Investing or Gambling? Part 8: Mathematical Similarities

Mathematics plays an important role in the decision making of both investors and gamblers. While some of the analytical quantification methods are substantially different, we believe that there are two common techniques that inherently similar. These are:

• Decision Trees, and
• Probability Analysis.

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Decision Trees

Whether written or conceived, both gamblers and investors continuously make (and often repeat) decisions based on possible outcomes. After each decision is reached, a new set of possibilities brings forth a new set of possible outcomes. Each decision node may have two or more potential choices that can then be made. The diagram below illustrates a sample two level set of possible decision paths.

Source: Decision Tree: How to do it

From a financial viewpoint, a stock market investor typically has three choices he can initially make: (1) buy a stock; (2) sell a stock; or (3) do nothing. Once these decisions are made, the choices will vary depending on the path taken. In the case of one who buys a stock, he now has at least 4 new options available: (a) continue to hold; (b) sell the position; (c) buy more; or (d) hedge. Had the investor sold a stock short initially, he too has various choices to make regarding his position. And, if the investor initially did nothing, then he would circle back to the initial set of choices to be made.

From a gambling viewpoint, a player makes decisions based on the type of game or activity he is entertaining. If the person is playing poker, he has the choice to: (1) fold; (2) pass; (3) raise; or (4) call after each different card is dealt. Each time, his decision will be based on his previous choice and the final possible outcomes. Lottery players have the choices of: (1) playing; (2) not playing; or (3) playing and buying a multiplier. If the person decides to play, he must then decide to: (a) ask for quick picks or (b) pick his own number. If he choose the latter, then he decides: birthday numbers; even odd; hot cold; etc. Lastly, if he wins a large prize, he must then begin making decisions based on the financial decision tree above.

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Probability Distributions

Most of the decisions that the investor or gambler makes are based on the underlying probabilities of success. These probabilities are based on some type of mathematical model. In the financial world, a Normal Probability Density Function is typically used. Ranges of numbers are quantified, or counted, in terms of Standard Deviations as shown in the figure below.

Source: SPC Tools - Control charts

Let us return to the investor above who initially purchased a stock at decision point 1. His decision to sell, hold, or buy more will be determined by the the price change in his stock. If the change remains within 1 standard deviation (based on volatility), he will most likely hold. If it drops more than 2 or 3 standard deviations, he will probably sell. If new positive economic information about the stock is released, he will probably buy more.

Some financial instruments are priced and valued strictly on the amount of price change and probability of occurrence. In particular, Call and Put Stock Options are priced this way. As seen below, a call option price increases when the stock goes up, but this is based on a probability weighted amount. Thus, the stock price change movement must be positively larger than the initial premium paid in order for the investor to earn a profit.

Source: Option Pricing Models

Similarly, poker player make similar decisions based on probabilities. Consider a 5 card stud player that remains until all 5 cards are dealt. If he holds a pair, then he knows that approximately 42% of all hands will have pair. He also knows that his hand is better than 50% of hands, and that approximately 8% of all hands will beat his. Using this information, he will then decide to call, raise, or fold.

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Summary

In this brief article, we illustrated how similar investors and gamblers are in decision making. Underlying each conscious decision is the understanding of the underlying mathematical probabilities of successfully earning a profit. While the investments or games may vary from simple (buy a stock or flip a coin), to complex (derivative options & swaps or poker and backgammon), nearly the same mathematical properties can be used to quantify success.

Investing or Gambling? Part 7: Profile of a Typical Investor and Gambler

When we first began researching the profiles of typical investors and gamblers, we found many sources describing gamblers but relatively few discussing investors. The information we read about gamblers was written from either the "problem gambler" viewpoint, or that of a "casino operator". The investing articles were written for purposes of attracting "day traders" to discount brokers, or describing why investors typically lose money.

Rather than summarizing this information once again, we decided to explore the underlying traits and skills that both participants exhibit.   

In the old days, we all have images of savvy boardroom executives smoking cigars while formulating important business decisions in a smoke filled boardroom. In contrast, we also envision the small old wiry racetrack bettor studying his racing forms while the cigar ashes threatened to fall off.

Source: Frontier Gamblers - Poker Alice

Today, we find that the cigars have mostly disappeared and that the executives and gamblers have become much much younger.

It appears that youth has overtaken our society.

But not so quick. During the past few years, our economy has faltered, leading to widespread unemployment. Executives and thousands of regular employees have been laid off. Graduates from colleges cannot find jobs in fields of their study. Out of frustration, many of these individuals have turned to gambling or investing in hopes of earning a living to support their families.

From a demographic viewpoint, we find that age has no bearing on the profile of these persons. In Wall Street, the mentality is the younger the better. They believe the younger you are, the more mathematical and abstract you think, the better you will trade. However, the major difference between these individuals and the ordinary person is that they are playing with someone else's money. These young mavericks will earn a very handsome bonus regardless of whether they win or lose.

The illustration below was designed to describe the thinking of various gamblers. However, those involved in investing (or trading their own accounts) are depicted as well.  What we learn is that the average individual  is best described as an entrepreneur. They try to be middle of the road, balancing amusement with gaming while taking average risks. Whereas, individuals and amateurs lean more toward amusement, and elitists take more risk.

Source: Gambling - Contexts and addictions

According to the Forbes article, The Average Investor Is His Own Worst Enemy, average investors fail to succeed because they are overly confident, shortsighted, and have bad timing. The same is true with the average gambler.

What novice investors and gamblers believe is that they are playing on an equal level with all the other participants. Both fail to realize that they are actually playing against highly educated and highly financed professionals. These professionals have more information at there disposal, and know the underlying probabilities by heart. Consider a professional poker player. He knows his probability of winning as each card is drawn while the common individual just thinks in terms of luck. To further complicate the equation, the professionals are playing in teams while the individual is playing alone.

Whether the professionals work independently or for a company, they have dedicated their livelihood to learning their trade. Most began small and have worked their way up the income chain. Most have made associated contacts that help to keep them informed.

If you have dreams to pursue your own career as a professional investor or gambler, be prepared to study, memorize, and practice. Learn to make your own decisions but always consider the advice of others. You must always be retrospective and analyze the plays that succeeded and failed. And, never make reckless decisions, especially out of dispair.

According to Harrah's Gambling Survey 2006, successful gamblers (and we interject investors) believe they are more:

• in control of their spending and borrowing
• optimistic about the future
• prepared financially for retirement

and more likely to:

• view work as a career
• research purchases more
• dine out
• have higher earnings

than the common investor. If you fit these profiles and are willing to spend years (rather than days) preparing for your future, then you too may become a successful gambler or investor as well.

Investing or Gambling? Part 6: Investment Options

Both gamblers and investors have a wide range of investment options in which they can place their money and hope to earn a profit. In both cases, a person puts down some money with the hope of having more sometime in the future.

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Investing

From the investing side, the vehicles that are available range from near zero risk to highly leveraged and very risky strategies. The charts below illustrate various investments that a person can make, along with the associated risk taken. For purposes of this paper, we define risk as the chances of losing all or part of their money.

Source: Create Wealth Through Long-Term Investing ...

Below we have listed a number of investing options that individuals can make. Typically, most people are aware of putting their money in bank CDs and Savings Bonds. Additionally, many have purchased outright stocks, mutual funds, and sometimes commodities. As one's wealth increases, investors have branched out of these and invested in currencies, private equity companies, hedge funds, real estate, and various sports related items.

• CDs & Bonds (Savings Bonds, US Govt Debt, Municipal, Corporates)
• Asset Backed Bonds (Mortgages, Credit Cards)
• Stocks
• Commodities (Gold, Silver, Oil, etc)
  
• Currencies
• Mutual Funds
• Hedge Funds
• Private Equity (Small companies)
• Collectibles (Fads, Antiques, Art)
• Real Estate (Outright land, REITs)
• Sports (Teams, Horses, Race cars)

Most common individuals that invest in stocks do so with the idea that they will always make money. However, that is not the case anymore. The graph below shows the Dow Jones Average from 1975 to 2008. As we can see, those who invested early were almost assured a profit. But from 1996 to 2008, there was a bumpy ride. Lots of money was lost around 2001 to 2003 and then again in 2008.

Source: Large Scale Fibonacci in the Dow Jones | Afraid to Trade

After a while, investors who have become comfortable with stocks begin to buy futures and options. These exotic vehicles allow the persons to leverage their investments by outlaying a small portion of their money and purchasing the underlying stock or bond only when a profitable return is met. The image below is a payout graph for a call option. In this example, the $40 call option would be purchased for $2 only. If the price of the stock rises above $42, then the investor would exercise his option to buy the stock at $40 and lock in a guaranteed profit. However, if the price never reached $42, then the investor would simply lose his $2 investment.

 

Source: Call Options | Trading Graphs

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Gambling

For the gambling investor, there are numerous legalized vehicles that allow participation. Most notably are lotteries, organized parimutuel racing, casinos, and charitable games. Without ranking these in order of risk, gamblers have the opportunity to play:

• Lottery (+ Keno)
• Card Games (Poker, Blackjack, etc)
• Craps (Dice)
• Roulette
• Slot Machines
• Sports Games (Outcomes, Scores, etc)
• Racing (Horses, Dogs, etc)
• Games of Skill (Backgammon, Chess, etc)

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Summary

The risks of gambling are quite different than investing. Most notably is that the event horizon is relatively short. For example: a lottery drawing may take several days before it occurs; a football or baseball game may take hours to play; a poker hand may take minutes; and a roulette spin may take seconds.

source: THE GAMBLER - Pragmatic Capitalism

A secondary difference is that the gambler usually has direct involvement in the game, whether he is a participant or a spectator. Third, gambling payouts are usually all or nothing, win or lose. For example, only one person wins a poker hand or racing event. Investors, on the contrary, do not typically lose their entire investment.

One may argue that the gambler has an advantage over the investor because there may be an individual skill involved. While that is true, a successful investor is also skilled in understanding their own underlying products. Thus, they too have control over their destiny.

Lastly, many may say that gambling only involves luck. That can also be said about investing. Luck has a lot to do with timing and market sentiment as well.

Investing or Gambling? Part 5: Spotlight on Successful People

Image via Wikipedia

We are all enamored by the success stories of many individuals. For those of us interested in investing, we have role models that we wish to emulate. Similarly, for those of us who wish to be successful gamblers, we point to those people who have made it big and say we can do it too.

Below,  we have highlighted six practitioners from both the gambling and investing professions who have made significant contributions to their societies and amassed a fortune at the same time. The list is intended to be a cross-section of representatives who have helped their professions advance. The list is not prioritized nor is it complete, as there are many more people who have succeeded as well.

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Successful Gamblers

Doyle Brunson: Considered to be the patriarch of modern poker, this famous gambler revolutionized poker in 1978 when he published his book called Super System. Times were not always easy for this Texan who went to college on basketball and track scholarships. But, after he shattered his leg in an accident, and was diagnosed with terminal cancer in 1962, this legend learned to become successful playing the game that he loved. Quote: Through the years I've never stopped doing things, thinking about things, and I still think young.

Gonzalo Garcia-Pelayo: A Spanish mathematician and record producer who believed that roulette wheels were not completely random. Began to exploit the game by recording winning numbers on thousands of spins, and then analyzed the data. Afterward, he used this data to win over €2 million.

Dominic LoRiggio: Became famous for controlling dice while playing Craps. Learned the skill through years of practice and identified ways to set, grip, and toss the dice to achieve a desired roll. Called the Dominator, he says it is a matter of simple physics. Claims to have won thousands of dollars at various casinos.

Edward Thorp: The creator of card counting, a technique by which a player can keep track of the cards that are played and those left in the deck. Most notably recorded in his 1962 book called Beat the Dealer. He has a M.A. in Physics and a PhD in mathematics, and taught at M.I.T. He published a second book in 1967 called Beat the Market and then started a derivatives based hedge fund.

Admiral Henry John Rous: Devised the first methodology for handicapping horse racing. It was based on the Weight for Age Scale which tabulates results based on a jockeys weight and a horses age.


Billy Walters: One of the instrumental managers of The Computer Group, a sports betting operation, that won millions by analyzing all the statistical data about the teams, weather, and more. The Computer Group was forced to break up in 1987, but Billy Walters has continues to win annually using a team of associates who specialize in various aspects of the games.

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Successful Investors

Myron Scholes: Co-inventor of the Black-Scholes Option Pricing Model, he was a managing director and co-head of fixed-income derivatives at Solomon Brothers. Then, he co-founded the hedge fund, Long-Term Capital Managment which obtained annualized returns over 40%. The fund failed in 1998 after losing $4.6 billion in four months. He is now chairman of Platinum Grove Asset management.

Tutor Jones: the founder of Tudor Investment Corporation. Later organized the Tutor Group that includes the former and a variety of affiliates. Is actively involved in trading, investing research and more. Current estimated net worth is $3.2 billion. Quote: The most important rule of trading is to play great defense, not great offense.

Warren Buffet: Formed Buffet Associates in 1956 with 7 limited partners and $150,000. Buffet used $100 of his own money. After 10 years, his assets rose by 1,156%.  Then he bought control of Berkshire Hathaway and became Chairman in 1970. Now has net worth of $47 billion. Quote: Rule No.1: Never lose money. Rule No.2: Never forget rule No.1

Peter Lynch: Earned the reputation of being one of the best stock-pickers in the world after managing Fidelity Magellan fund from 1977 to 1990. Those who invested $1,000 in 1977 would have worth of $28,000 in the 13 years during his control. Favorite Principal: Invest in what you know.

Benjamin Graham: The Father of security analysis and value investing. Wrote two books on these topics in 1934 and 1949 which are considered to be requites for all investors. A mentor and early employer of Warren Buffet. Principle: Know What Kind of Investor You Are

George Soros: Co-founded the Quantum Fund in 1970 at age 40. Aquired most wealth by acheiving  returns of 4000% during the next 10 years. Is now estimated to have $11 billion. Quote: The financial markets generally are unpredictable. So that one has to have different scenarios.. The idea that you can actually predict what's going to happen contradicts my way of looking at the market.

Michael Moritz: A journalist for Time that became a Venture Capitalist two years later in 1986. Joined Sequoia Capital and had made huge returns by investing in Google, Yahoo, PayPal, and many others. Fell out of the Billionaires club in 2008, but still has lots more money.

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Summary

By reading the stories of the individuals above, we can identify certain traits common to all. First, most are highly educated.  They all share a deeper knowledge of mathematics and used this skill as a tool to analyze their content. All are hard working and highly dedicated. Success didn't come overnight, but after years of studying, practicing, and hard work.

For us to succeed then, we must conclude that we can't give up. Some have made mistakes, earning a fortune and then losing all or part of it. However, they never gave up on their pursuits and all succeeded in the long run.

Investing or Gambling? Part 4: The differences between the two.

Image via Wikipedia

There are two primary differences between investing and gambling:

1. Ownership of an asset, and
2. Entertainment.

First, in investing, an investor purchases an asset with the expectation that it will appreciate in value and be worth more in the future than it is at the present time. When gambling, a participant also invests a certain amount of money with the anticipation of winning. However, most gamblers understand that the chances of losing their investment far outweighs their chances of winning.

Second, gambling is entertainment, it is fun. Many people love to go to casinos to play the slots, poker, roulette, or craps. Whether they return home with the same (more, or less) amount of money, the person is usually happy knowing that they purchased a few hours of entertainment. To the lottery player, they have purchased a day or two of dreams. However, investing is work and that is not typically fun. Except for those who purchase antiques or collectibles, an investor obtains very little entertainment value.

Similarities
Aside from the outlay of money, there are few similarities to investing an gambling. In these, both:

• Risk capital to earn a profit.
• Are trying to predict the future outcomes of a certain event.
• Require skill to be successful.
• Are subject to external manipulation.
• Hope to get rich.
• Can lose money.
• Value may be arbitrarily contrived.

Examples of Investing and Gambling
Investing	Gambling
Stocks	Lottery
Bonds	Poker
Coins	Backgammon
Real Estate	Horse Racing
Options	Craps
Cars & Horses	Slot Machines
Collectables	Football Games

Differences
 When considering the two, there are many more differences between investing and gambling that can be identified:

• An investor's time horizon is endless, whereas a gamblers horizon is fixed.
• An investor expects to earn a profit, but a gambler expects to lose.
• The financial return on most investments is quantified, but a gambler's is infinite.
• Investing returns are incremental, but gambling is all or nothing
• An investor's asset fluctuates based on supply and demand. A gambler's asset changes only on anticipated success.
• Investors do not typically influence the value of their asset. Gamblers have direct control over the value of their asset.
• Investors rarely lose their entire investment. Gamblers usually lose most of the money wagered.
• Investments are subject to economic pressures. Gambling games have no economic pressure.

Negative, Zero, and Positive Sum Games.

Most educators consider most forms of gambling to be Negative Sum Games. This means that less money is returned back to the players than the money raised. However, economists liken investing to a Zero Sum Game, meaning that all the money invested is returned back to the investors. Depending on your viewpoint, this may or may not be true. For example, assume that you bought an asset that was destroyed in a fire, lost or stolen. Unless you had insurance (and paid more for this risk), you would lose your entire investment. Depending on the type of asset, others may then become more valuable, or not change in value at all. Investing in bonds can be a Positive Sum Game to the purchaser. Depending on the security, there would be very little risk of losing money, and the payouts would certainly exceed the amount invested.

Summary

In summary, most investors and gamblers participate with the ultimate intention to earn more income. Investors utilize their financial capital to purchase assets that they hope will appreciate. Gamblers, on the other hand, play games with the hope of winning money. Both want to become rich and are faced with skillful competition that can out buy or out play them. Thus, our conclusion is that both these are risky and the unprepared are subject to losing all or part of their money.

Investing or Gambling? Part 3: Why Its Important.

Americans are enamored by wealth. We all dream about being independently wealthy, working as little as possible, and obtaining the most amount of money as possible. But, the harsh reality is that very few of us achieve our goals of becoming millionaires.

For the past few years, the United States has been in a recession. Many individuals have lost their jobs and have remained unemployed for two years or more. At the same time, students graduating from college have found it increasingly more difficult to find employment opportunities. Many students have taken the opportunity to earn a Graduate degree with the hope that they will be more marketable when they finish their advanced education.

People are desperate.

With financial pressures mounting, many unemployed individuals have sought alternate avenues for generating family revenue. Some have become day traders, and others have become professional gamblers.

Temptation is everywhere.

The radio and television advertisements are full of get rich quick schemes, telling us to buy gold, refinance our houses, play the stock market, play the lottery, go to a casino, and more. We are bombarded with stories of successful investors such as Warren Buffet, George Soros, Donald Trump, and Wall Street tycoons who made fortunes playing the markets. At the same time, we see the glamorous lifes of the ESPN World Series of Poker stars, and hear about the fabulous casino and lottery winners.

Taking a gamble.

In the past, the division between gambling and investing was clearly defined. Our images of gamblers were those betting at race tracks, the down on their luck poker player, or the gambling addict. Investors wore suits and ties. They attended meetings and lunches, and put together multi-million dollar deals that rewarded them handsomely.

The internet breaks the barriers.

But with the recent advances in technology, the trading tools previously available only to those in the investment business are now available to all of us. We can now learn to use technical trading tools right in our home for buying and selling stocks. As we learn more, we can buy more exotic products, like options. A few years ago, everyone could play online poker. Although this is now banned, players can continue to refine their skills by playing for fun on a variety of sites.

This past January, 60 Minutes aired a Sports Bedding feature on Billy Walters, a sports betting legend who has never had a losing year.



Because temptation is everywhere, many individuals are attempting to earn a living as either a professional investor or a gambler. I have several friends who stopped working years ago and now earn their income solely from trading stocks. Lately, I've seen a few young college graduates decide to become professional poker players in Atlantic City and Las Vegas, rather than working in the corporate world.

Everyone wants your money.

What I've learned from analyzing lottery games and talking to these individuals is that achieving success is difficult.  Everyone out there wants your money. The more desperate you are, the easier it is to lose everything. Regardless of whether you participate in investing or gambling, you are competing against professionals that have much more money and much more knowledge. They all know the odds of winning and losing, and make their bets accordingly.

Don't be a fool.

Therefore, we felt that it is important to write this series of articles about investing and gambling. In last weeks article, we defined these two concepts and showed how they are different. In subsequent weeks, we will illustrate why the distinction between the two is blurred. In the end, we hope to educate you to the risks of each profession, and to help you keep your hard earned money.

Investing or Gambling? Part 2: The Definitions

In this second installment of our analysis, we will examine the definitional differences between gambling and investing. This information will form the basis by which we will judge future comparisons of each discipline.

To begin, there are fundamental similarities and differences between gambling and investing. Both involve a participant's initial outlay of money for purposes of receiving future payments that exceed the investment amount. The definitions below describe the expectations that each monetary outlay will purchase.

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Investing Defined

Those who invest receive partial or full ownership of a physical asset, whether it be a company, commodity, real-estate, manufactured good, production rights, etc. which can be redeemed at a future date at the discretion of the owner. The vast majority of investors typically have no direct financial control of the asset. Appreciation of value is acheived based on fundamentals of supply and demand, and operating efficiencies. When an asset grows in value, an investor may realize a profit on his investment; and when an asset drops in value, the investor may incur a loss. But, the actual profit or loss is only realized when the investor sells the asset. The key here is that the investor has the sole opportunity to act.

Definitions

• To commit (money) in order to earn a financial return (TheFreeDictionary & Merriam-Webster)
• Laying out money capital in an enterprise with the expectation of profit (Princeton WorldNetWeb)

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Gambling Defined

Gambling involves purchasing the right to participate in the possible ownership of a product or prize based on a certain outcome of a particular event. Depending on the prize structure, a gambler only receives income if his predicted guess correctly matches the ordered result of the event, such a lottery drawing, horse race, the win or loss of a sports team, a poker hand, etc. Once the event is completed, the gamblers asset value (if any) is returned to the player. These investors either win or lose, and the participation right is valueless once the event is over. Important here is that gamblers have no influence over the outcome of the event.

Definitions

• To play a game for money or property (Merriam-Webster)
• To bet on an uncertain outcome
• To bet on an uncrtain outcome, as of a contest (TheFreeDictionary)
• To play a game of chance for stakes
• To take a risk in the hope of gaining an advantage or benefit

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Three Major Distinctions

From the definitions above, we can identify three major distinctions between investing and gambling.

First, the primary distinction between investing and gambling is ownership of an asset. An investor purchases an asset of value whereas a gambler purchase an outcome. The investor's asset maintains value for the life of the asset. Whereas, a gambler's outcome has no value in itself. The only means of profit is derived from the investments of the other gamblers involved.

Secondly, an investor's asset derives value from market demand, which can cause the value of the asset to fluctuate. However, a gambler's asset has value limited by the expectations of others. Any changes are based on parimutuel betting odds or a gambler's expectation of winning. Please realize that neither of these are physical factors.

Third, an investor has an option to sell his asset. But, a gambler's asset rarely has any secondary retail value. It's not very often that: a race track bettor or lottery player will sell his ticket; or, a poker player will sell his hand. But stock market and bond investors continually buy and sell these assets.

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Hidden Ambiguity

Occasionally, the lines of distinction between investing an gambling can appear to be blurred. For example, consider an options investor. In this case, the investor purchases the right to buy (or sell) an asset for a predetermined period of time. At the expiration of the term, the asset may or may not have any value. This sounds like gambling.

However, two things differentiate options investing from gambling. First, there is an underlying physical product to the option. Second, the investor has the opportunity to sell, exercise, or expire the option. These are all directly under the investors control.

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Summary of the Subtle Similarities

Both successful gamblers and investors understand that favorable outcomes involve probabilities. The skilled player of both professions understands the risks and chances for success. They invest (bet) accordingly.

Both are investing in the unknown. Neither the investor or gambler knows what will happen in the future,  but both are willing to invest their earning with the hope of receiving a future profitable payout.


In our forthcoming articles, we will utilize these definitions to clarify and identify the differences and times to show when investing becomes gambling, and when gambling becomes investing.

Investing or Gambling? Part 1: Introduction

Image by BlatantNews.com via Flickr

When we first created our website and blogs, we strongly believed that playing the lottery was not gambling. Our thought was that since the chances of winning a jackpot prize was so small, one could not realistically gamble on their winning. To us, gambling involved having a reasonable expectation of winning. In games such as Powerball and Mega Millions, it is nearly impossible to have this expectation. Thus, we concluded, these games were not gambling.

However, as we began to study smaller games, such as the Pick 3, we realized that given the right circumstances, a player could achieve a reasonable expectation of winning. In these cases, we do not believe one can expect to receive a mutli-million dollar windfall, but perhaps a continuous 10% or 20% return was possible.

Considering these realistic return percentages, we began to compare realistic returns that investors achieve in the stock or other markets. In good times, a stellar fund may reward investors with similarly high rates of returns. So we wondered:

Can Gambling be Considered Investing?

or

Is Investing Gambling?

To help understand these answers, we have decided to write an investigative comparison of both gambling and investing.

In the issues that follow, we will present:

1. The definitions of investing and gambling
2. Outline why this topic is important at this time
3. Identify the differences between the two of these
4. Present examples of successful investors and gamblers
5. Examine various gambling games and investment options
6. Look at the profile of a typical investor and gambler
7. Compare the mathematics involved in both disciplines
8. Consider whether the outcomes can be manipulated
9. Conclude by quantifying whether investing is also gambling.

During the next 9 weeks or more, we will address each of these topics in detail.  We will try to illustrate the differences between the two concepts and reinforce why all folks should be conservative with their investments. At the end of this series, we will, hopefully, reach a solid conclusion about whether investing may also be gambling; and perhaps more importantly, why you should even care.

A Revised Look at the Mega Millions Megaplier Option

Introduction
When the Mega Millions and Powerball lotteries began cross selling in the previous proprietary States in early 2010, the Megaplier Option was immediately available in the original Powerball states. This has been a popular option to increase prize payouts especially when the Jackpot prizes were low. To help stimulate even more interest, Powerball established a fixed $1 million second place prize for those players who bought the Powerplay. This change helped to increase sales of this option.

To keep pace, Mega Million states pushed to implement the Megaplier. More importantly, the Megaplier second place prize was also increased to a guaranteed $1 million as well. At the time of this writing, nearly every state that sells Mega Millions tickets now offers the Megaplier Option with a fixed $1M prize for those fortunate to match all 5 of the white balls, but not the Megaball.

Thanks to a comment written by an Anonymous author, we were alerted to the recent prize structure change. This post provides the an up-to-date revision of our original Megaplier research post written in December 20007 entitled Should You Buy the Power Play, Sizzler, or Megaplier?

As Mega Million lottery interest has grown since the January 2011 record Jackpot of $355 milllion, many players continue to ask:

Should I Buy the Megaplier Option?

As originally advised,
The correct answer remains both Yes and No!
It depends on the size of the Jackpot,
And Your Strategy.

How would you know when to buy it?
If your lottery playing strategy is to win the Jackpot, we advise that you always buy the Megaplier option whenever the current jackpot value is below its Jackpot Breakeven level.

• For Mega Millions, Breakeven is now $53.1 million: Buy the Megaplier Option whenever the Jackpot is below this value. Never above this. Buy 2 tickets instead.

However, if you strategy is to maximize your prize winnings by religiously playing a consistent set of  numbers, we recommend that you always buy the Megaplier.


Effect of Change?
Because the 2nd place prize is now always fixed, the amount of money returned to Megaplier players has also increased. The net effect of this increase means that the Mega Millions breakeven has increased by $5.9 million from $47.2M to $53.1M.

Note, however, that as the Jackpot increases above its minimum, only the probability weighted amount of jackpot money returned to players increases. This means that all other prize payouts are fixed. Thus, there is always a fixed point (jackpot level) at which the return of single ticket payouts equals the return of the Megaplier ticket payouts.

As lottery players, we want to play the option that returns the most money back to us, the players. As you will see below, your option changes depending on the jackpot level.

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Mega Millions Megaplier
When a player buys the Megaplier option, all  prizes that the player wins, except the Jackpot, will be multiplied by either 2, 3, or 4, depending on what Megaplier was selected. Additionally, the new rules fix the 2nd place prize Megaplier multiplier at 4, regardless of what was picked. This means that the top non-jackpot prize for matching 5 white balls is always $1,000,000. Accounting for this new change, the probability weighted average of all other non-jackpot prizes remains at a multiplier equal to 3.476 times.

Based on this information, the graph below illustrates both the expected Megaplier return (in blue) against the expected return of a single Mega Millions ticket without the Megaplier (in red).

When the jackpot is set to the minimum $12 million, Megaplier returns $0.367 (increased from $0.350) of each dollar received, compared to $0.250 for those without the option.

When the jackpot level reaches $53.1 million, both tickets with and without the Megaplier returns $0.484 of each dollar received. We refer to this $53.1 million as the Jackpot Breakeven level. (Note that previously, the breakeven return was $0.451 at a $47.2M level).

Above this breakeven level, tickets purchased without Megaplier return more to the players. When the jackpot grows to $90 million, $0.694 is returned to straight ticket holders compared to only $0.589 (previously $0.572) to those who bought the Megaplier.







Because the new Megaplier rule is now in effect in most Mega Millions states, the overall monetary return of money received has increased.

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Conclusion
We suggest that all lottery playersshould purchase Lottery Tickets like they would any other investment, and always seek the highest return on their dollars. Thus, when the Mega Millions jackpot is below $53.1 million, the Megaplier should be purchased. When the jackpot is above this level, never purchase the Megaplier. Go for the Jackpot instead.


Learn More
To learn more about this subject, visit our in-depth pages that provide the detailed numbers behind each of these options.

• Revised Mega Millions Megaplier Analysis (February 2011)
• Superceded Mega Millions Megaplier Analysis (Original)
• Powerball Power Play Analysis
• Hot Lotto Sizzler Analysis

The Average 18 Year Old Has 6,255 Chances to Win the Lottery

Have you ever wondered how many chances you have to win a major lottery in your lifetime?

We too have asked ourselves this question many times. So we consulted the U.S. World Factbook and found the average life expectancy of a U.S. resident is 78.4 years. Since a person must be 18 years old to legally purchase lottery tickets, we find that a person has about 60 years in which they can buy Powerball, Mega Millions, or other lottery tickets.

Since these major lotteries have drawings twice a week, there are 104 opportunities to win each year. Multiplying 104 times 60 years, we obtain 6,240. Because of leap years, a player gets another 15 drawings to play. Adding 6,240 and 15 together, we find that there are a total of 6,255 drawings that may be played

Thus, we conclude, that: The Average 18 Year Old Has 6,255 Chances to Win the Lottery

As you get older, the number of opportunities becomes smaller. You can check the table below to see how many drawing you may have left to play.

Age	Drawings
18	6,255
20	6,047
25	5,526
30	5,005
35	4,483
40	3,962
45	3,441
50	2,920
55	2,398
60	1,877
65	1,356
70	835
75	313

Note: These are only averages. Unfortunately, some players may pass away before they reach 78 years old. Others who are more fortunate, can have many more years left to dream.

Lottery Full Wheel Calculators Released

We are proud to announce that we have begun to roll out our new Full Wheel Payout Calculators for the following lotteries:

• Mega Millions Full Wheel Calculator
• Powerball Full Wheel Calculator
• Hot Lotto Full Wheel Calculator 

You can access these pages from the links above, from our Lottery Research Page, or the "Lottery Combo Tables" link on our Lottery Power Picks home page.

While we are still in the bug/shakeout mode, we have decided to provide these calculators to you in a phased mode.

The purpose of these pages are to help you, the lottery players, better understand how much money: it would cost you to purchase a full lottery wheel; you would win if any or all of your numbers were to appear in the associated lottery drawing; and, lastly, how much your profit or loss from that transaction was.

During the coming weeks, we will be testing these pages to make sure that everything works properly. We will also be expanding these pages to include all of our covered lotteries.

We hope this information is helpful and gives you more information about the financial risks associated with playing the large lottery games.

All Hot Numbers Picked in Last Mega Millions Drawing

As many of our readers have discovered, the winning Mega Millions lottery numbers drawn on Tuesday, December 17, 2010 were all Hot Numbers!  The winning numbers were: 11 - 20 - 26 - 46 - 53 and Megaball 12. We have provided an excerpt of these results from our Mega Millions Hot Cold Number Analysis page at left.

While this is a rare occurrence, we believe it is important for players to realize that all systems have merit.

The subset of Hot white ball numbers that we identified consisted of 14 balls; and 9 Megaballs. Limiting ourselves to the white balls only, we would have played only 2,002 combinations.

If we then wheeled each of the 9 Megaballs, we would have purchased 18,018 total combinations.

 The subset of Hot balls (white and Mega) numbers that we identified are shown at right.

The annuity jackpot prize for that drawing was $133 million, but nobody won. Had we played all 18 thousand combinations, we would have won over $135 million.

And, if we chose to play these numbers with the Megaplier, our total winnings would have increased to $141 million because the 4x megaplier was picked as well. This would have been a great return from the $36,036 we would have spent!

Win Money Playing UK Lotto's Hot Picks

Introduction

We recently discovered the UK HotPicks Lottery game. In it, a player can select combinations containing anywhere from 1 to 5 numbered balls. Depending on the balls played, the game offers players a chance to win prizes ranging from £5 to £130,000.

Since the results are based on the first 6 numbers drawn in the UK Lotto (bonus balls are not considered), we examined our UK Lottery Hot and Cold Lottery Analysis results to see if any patterns emerged. What we found was that there was an abundant amount of hot numbers that were selected in a 3-month period (26 drawings).

This led us to investigate whether a winning strategy could be identified, and we concluded that:

Hot Picks Players Could Make
£1,000 to £40,000 per year.

Accordingly, this article explains the following to give you a winning edge:

• How HotPicks is Played
• Winning Ticket Combinations
• How to Select the Balls to Play in the Wheeling Pool
• Example of Wheeling Hot Balls Potential Payout

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How HotPicks is Played

Playing HotPicks is relatively simple. As a player, you first identify if you are playing 1, 2, 3, 4 or 5 numbers. Then, you select the numbers that you want to play from 1 to 49 (no duplicates).

Each ticket costs £1, and the winning numbers are determined from the UK Lotto draw. If all of the numbers you choose on that playing ticket appears in the main first 6 numbers drawn, you win the associated prize.

Table 1: Prizes and Combinations

Balls	Win	Combinations  For Various Balls Played
Played	Prize	49	8	9	10	11	12
1	5	49	8	9	10	11	12
2	40	1,176	28	36	45	55	66
3	450	18,424	56	84	120	165	220
4	7,000	211,876	70	126	210	330	495
5	130,000	1,906,884	56	126	252	462	792

Table 1 above summarizes the various prizes that are paid. Column 1 indicates the amount of numbers you want to match, and Column 2 indicates the prize you will win. For example, if you wish to play 2 numbers, and they are part of the winning UK Lotto combination, you win £40. 

For reference purposes, we have also listed the total number of possible wheeling combinations that may be constructed using various balls. The combinations under the Column Header 49 indicate all the possible combintions available.

The remaining columns indicate the number of possible combinations for limited subsets of 8, 9, 10, 11, and 12 balls. This is important because you have to limit your playing pool if you wish to generate a profit. We will refer to this as your Wheeling Pool which will be discussed below.

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Winning Ticket Combinations

Regardless of the size of your Wheeling Pool, whenever the number of balls that were  selected equal or exceed the number you played, you will own one or more winning HotPicks  tickets.

For example, assume you are playing a 2 ball combinations, and 4 of the selected balls are members of your Wheeling Pool, you will have then have 6 winning tickets.

Table 2: Number of Winning Tickets You Will Have

Balls	Winning Ticket Combinations For Numbers Matched
Played	0	1	2	3	4	5	6
1	0	1	2	3	4	5	6
2	0	0	1	3	6	10	15
3	0	0	0	1	4	10	20
4	0	0	0	0	1	5	15
5	0	0	0	0	0	1	6

The easiest way to determine how many tickets have won is follow these steps:

• Write Down the numbers in your Wheeling Pool
• Write Down how many of these numbers were drawn in the UK Lotto that night
• Look for the number of balls you played in the first column
• Then read across that line to find the number in the heading you matched.

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How to Select the Balls to Play in the Wheeling Pool

Since the Hot Picks results are based on the first 6 numbers drawn in the UK Lotto (bonus balls are not considered), we can easily examine the UK Lotto Hot Cold Number Analysis page to determine which subset of numbers we should play in our Wheeling Pool. Looking at the table in the top right portion of the page, we will see the White Balls listed in the "Warm + Hot" cell. These are the latest set of Hot Numbers and should be played.

By clicking on the Tab labeled "Last 26 Results", you will be able to see how these numbers performed during the past 26 weeks. The Hot Numbers will be displayed in Red and would be the numbers that you played.

Note however, that as time goes by, the balls will change. Therefore, you should always refer to this page before playing in the next Hot Picks drawing.

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Example of Wheeling Hot Balls Potential Payouts

At present, our Hot Ball Wheeling Pool contains 9 numbers. Table 3 below summarizes the Potential Earnings we would won playing these numbers for the past 3 months (26 drawings).

As shown, the vertical columns labeled 1, 2, 3, 4, and 5 indicate the number of balls we wish to play. Immediately below is the amount of money we would have spent  buying all the possible combinations.

In each horizontal row, we summarize how many times we would have matched 0 to 6 of our Hot Ball numbers. The total number of tickets equals the number of times we won times the  number of winning tickets for each drawing.

The last (bottom) row displays the profit or loss that we would have earned playing these 9 numbers.

Table 3: Example of 3 Month Potential Earnings 
(September 8 - December 4, 2010)

		Total Number of Tickets Won Past 26 Weeks
	Numbers Played	1	2	3	4	5
Combos	Bought	9	36	84	126	126
Matched	Times Won
0	6	0	0	0	0	0
1	4	4	0	0	0	0
2	11	22	11	0	0	0
3	3	9	9	3	0	0
4	2	8	12	8	2	0
5	0	0	0	0	0	0
6	0	0	0	0	0	0
26 Game	Total	43	32	11	2	0
	Unit Prize	5	40	450	7,000	130,000
26 Game	Total Won	215	1,280	4,950	14,000	0
26 Game	Total Spent	234	936	2,184	3,276	3,276
26 Game	Profit	-19	344	2,766	10,724	-3,276

As shown,  players would have won anywhere from £344, £2,766, to £10,724 if they played either 2, 3, or 4 ball combinations.  Since these results are for a three month period, it is estimated that UK Lottery Players could profit approximately £1,000, £8,000, to £42,000 annually.

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Conclusion

If you are a serious Lottery Player who is trying to earn extra income, we recommend that you seriously consider adopting the strategy described above and play the UK HotPicks game.

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Learn More

• Players' Guide to Lotto HotPicks
• Play Lotto HotPicks Game Procedures

HotPicks Analysis Delayed

Image via Wikipedia

As we were preparing our new analysis for this lottery game last night, our computer system became infected with a virus named: "Antivirus Action".  This malicious intruder has crippled our computer entirely, preventing us from accessing and running most of our programs, including the internet.

We are working with tech support representatives of our Anti Virus provider to help us restore functionality.

At present, we are unsure how long this process will take, but once everything is back to normal, we will complete and publish this important UK Lotto Hot Picks guide.

Thanks for your understanding and patience.

Lotto HotPicks Analysis to be Published Next Week

As part of our Lottery Wheeling Calculator development, we have been re-examining our various covered lotteries. To this extend, we discovered the UK Lotto HotPicks game which allows a player to simply select and play a 1, 2, 3, 4, or 5 digit combination. If their chosen numbers are present in the official UK Lotto drawing numbers, then the player wins £5, £40, £450, £7,000 or £130,000.

While this game features smaller prizes than the UK Lotto, it only costs the player  £1 per entry.

And, after reviewing our UK Lotto Hot Cold Number results, we believe that utilizing those numbers with this game could reward lottery players often with a positive cashflow.


The results of our analysis will be published on this blog by the end of next week, so remember to visit our site and learn more.

Estimating Probability of Back to Back Lottery Jackpot Winners Using the Poisson Distribution - Part 3

Part 3: Introduction
In our previous article, we provided an example of how the Poisson Distribution could be used to estimate the probability of multiple jackpot winners (Poisson Distribution Example of Use in Lotteries - Part 2). To carry the application of this statistical model forward, we will calculate the likelihood of there being back to back lottery jackpot winners in both Powerball and UK Lotto. We choose these two games because the frequency of winners in these two games vary immensely.

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Poisson Distribution Utilization Review
The Poisson Distribution is a tool used to predict the probability of a discreet event occurring. To use it, there must be a clearly defined observed set of outcomes. Those outcomes are summarized and described as a single average. The distribution of varying events therefore becomes a function of this average.

For example, assume that we wish to define the probability that we will observe 3 automobiles queued at a stop light. The traffic signal changes to red only once an hour. From our previous collection of data, we know that the average length of the queue is 4.8 cars per hour. Substituting these numbers into our Poisson equation, we find that there is a 15.2% chance that the following queue will contain 3  cars.

Now we shall apply these same principles to estimating the probability of a lottery jackpot being won two consecutive drawings in a row.

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Example 1: Estimating the Probability of Back to Back UK Lotto Jackpot Winners.
The UK Lotto is the national lottery of the United Kingdom. Since it is a 6/49 game, the approximate number of combinations is about 14 million. By U.S. standards, this is rather small. Being the country's primary game, the average drawing ticket sales range from approximately 14 to 32 million.

Since ticket sales meet or exceed the number of combinations, the UK Lotto jackpot is won on an average of every 1.283 drawings. To calculate the likelihood of there being successive jackpot winners, we must reduce this average by one (to 0.283), and solve for the 0 (zero) event. In effect, we do this to change from a one base to a zero base.

Solving, we find that there is a 75.4% chance that two UK Lotto jackpots will be won in two consecutive drawings. By comparison, we calculated that back to back winners occurred 77.9% of actual time.

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Example 2: Estimating the Probability of Back to Back Powerball Jackpot Winners.
By comparison, Powerball is one of two national lotteries of the United States. Its format requires players to correctly pick 5 of 59 white balls and 1 of 39 Power balls in order to win the jackpot. Expanding this out, we find that there are over 195 million possible combinations. Since this is so large, the jackpot is not won as often as the UK Lotto.

Summarizing Powerball drawing results from 2001 to present, we learn that there are approximately 8.95 drawings between jackpot winning draws. Converting this average to a zero base (7.95 average) and solving for the 0 event (back to back winners), we calculate that there is only a 0.04% chance that there the jackpot will be won in two sequential drawings.

By counting the actual number of times this has occurred in Powerball, we find this happened only 7 times since 2001, or 0.68% of the time.

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Conclusion
Comparing the expected probabilities derived from the Poisson distribution to the actual number of occurances, we conclude that the statistical results of back to back winners is a fairly good approximation of reality. While the Poisson distribution underestimates reality in both cases, we believe that the results obtained can be confidently used to predict these lottery events.

Related articles

• Free Lottery: Tips to improve your chances of winning the lottery (mirror.co.uk)
• Man considers the lottery his "job" (seattletimes.nwsource.com)

Poisson Distribution Example of Use in Lotteries - Part 2

Part 2: Introduction
Last week we introduced the Poisson Distribution stating that it is used in statistics for quantifying the probabilities of discreet  random events. In our post Using Poisson Distribution to Understand Lottery Events - Part 1, we described its mathematical properties, formula, and variables. In this article, we will provide an example of how the Poisson Distribution can be used to help us understand events related to lotteries.

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Example: Estimating the Probability of Multiple Jackpot Winners.
In this example, we will estimate the the probability that there will be 0, 1, 2, ... 5 winning tickets in tonight's Mega Millions lottery drawing which offers an annuity jackpot of $84 million.

In order to do this, we must first calculate the "expected number of winners" as defined in How to Analyze the Lottery. There, we learn that we need 2 pieces of information:

1. The expected number of ticket sales, and
2. The total number of unique combinations.

Using Mega Millions Lottery Sales By State, we find that last Friday's ticket sales were 25.4 million when the jackpot was $72M. Using a simple proportion, we will expect tonight's tickets sales to be 29.6 million. Then, from our Lottery Power Picks website, we find that there are 175.7 million combinations. By dividing the expected number of ticket sales by the total number of available combinations, we calculate the "expected number of winners" to be 0.169. In Poisson Distribution terms, this number becomes the known mean, or constant variable r = 0.169

Next we construct a table where: the mean variable r remains constant; and the variable k (which represents the random number of winners) ranges from 0 to 5; and, the associated Poisson probability is solved as variable p(k).

r	k	p(k)
0.169	0	0.8445
0.169	1	0.1427
0.169	2	0.0121
0.169	3	0.0007
0.169	4	0.0000
0.169	5	0.0000

Thus reading our table, we learn that there is: an 84.45% chance that there will be no winners in tonight's Mega Millions drawing; a 14.27% chance that there will be one winner; a 1.21% chance that there will be 2 winners; a 0.07% chance that we will have 3 winning tickets; and virtually 0.0% chance that there will be four or more winners.

So, we'll look tomorrow at the Mega Millions drawing results to determine which of our random scenarios occurred.