on expiry. In other words, when you buy a fixed-odds bet from BetOnMarkets, you are entitled to receive a payout, which is a fixed multiple of the amount you have staked. With the BetOnMarkets dealing system a client expresses a view and makes a prediction. If the prediction comes true, the client will profit by a predetermined amount. Before any bet is placed, the client knows the entire possible downside as well as the exact possible profit.However, with most bets, you are also able to sell your bet before the final settlement date to mitigate your losses or take your profits out early. This means that your risk level is clearly defined at all times.Bet sensibly and familiarize yourself with the risks of fixed odds financial betting. The maximum loss is always limited to the premium (i.e. stake) but losses are still possible. Always remember to play only with money THAT YOU CAN AFFORD TO LOSE.In my first day of betting on forex using BetOnMarkets I made a 100% pure profit in my first day, of course I had losses too but I am in profit at the end of the month.

Money Making

2008-09-05T15:34:00.000-07:00

Make money working from home online and you can make big profits from affiliate marketing and I recommend you FREE Money Maker for learning all the inside secrets.

First you must know that FREE Money Maker advertising methods has nothing to do with any of the following:

- Co-Registration
- Blackhat seo
- Banners
- FFAs
- Email Marketing
- Cloaking
- Pay Per Click
- Any Type Of Page Generation Software
- MLM
- Safelists
- Traffic Exchanges
- writing articles
- press releases
- reciprocal linking
- creating blogs

GET Your FREE Money maker

Hollywood Poker Review

2008-07-06T02:15:00.000-07:00

Hollywood Poker Presents…

Big names, big money, big events – it’s all part of the Hollywood Poker experience. Since its triumphant launch in November 2004, Hollywood Poker has fast gained a reputation for dealing its players with a winning spread of star-appeal, spectacular events, fabulous promotions and a friendly and supportive community.

Features

Celebrity Events

Hollywood Poker is best known for these highly popular weekly Celebrity tournaments:

• Michael Woods Celebrity Invitational

• Hollywood Poker Celebrity Classic

• Canadian Poker Night

These star-studded tourney’s give players the chance to collect Celebrity Bounties for up to $2,000 while they pit their skills against Hollywood Poker’s host of Celebrity Players, like James Woods, Vince Van Patten, Mimi Rogers, Donnie Wahlberg, Mena Suvari and Jason Alexander.

Featured Tournaments

We also host an amazing spread of regular featured events, like the ever-popular Easy Money, **Bonner Avenue Sit ‘n’ Go and Grand Prix tournaments. Our events range from low to mid to high stakes, so there’s bound to be a perfect fit for every type of player.

Promotions

Our VIP Program, clubHOLLYWOODpoker, rewards all styles and stakes of players by dealing out $6K in monthly freerolls. For new users, becoming a member is as easy as real money activating your account, hitting the tables and racking up Poker Points. Your monthly Poker Point accumulation determines whether you are a Bronze, Silver, Gold, Platinum or Titanium Club Member. The value of the freeroll you qualify for corresponds to your clubHOLLYWOODpoker status and they’re all guaranteed to give you a shot at some easy money.

Invite-A-Friend

Hollywood Poker extends the star-treatment by offering players access to exclusive promotions, like the lucrative Invite-A-Friend program. When players successfully tell their pals about the site using this feature, they’ll split a nice slice of cold hard cash with their friends. The more people you invite, the more you win – it’s that simple.

Bonuses

A spread of exclusive deposit bonuses up to $1,500 makes sure that playing with the big names doesn’t have to cost you big bucks. It doesn’t matter what level or style of player you are: Hollywood Poker’s got a bonus to suit any player. Our bonuses are headlined by a choice of THREE Celebrity Tournament Packages, which deal out incentives like free Celebrity Tournament tickets.

Customer Service

The tournaments, promotions and bonuses are only a few of the many features that have made Hollywood Poker A-list among online poker sites. Hollywood Poker also offers unparalleled customer support, 24 hours a day, 7 days a week.

Hollywood Poker Community

Support doesn’t only come from the Hollywood Poker staff. The vibrant and friendly online community is a constant source of support and encouragement. Whether it’s cheering fellow players on at the tables, exchanging advice and ideas in the forums or chatting in the lobby, the players embody the fun, flare and fabulous experience anyone will experience at Hollywood Poker.

FOREX

2008-06-16T04:48:00.000-07:00

If you need a serious and professional Forex Broker then Forex Yard is the one for you.

The Forex Yard is a great platform to start with investment for a beginner or an expert. The minimum deposit for Forex yard is as low as $100; the pip spread value is as low as 4-5. Forex Yard is a reliable and competitive agent that does provide with user friendly trading software that can be exclusively used for Forex.
Forex Yard provides with a reasonably good leverage, low pip spreads, explicit client support, and user friendly software. The highlight of Forex Yard is the loss protection feature.
With regards to the account package Forex Yard does offer need appropriate solutions:
They offer a free practice account for the beginner. Regular $100 investors will benefit from the mini account. Experienced investors that are working with Forex Yard with receive a pro account package. The deposit options for Forex Yard is pretty liberal in that you can invest even with your credit card or online Paypal account. In addition to all this, the investor gets a guaranteed fixed spread, which makes the deal pretty much reliable.
The flexibility in deposits, the account packages, and the guaranteed spread limits offered to the investors is the major reason for the current growth of Forex Yard. The most attractive marketing strategy of Forex Yard is that they also operate on a negative balance security.
In cases where you are going to have your funds run to a bare minimum, then all your investments and trades will be closed mechanically. This option limits your risk process by not letting you to risk more than the balance you have in your account. Even if you lose, you will be losing within your existing balance limit and not beyond. Forex Yard review given by the existing users has marked it as one of their best Forex agents. Most of the Forex Yard Review highlights the point that the pips and spreads are pretty competitive and the 200:1 leverage is also pretty generous.
Top rated Forex Yard review from most users has the recommendation for fresh investors to sign up for the demo account and work with it until they are comfortable with the process. The next famous Forex Yard review from most users has the opinion that the users should subscribe to the news reviews and signal information and get used to making their decisions based on it and then slowly they have to graduate to pro accounts, because demo account is not the place where one can make money.

Our Forex Yard Findings:
The first thing that we discovered about this platform is the fact that it is not only user friendly for those who are just starting out trading in Forex, it is also excellent for those who are already doing it and have been doing so for quite some time.
As a matter of fact, it had all the tutorials that were needed in order for us to walk step-by-step through the entire process of trading and in our independent testing, we were able to do so successfully.
It is also a platform that will grow with you nicely, especially considering the fact that it has some advanced tools that will keep you working, long after you have left the beginner stage.
Getting Started with Forex Yard
Getting started with Forex Yard is also an easy thing, especially with the number of different ways that you have of making your initial deposit. Not only that, the initial deposit requirement is rather small and you can start out with a test account in order to make sure that everything is working well for you. This is one of the criteria that we always look for whenever we are testing out a new platform, the fact that it allows a person to test whether they are going to be successful with it or not. It’s a good idea for you to make sure these things before you put your hard-earned money on the line.
For those of you that are impatient and would like to get started right away, you can begin trading immediately upon making your deposit. Of course, if you use a bank check you’re going to need to wait for the check to clear but as long as you are using a credit card to fund your account, those funds will be immediately available. Since they also have a bank wire option available, many people find it convenient to use this in order to fund their account on a regular basis.
Forex Yard - Excellent Customer Service
One of our favorite things about our account at Forex Yard is the fact that the customer service really seems to be on the ball. Since trading in Forex is a 24 hour a day possibility, you don’t want to be left out in the middle of the night because of limited support hours.
They are available via e-mail, online chat and you can even pick up the phone and talk to somebody if necessary.
Whenever you are making your choice for which platform you are going to use to trade on the Forex market, we suggest you take a long, hard look at Forex Yard.
They are one of our platforms of choice and one of the highest rated platforms
on our website.

Make Money Online MLM

2008-02-27T14:23:00.001-08:00

You can play e-lottery in a syndicate, this way your chances to win increase with 1600%, click here for more information.

I recently joined a new MLM program called Rolution.
Usually these kind of programs reach about one million members and Rolutions has only 35 thousands members and started only a couple of months ago so it is a great money making opportunity.

My next post will be about maybe the best money maker in the world but for now I will Recommend you Rolution, a program that for only $12 / month can make you rich.

There are several ways to earn money with Rolution plan. It’s is an excellent opportunity to maximize your revenues and leave you free to enjoy life at you own pace. By subscribing, you get a position in a three by eight matrix and your goal is to fill the vacant positions around you.

Inside Yuwie

2007-11-30T01:26:00.001-08:00

Ok, I decided to show you a small preview about inside of Yuwie member's area :)

As you see, this is a small box that you will find in member's area after you will join Yuwie, but it is one of the most important info box because gives you information about your views and your referral views, and that is MONEY on Yuwie.

Fortunate Way

2007-10-29T11:51:00.001-07:00

I want to recommend you the new money blog Fortunate Way.

You can find some interesting articles there, like: Basic Concept Of Forex, Why Invest Offshore or about how to Make money With eBay.

Yuwie Money

2007-10-11T07:42:00.000-07:00

So, my first earnings were credited to my Yuwie account.From what I see, you can earn about $0.50 per referral with Yuwie.That is great because you can earn that commission monthly, for example if you have 100 referrals you can earn $50 each month without doing nothing. And more, you can earn referral commissions on 10 LEVELS , meaning that you refer JUST 2 friends that refer 2 friends you could have over one thousands referrals after one month meaning $500 or more profits for you each month without doing nothing, just joining Yuwie for FREE!
You can read more About Yuwie or how can you make money from Yuwie or with Yuwie Affiliates on Yuwie Wealth Blog.

Casino Math Guide

2007-09-20T22:28:00.000-07:00

Casino Math Guide

UNLV Gaming Studies Research Center 1

A Guide to Casino Mathematics

Robert C. Hannum

University of Denver

This guide contains a brief, non-technical discussion of the basic mathematics

governing casino games and shows how casinos make money from these

games. The article addresses a variety of topics, including house advantage,

confusion about win rates, game volatility, player value and comp policies, casino

pricing mistakes, and regulatory issues. Statistical advantages associated with

the major games are also provided.

Introduction

At its core the business of casino gaming is pretty simple. Casinos make money on their games

because of the mathematics behind the games. As Nico Zographos, dealer-extraordinaire for

the ‘Greek Syndicate’ in Deauville, Cannes, and Monte Carlo in the 1920s observed about

casino gaming: “There is no such thing as luck. It is all mathematics.”

With a few notable exceptions, the house always wins – in the long run – because of the

mathematical advantage the casino enjoys over the player. That is what Mario Puzo was

referring to in his famous novel Fools Die when his fictional casino boss character, Gronevelt,

commented: “Percentages never lie. We built all these hotels on percentages. We stay rich on

the percentage. You can lose faith in everything, religion and God, women and love, good and

evil, war and peace. You name it. But the percentage will always stand fast.”

Puzo is, of course, right on the money about casino gaming. Without the “edge,” casinos would

not exist. With this edge, and because of a famous mathematical result called the law of large

numbers, a casino is guaranteed to win in the long run.

Why is Mathematics Important?

Critics of the gaming industry have long accused it of creating the name “gaming” and using this

as more politically correct than calling itself the “gambling industry.” The term “gaming,”

however, has been around for centuries and more accurately describes the operators’ view of

the industry because most often casino operators are not gambling. Instead, they rely on

mathematical principles to assure that their establishment generates positive gross gaming

revenues. The operator, however, must assure the gaming revenues are sufficient to cover

deductions like bad debts, expenses, employees, taxes and interest.

Despite the obvious, many casino professionals limit their advancements by failing to

understand the basic mathematics of the games and their relationships to casino profitability.

One casino owner would often test his pit bosses by asking how a casino could make money on

blackjack if the outcome is determined simply by whether the player or the dealer came closest

to 21. The answer, typically, was because the casino maintained “a house advantage.” This was

fair enough, but many could not identify the amount of that advantage or what aspect of the

game created the advantage. Given that products offered by casinos are games, managers

must understand why the games provide the expected revenues. In the gaming industry,

nothing plays a more important role than mathematics.

Casino Math Guide

UNLV Gaming Studies Research Center 2

Mathematics should also overcome the dangers of superstitions. An owner of a major Las

Vegas strip casino once experienced a streak of losing substantial amounts of money to a few

“high rollers.” He did not attribute this losing streak to normal volatility in the games, but to bad

luck. His solution was simple. He spent the evening spreading salt throughout the casino to

ward off the bad spirits. Before attributing this example to the idiosyncrasies of one owner, his

are atypical only in their extreme. Superstition has long been a part of gambling – from both

sides of the table. Superstitions can lead to irrational decisions that may hurt casino profits. For

example, believing that a particular dealer is unlucky against a particular (winning) player may

lead to a decision to change dealers. As many, if not most, players are superstitious. At best, he

may resent that the casino is trying to change his luck. At worst, the player may feel the new

dealer is skilled in methods to “cool” the game. Perhaps he is even familiar with stories of old

where casinos employed dealers to cheat “lucky” players.

Understanding the mathematics of a game also is important for the casino operator to ensure

that the reasonable expectations of the players are met. For most persons, gambling is

entertainment. It provides an outlet for adult play. As such, persons have the opportunity for a

pleasant diversion from ordinary life and from societal and personal pressures. As an

entertainment alternative, however, players may consider the value of the gambling experience.

For example, some people may have the option of either spending a hundred dollars during an

evening by going to a professional basketball game or at a licensed casino. If the house

advantage is too strong and the person loses his money too quickly, he may not value that

casino entertainment experience. On the other hand, if a casino can entertain him for an

evening, and he enjoys a “complimentary” meal or drinks, he may want to repeat the

experience, even over a professional basketball game. Likewise, new casino games themselves

may succeed or fail based on player expectations. In recent years, casinos have debuted a

variety of new games that attempt to garner player interest and keep their attention. Regardless

of whether a game is fun or interesting to play, most often a player will not want to play games

where his money is lost too quickly or where he has a exceptionally remote chance of returning

home with winnings.

Mathematics also plays an important part in meeting players’ expectations as to the possible

consequences of his gambling activities. If gambling involves rational decision-making, it would

appear irrational to wager money where your opponent has a better chance of winning than you

do. Adam Smith suggested that all gambling, where the operator has an advantage, is irrational.

He wrote “There is not, however, a more certain proposition in mathematics than that the more

tickets [in a lottery] you advertise upon, the more likely you are a loser. Adventure upon all the

tickets in the lottery, and you lose for certain; and the greater the number of your tickets, the

nearer you approach to this certainty.”

Even where the house has an advantage, however, a gambler may be justified if the amount

lost means little to him, but the potential gain would elevate him to a higher standing of living.

For example, a person with an annual income of $30,000 may have $5 in disposable weekly

income. He could save or gamble this money. By saving it, at the end of a year, he would have

$260. Even if he did this for years, the savings would not elevate his economic status to another

level. As an alternative, he could use the $5 to gamble for the chance to win $1 million. While

the odds of winning are remote, it may provide the only opportunity to move to a higher

economic class.

Since the casino industry is heavily regulated and some of the standards set forth by regulatory

bodies involve mathematically related issues, casino managers also should understand the

mathematical aspects relating to gaming regulation. Gaming regulation is principally dedicated

Casino Math Guide

UNLV Gaming Studies Research Center 3

to assuring that the games offered in the casino are fair, honest, and that players get paid if they

win. Fairness is often expressed in the regulations as either requiring a minimum payback to the

player or, in more extreme cases, as dictating the actual rules of the games offered. Casino

executives should understand the impact that rules changes have on the payback to players to

assure they meet regulatory standards. Equally important, casino executives should understand

how government mandated rules would impact their gaming revenues.

The House Edge

The player’s chances of winning in a casino game and the rate at which he wins or loses money

depends on the game, the rules in effect for that game, and for some games his level of skill.

The amount of money the player can expect to win or lose in the long run – if the bet is made

over and over again – is called the player’s wager expected value (EV), or expectation. When

the player’s wager expectation is negative, he will lose money in the long run. For a $5 bet on

the color red in roulette, for example, the expectation is –$0.263. On the average the player will

lose just over a quarter for each $5 bet on red.

When the wager expectation is viewed from the casino’s perspective (i.e., the negative of the

player’s expectation) and expressed as a percentage, you have the house advantage. For the

roulette example, the house advantage is 5.26% ($0.263 divided by $5). The formal calculation

is as follows:

EV = (+5)(18/38) + (–5)(20/38) = –0.263

(House Advantage = 0.263/5 = 5.26%)

When this EV calculation is performed for a 1-unit amount, the negative of the resulting value is

the house edge. Here are the calculations for bets on a single-number in double-zero and

single-zero roulette.

Double-zero roulette (single number bet):

EV = (+35)(1/38) + (–1)(37/38) = –0.053

(House Advantage = 5.3%)

Single-zero roulette (single number bet):

EV = (+35)(1/37) + (–1)(36/37) = –0.027

(House Advantage = 2.7%)

The house advantage represents the long run percentage of the wagered money that will be

retained by the casino. It is also called the house edge, the “odds” (i.e., avoid games with bad

odds), or just the “percentage” (as in Mario Puzo’s Fools Die). Although the house edge can be

computed easily for some games – for example, roulette and craps – for others it requires more

sophisticated mathematical analysis and/or computer simulations. Regardless of the method

used to compute it, the house advantage represents the price to the player of playing the game.

Because this positive house edge exists for virtually all bets in a casino (ignoring the poker room

and sports book where a few professionals can make a living), gamblers are faced with an uphill

and, in the long run, losing battle. There are some exceptions. The odds bet in craps has zero

house edge (although this bet cannot be made without making another negative expectation

wager) and there are a few video poker machines that return greater than 100% if played with

perfect strategy. Occasionally the casino will even offer a promotion that gives the astute player

a positive expectation. These promotions are usually mistakes – sometimes casinos don’t check

Casino Math Guide

UNLV Gaming Studies Research Center 4

the math – and are terminated once the casino realizes the player has the edge. But by and

large the player will lose money in the long run, and the house edge is a measure of how fast

the money will be lost. A player betting in a game with a 4% house advantage will tend to lose

his money twice as fast as a player making bets with a 2% house edge. The trick to intelligent

casino gambling – at least from the mathematical expectation point of view – is to avoid the

games and bets with the large house advantages.

Some casino games are pure chance – no amount of skill or strategy can alter the odds. These

games include roulette, craps, baccarat, keno, the big-six wheel of fortune, and slot machines.

Of these, baccarat and craps offer the best odds, with house advantages of 1.2% and less than

1% (assuming only pass/come with full odds), respectively. Roulette and slots cost the player

more – house advantages of 5.3% for double-zero roulette and 5% to 10% for slots – while the

wheel of fortune feeds the casino near 20% of the wagers, and keno is a veritable casino cash

cow with average house advantage close to 30%.

Games where an element of skill can affect the house advantage include blackjack, video

poker, and the four popular poker-based table games: Caribbean Stud poker, Let It Ride, Three

Card poker, and Pai Gow poker. For the poker games, optimal strategy results in a house edge

in the 3% to 5% range (CSP has the largest house edge, PGP the lowest, with LIR and TCP in

between). For video poker the statistical advantage varies depending on the particular machine,

but generally this game can be very player friendly – house edge less than 3% is not uncommon

and some are less than 1% – if played with expert strategy.

Blackjack, the most popular of all table games, offers the skilled player some of the best odds in

the casino. The house advantage varies slightly depending on the rules and number of decks,

but a player using basic strategy faces little or no disadvantage in a single-deck game and only

a 0.5% house edge in the common six-deck game. Despite these numbers, the average player

ends up giving the casino a 2% edge due to mistakes and deviations from basic strategy.

Complete basic strategy tables can be found in many books and many casino-hotel gift shops

sell color-coded credit card size versions. Rule variations favorable to the player include fewer

decks, dealer stands on soft seventeen (worth 0.2%), doubling after splitting (0.14%), late

surrender (worth 0.06%), and early surrender (uncommon, but worth 0.24%). If the dealer hits

soft seventeen it will cost you, as will any restrictions on when you can double down.

Probability versus Odds

Probability represents the long run ratio of (# of times an outcome occurs) to (# of times

experiment is conducted). Odds represent the long run ratio of (# of times an outcome does not

occur) to (# of times an outcome occurs). If a card is randomly selected from a standard deck of

52 playing cards, the probability it is a spade is 1/4; the odds (against spade) are 3 to 1. The

true odds of an event represent the payoff that would make the bet on that event fair. For

example, a bet on a single number in double-zero roulette has probability of 1/38, so to break

even in the long run a player would have to be paid 37 to 1 (the actual payoff is 35 to 1).

Confusion about Win Rate

There are all kinds of percentages in the world of gaming. Win percentage, theoretical win

percentage, hold percentage, and house advantage come to mind. Sometimes casino bosses

use these percentages interchangeably, as if they are just different names for the same thing.

Admittedly, in some cases this is correct. House advantage is just another name for theoretical

Casino Math Guide

UNLV Gaming Studies Research Center 5

win percentage, and for slot machines, hold percentage is (in principle) equivalent to win

percentage. But there are fundamental differences among these win rate measurements.

The house advantage – the all-important percentage that explains how casinos make money –

is also called the house edge, the theoretical win percentage, and expected win percentage. In

double-zero roulette, this figure is 5.3%. In the long run the house will retain 5.3% of the money

wagered. In the short term, of course, the actual win percentage will differ from the theoretical

win percentage (the magnitude of this deviation can be predicted from statistical theory). The

actual win percentage is just the (actual) win divided by the handle. Because of the law of large

numbers – or as some prefer to call it, the law of averages – as the number of trials gets larger,

the actual win percentage should get closer to the theoretical win percentage.

Because handle can be difficult to measure for table games, performance is often measured by

hold percentage (and sometimes erroneously called win percentage). Hold percentage is equal

to win divided by drop. In Nevada, this figure is about 24% for roulette. The drop and hold

percentage are affected by many factors; we won’t delve into these nor the associated

management issues. Suffice it to say that the casino will not in the long term keep 24% of the

money bet on the spins of roulette wheel – well, an honest casino won’t.

To summarize: House advantage and theoretical win percentage are the same thing, hold

percentage is win over drop, win percentage is win over handle, win percentage approaches the

house advantage as the number of plays increases, and hold percentage is equivalent to win

percentage for slots but not table games.

· Hold % = Win/Drop

· Win % (actual) = Win/Handle

· H.A. = Theoretical Win % = Limit(Actual Win %) = Limit(Win/Handle)

· Hold Percentage ¹ House Edge

Furthermore, the house advantage is itself subject to varying interpretations. In Let It Ride, for

example, the casino advantage is either 3.51% or 2.86% depending on whether you express the

advantage with respect to the base bet or the average bet. Those familiar with the game know

that the player begins with three equal base bets, but may withdraw one or two of these initial

units. The final amount put at risk, then, can be one (84.6% of the time assuming proper

strategy), two (8.5%), or three units (6.9%), making the average bet size 1.224 units. In the long

run, the casino will win 3.51% of the hands, which equates to 2.86% of the money wagered. So

what’s the house edge for Let It Ride? Some prefer to say 3.51% per hand, others 2.86% per

unit wagered. No matter. Either way, the bottom line is the same either way: assuming three $1

base bets, the casino can expect to earn 3.5¢ per hand (note that 1.224 x 0.0286 = 0.035).

The question of whether to use the base bet or average bet size also arises in Caribbean Stud

Poker (5.22% vs. 2.56%), Three Card Poker (3.37% vs. 2.01%), Casino War (2.88% vs. 2.68%),

and Red Dog (2.80% vs. 2.37%).

For still other games, the house edge can be stated including or excluding ties. The prime

examples here are the player (1.24% vs. 1.37%) and banker (1.06% vs. 1.17%) bets in

baccarat, and the don’t pass bet (1.36% vs. 1.40%) in craps. Again, these are different views on

the casino edge, but the expected revenue will not change.

Casino Math Guide

UNLV Gaming Studies Research Center 6

That the house advantage can appear in different disguises might be unsettling. When properly

computed and interpreted, however, regardless of which representation is chosen, the same

truth (read: money) emerges: expected win is the same.

Volatility and Risk

Statistical theory can be used to predict the magnitude of the difference between the actual win

percentage and the theoretical win percentage for a given number of wagers. When observing

the actual win percentage a player (or casino) may experience, how much variation from

theoretical win can be expected? What is a normal fluctuation? The basis for the analysis of

such volatility questions is a statistical measure called the standard deviation (essentially the

average deviation of all possible outcomes from the expected). Together with the central limit

theorem (a form of the law of large numbers), the standard deviation (SD) can be used to

determine confidence limits with the following volatility guidelines:

Volatility Analysis Guidelines

· Only 5% of the time will outcomes will be more than 2 SD’s from expected outcome

· Almost never (0.3%) will outcomes be more than 3 SD’s from expected outcome

Obviously a key to using these guidelines is the value of the SD. Computing the SD value is

beyond the scope of this article, but to get an idea behind confidence limits, consider a series of

1,000 pass line wagers in craps. Since each wager has a 1.4% house advantage, on average

the player will be behind by 14 units. It can be shown (calculations omitted) that the wager

standard deviation is for a single pass line bet is 1.0, and for 1,000 wagers the SD is 31.6.

Applying the volatility guidelines, we can say that there is a 95% chance the player’s actual win

will be between 49 units ahead and 77 units behind, and almost certainly between 81 units

ahead and 109 units behind.

A similar analysis for 1,000 single-number wagers on double-zero roulette (on average the

player will be behind 53 units, wager SD = 5.8, 1,000 wager SD = 182.2) will yield 95%

confidence limits on the player win of 311 units ahead and 417 units behind, with win almost

certainly between 494 units ahead and 600 units behind.

Note that if the volatility analysis is done in terms of the percentage win (rather than the number

of units or amount won), the confidence limits will converge to the house advantage as the

number of wagers increases. This is the result of the law of large numbers – as the number of

trials gets larger, the actual win percentage should get closer to the theoretical win percentage.

Risk in the gaming business depends on the house advantage, standard deviation, bet size, and

length of play.

Player Value and Complimentaries

Using the house advantage, bet size, duration of play, and pace of the game, a casino can

determine how much it expects to win from a certain player. This player earning potential (also

called player value, player worth, or theoretical win) can be calculated by the formula:

Earning Potential = Average Bet ´ Hours Played ´ Decisions per Hour ´ House Advantage

For example, suppose a baccarat player bets $500 per hand for 12 hours at 60 hands per hour.

Using a house advantage of 1.2%, this player’s worth to the casino is $4,320 (500 ´ 12 ´ 60 ´

Casino Math Guide

UNLV Gaming Studies Research Center 7

.012). A player who bets $500 per spin for 12 hours in double-zero roulette at 60 spins per hour

would be worth about $19,000 (500 ´ 12 ´ 60 ´ .053).

Many casinos set comp (complimentary) policies by giving the player back a set percentage of

their earning potential. Although comp and rebate policies based on theoretical loss are the

most popular, rebates on actual losses and dead chip programs are also used in some casinos.

Some programs involve a mix of systems. The mathematics associated with these programs will

not be addressed in this article.

Casino Pricing Mistakes

In an effort to entice players and increase business, casinos occasionally offer novel wagers,

side bets, increased payoffs, or rule variations. These promotions have the effect of lowering the

house advantage and the effective price of the game for the player. This is sound reasoning

from a marketing standpoint, but can be disastrous for the casino if care is not taken to ensure

the math behind the promotion is sound. One casino offered a baccarat commission on winning

banker bets of only 2% instead of the usual 5%, resulting in a 0.32% player advantage. This is

easy to see (using the well-known probabilities of winning and losing the banker bet):

EV = (+0.98)(.4462) + (–1)(.4586) = 0.0032

(House Advantage = –0.32%)

A casino in Biloxi, Mississippi gave players a 12.5% edge on Sic Bo bets of 4 and 17 when they

offered 80 to 1 payoffs instead of the usual 60 to 1. Again, this is an easy calculation. Using the

fact that the probability of rolling a total of 4 (same calculation applies for a total of 17) with three

dice is 1/72 (1/6 x 1/6 x 1/6 x 3), here are the expected values for both the usual and the

promotional payoffs:

Usual 60 to 1 payoff: EV = (+60)(1/72) + (–1)(71/72) = –0.153

(House Advantage = 15.3%)

Promotional 80 to 1 payoff: EV = (+80)(1/72) + (–1)(71/72) = +0.125

(House Advantage = –12.5%)

In other promotional gaffes, an Illinois riverboat casino lost a reported $200,000 in one day with

their “2 to 1 Tuesdays” that paid players 2 to 1 (the usual payoff is 3 to 2) on blackjack naturals,

a scheme that gave players a 2% advantage. Not to be outdone, an Indian casino in California

paid 3 to 1 on naturals during their “happy hour,” offered three times a day, two days a week for

over two weeks. This promotion gave the player a whopping 6% edge. A small Las Vegas

casino offered a blackjack rule variation called the “Free Ride” in which players were given a

free right-to-surrender token every time they received a natural. Proper use of the token led to a

player edge of 1.3%, and the casino lost an estimated $17,000 in eight hours. Another major

Las Vegas casino offered a “50/50 Split” blackjack side bet that allowed the player to stand on

an initial holding of 12-16, and begin a new hand for equal stakes against the same dealer up

card. Although the game marketers claimed the variation was to the advantage of the casino, it

turned out that players who exercised the 50/50 Split only against dealer 2-6 had a 2%

advantage. According to one pit boss, the casino suffered a $230,000 loss in three and a half

days.

In the gaming business, it’s all about “bad math” or “good math.” Honest games based on good

math with positive house advantage minimize the short-term risk and ensure the casino will

Casino Math Guide

UNLV Gaming Studies Research Center 8

make money in the long run. Players will get “lucky” in the short term, but that is all part of the

grand design. Fluctuations in both directions will occur. We call these fluctuations good luck or

bad luck depending on the direction of the fluctuation. There is no such thing as luck. It is all

mathematics.

Gaming Regulation and Mathematics

Casino gaming is one of the most regulated industries in the world. Most gaming regulatory

systems share common objectives: keep the games fair and honest and assure that players are

paid if they win. Fairness and honesty are different concepts. A casino can be honest but not

fair. Honesty refers to whether the casino offers games whose chance elements are random.

Fairness refers to the game advantage – how much of each dollar wagered should the casino

be able to keep? A slot machine that holds, on average, 90% of every dollar bet is certainly not

fair, but could very well be honest (if the outcomes of each play are not predetermined in the

casino’s favor). Two major regulatory issues relating to fairness and honesty – ensuring random

outcomes and controlling the house advantage – are inextricably tied to mathematics and most

regulatory bodies require some type of mathematical analysis to demonstrate game advantage

and/or confirm that games outcomes are random. Such evidence can range from

straightforward probability analyses to computer simulations and complex statistical studies.

Requirements vary across jurisdictions, but it is not uncommon to see technical language in

gaming regulations concerning specific statistical tests that must be performed, confidence

limits that must be met, and other mathematical specifications and standards relating to game

outcomes.

Summary Tables for House Advantage

The two tables below show the house advantages for many of the popular casino games. The

first table is a summary of the popular games and the second gives a more detailed breakdown.

House Advantages for Popular Casino Games

Game House Advantage

Roulette (double-zero) 5.3%

Craps (pass/come) 1.4%

Craps (pass/come with double odds) 0.6%

Blackjack – average player 2.0%

Blackjack – 6 decks, basic strategy* 0.5%

Blackjack – single deck, basic strategy* 0.0%

Baccarat (no tie bets) 1.2%

Caribbean Stud* 5.2%

Let It Ride* 3.5%

Three Card Poker* 3.4%

Pai Gow Poker (ante/play)* 2.5%

Slots 5% - 10%

Video Poker* 0.5% - 3%

Keno (average) 27.0%

*optimal strategy

Casino Math Guide

UNLV Gaming Studies Research Center 9

HOUSE ADVANTAGES FOR MAJOR CASINO WAGERS

Game Bet HA*

Baccarat Banker (5% commission) 1.06%

Baccarat Player 1.24%

Big Six Wheel Average 19.84%

Blackjack Card-Counting -1.00%

Blackjack Basic Strategy 0.50%

Blackjack Average player 2.00%

Blackjack Poor Player 4.00%

Caribbean Stud Ante 5.22%

Casino War Basic Bet 2.88%

Craps Any Craps 11.11%

Craps Any Seven 16.67%

Craps Big 6, Big 8 9.09%

Craps Buy (any) 4.76%

Craps C&E 11.11%

Craps don’t pass/Don’t Come 1.36%

Craps don’t pass/Don’t Come w/1X Odds 0.68%

Craps don’t pass/Don’t Come w/2X Odds 0.45%

Craps don’t pass/Don’t Come w/3X Odds 0.34%

Craps don’t pass/Don’t Come w/5X Odds 0.23%

Craps don’t pass/Don’t Come w/10X Odds 0.12%

Craps Don’t Place 4 or 10 3.03%

Craps Don’t Place 5 or 9 2.50%

Craps Don’t Place 6 or 8 1.82%

Craps Field (2 and 12 pay double) 5.56%

Craps Field (2 or 12 pays triple) 2.78%

Craps Hard 4, Hard 10 11.11%

Craps Hard 6, Hard 8 9.09%

Craps Hop Bet – easy (14-1) 16.67%

Craps Hop Bet – easy (15-1) 11.11%

Craps Hop Bet – hard (29-1) 16.67%

Craps Hop Bet – hard (30-1) 13.89%

Craps Horn Bet (30-1 & 15-1) 12.50%

Craps Horn High – any (29-1 & 14-1) 16.67%

Craps Horn High 2, Horn High 12 (30-1 & 15-1) 12.78%

Craps Horn High 3, Horn High 11 (30-1 & 15-1) 12.22%

Craps Lay 4 or 10 2.44%

Craps Lay 5 or 9 3.23%

Craps Lay 6 or 8 4.00%

Craps Pass/Come 1.41%

Craps Pass/Come w/1X Odds 0.85%

Craps Pass/Come w/2X Odds 0.61%

Craps Pass/Come w/3X Odds 0.47%

Craps Pass/Come w/5X Odds 0.33%

Craps Pass/Come w/10X Odds 0.18%

Craps Place 4 or 10 6.67%

Craps Place 5 or 9 4.00%

Craps Place 6 or 8 1.52%

Craps Three, Eleven (14-1) 16.67%

Craps Three, Eleven (15-1) 11.11%

Casino Math Guide

UNLV Gaming Studies Research Center 10

Craps Two, Twelve (29-1) 16.67%

Craps Two, Twelve (30-1) 13.89%

Keno Typical 27.00%

Let It Ride Base bet 3.51%

Pai Gow Poker Skilled player (non-banker) 2.54%

Pai Gow Poker Average player (non-banker) 2.84%

Red Dog Basic bet (six decks) 2.80%

Roulette Single-zero 2.70%

Roulette Double-zero (except five-number) 5.26%

Roulette Double-zero, five-number bet 7.89%

Sic Bo Big/Small 2.78%

Sic Bo One of a Kind 7.87%

Sic Bo 7, 14 9.72%

Sic Bo 8, 13 12.50%

Sic Bo 10, 11 12.50%

Sic Bo Any three of a kind 13.89%

Sic Bo 5, 16 13.89%

Sic Bo 4, 17 15.28%

Sic Bo Three of a kind 16.20%

Sic Bo Two-dice combination 16.67%

Sic Bo 6, 15 16.67%

Sic Bo Two of a kind 18.52%

Sic Bo 9, 12 18.98%

Slots Dollar Slots (good) 4.00%

Slots Quarter Slots (good) 5.00%

Slots Dollar Slots (average) 6.00%

Slots Quarter Slots (average) 8.00%

Sports Betting Bet $11 to Win $10 4.55%

Three Card Poker Pair Plus 2.32%

Three Card Poker Ante 3.37%

Video Poker Selected Machines -0.50%

*House Advantages under typical conditions, expressed “per hand” and including ties,

where appropriate. Optimal strategy assumed unless otherwise noted.

Selected Bibliography

Cabot, Anthony N., and Hannum, Robert C. (2002). Gaming Regulation and Mathematics: A

Marriage of Necessity, John Marshall Law Review, Vol. 35, No. 3, pp. 333-358.

Cabot, Anthony N. (1996). Casino Gaming: Policy, Economics, and Regulation, UNLV

International Gaming Institute, Las Vegas, NV.

Eadington, William R., and Cornelius, Judy (eds.) (1999). The Business of Gaming: Economic

and Management Issues, Institute for the Study of Gambling and Commercial Gaming,

University of Nevada, Reno, NV.

Eadington, William R., and Cornelius, Judy (eds.) (1992). Gambling and Commercial Gaming:

Essays in Business, Economics, Philosophy and Science, Institute for the Study of

Gambling and Commercial Gaming, University of Nevada, Reno, NV.

Casino Math Guide

UNLV Gaming Studies Research Center 11

Epstein, Richard A. (1995). The Theory of Gambling and Statistical Logic, revised edition,

Academic Press, San Diego, CA.

Feller, William (1968). An Introduction to Probability Theory and Its Applications, 3rd ed., Wiley,

New York, NY.

Griffin, Peter A. (1999). The Theory of Blackjack, 6th ed., Huntington Press, Las Vegas, NV.

Griffin, Peter (1991). Extra Stuff: Gambling Ramblings, Huntington Press, Las Vegas, NV.

Hannum, Robert C. and Cabot, Anthony N. (2001). Practical Casino Math, Institute for the Study

of Gambling & Commercial Gaming, University of Nevada, Reno.

Humble, Lance, and Cooper, Carl (1980). The World’s Greatest Blackjack Book, Doubleday,

New York, NY.

Kilby, Jim and Fox, Jim (1998). Casino Operations Management, Wiley, New York, NY.

Levinson, Horace C. (1963). Chance, Luck and Statistics, Dover Publications, Mineola, NY.

Millman, Martin H. (1983). “A Statistical Analysis of Casino Blackjack,” American Mathematical

Monthly, 90, pp. 431-436.

Packel, Edward (1981). The Mathematics of Games and Gambling, The Mathematical

Association of America, Washington, D.C.

Thorp, Edward O. (1984). The Mathematics of Gambling, Gambling Times, Hollywood, CA.

Thorp, Edward O. (1966). Beat the Dealer, Vintage Books, New York, NY.

Vancura, Olaf, Cornelius, Judy A., and Eadington, William R. (eds.) (2000). Finding the Edge:

Mathematical Analysis of Casino Games. Institute for the Study of Gambling and

Commercial Gaming, University of Nevada, Reno, NV.

Vancura, Olaf (1996). Smart Casino Gambling, Index Publishing Group, San Diego, CA.

Weaver, Warren (1982). Lady Luck: The Theory of Probability, Dover Publications, New York,

NY.

Wilson, Allan (1970). The Casino Gambler’s Guide, Harper and Row, New York.

Selected Internet Resources

Urbino – a casino and gaming management site.

www.urbino.net

Institute for the Study of Gambling and Commercial Gaming, University of Nevada, Reno.

www.unr.edu/gaming

The Wizard of Odds – an excellent site for general game mathematics and odds.

Casino Math Guide

UNLV Gaming Studies Research Center 12

www.thewizardofodds.com

Blackjack (mainly) sites.

www.bjmath.com

www.bj21.com

www.advantageplayer.com

About the Author

Bob Hannum is an Associate Professor of Statistics at the University of Denver where he

teaches courses in probability, statistics and the theory of gambling. His publications include

Practical Casino Math (co-authored with Anthony N. Cabot) and numerous articles in scholarly

and gaming industry journals. Hannum regularly speaks on casino mathematics to audiences

around the globe. (Some of this guide has been excerpted from Practical Casino Math.)

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