"Gambling may be defined as an activity in which a person subjects something of value - usually money - to a risk involving a large element of chance in the hopes of winning something of greater value, which is usually more money."

"commercial gambling is the staking of money on the outcome of a random number generator"

"casinos are places of amusement but they are also serious business"

Question No. 1

Assuming gambling operators conduct legal businesses and that they sell entertainment, how does their product differ from other forms of entertainment such as the theatre, restaurants or golf courses? More precisely:

• What is the goal of gambling?
• What does the gambler pay for a gambling experience?

Notes on Question No. 1

The theatre-goer gains entertainment from becoming absorbed in the performance. The golfer is entertained by becoming absorbed in his game. The gourmet becomes absorbed in the smells and tastes of his food and the pleasure of eating it. In addition, these customers enjoy the environment and social interaction surrounding their chosen forms of entertainment.

In each case, the customer derives value from his activity: the satisfaction of viewing a good theatre performance, the satisfaction and exercise of a round of golf, the satisfaction of a gourmet meal.

And the customer pays a set price for the valuable service provided. A theatre company sells tickets to a customer who, in return for the purchase price, can sit and watch a performance. A golf club, in return for a fee, enables a customer to hit a ball around a golf course. A restaurateur, in return for the price of a meal, gives a customer a gourmet meal.

Gambling is different in two respects.

First, the satisfaction sought by the gambler is, strictly speaking, measured in terms of money. The gambler might enjoy the activity of gambling but his central objective is to make money. The great nineteenth-century card expert "Cavendish" (Henry Jones) justified playing a rubber of Whist for small stakes on the ground that the stake served to "define the interest of the players". [Source: David Parlett "The Oxford Guide to Card Games" Oxford University Press 1990 at page 12]

Secondly, the price paid for the gambling experience is not a fixed price but is variable. The gambler is placing his money in a chance ebb and flow environment where he will win or lose - or, perhaps, break even. The gambler may well come away with more money than he outlaid in short sessions of gambling.

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Quotation No. 1

[Glenn Schaffer, Chief Financial Officer, Circus Circus Enterprises - from David Spanier "Welcome to the Pleasure Dome" University of Nevada Press at page 108]

Quotation No. 2

[Source: Benny Binion, former Las Vegas casino owner - from David Johnston "Temples of Chance" Doubleday 1992]

Question No. 1

Licensed gambling operators in Australia today are honest. What reasons can you think of for this?

Notes on Question No. 1

Historically, gambling operators often cheated. Today, licensed gambling operators in Australia are conducted honestly. The reasons are the same as those given by Mario Puzo (author of "The Godfather") for the honesty of Las Vegas casinos:

Casino operators now understand the mathematics of gambling and know how to structure games so that on average the casino will make money.

Governments have very tough laws and close policing. (State governments have an enormous amount to lose with a dishonest gambling operator. Not only would the government lose taxes but dishonesty would encourage the infiltration of organized crime into the gambling industry and cause enormous embarrassment to the government resulting in loss of gambling turnover and risk of federal government intervention.)

Gambling operators' licenses are very valuable and the forfeiture of a licence because of dishonest behaviour would be an enormous loss.

A gambling operator which acted dishonestly would expose itself to blackmail.

A gambling operator which acted dishonestly would lose customers. Running a gambling operation is like any business - if you do not treat the customer well you will lose business.

[Source: Mario Puzo "Inside Las Vegas" Grossett & Dunlap 1977 at page 137]

Additionally, commercial gambling in Victoria is run by large corporations owned by numerous shareholders and employing large numbers of employees and consultants. Unlike some early USA casinos which were run by mob families, there is no real incentive or opportunity for the casino owners, who consist of large numbers of shareholders with no hands-on access to the business, to cheat.

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Quotation No. 1

[Source: John Scarne "Scarnes's New Complete Guide to Gambling" by Simon & Schuster 1986 at page 458]

Discussion

Gambling operators conduct businesses and the prime function of a business is to make a profit, so the gambling operator has to have a way of making a profit.

A gambling operator makes a profit by having the gamblers gamble at a disadvantage to the gambling operator. Another way of looking at this is that the gambling is structured so that, on average, the gambling operator pays out less than he gets in.

Consider a hypothetical gambling operator who provides a simple game: tossing a coin. The way of calculating the true odds of any game is to count up all the ways the gambler can win and compare it to all the ways the gambler can lose. Suppose in the case of the coin-tossing game the gambler bets on heads. The possible outcomes are heads or tails.

Thus the gambler has one chance of winning and one chance of losing; the odds are 1:1. If the gambling operator pays out at the true odds, one dollar for each dollar bet (this is known as an even money bet), the gambling operator will, on average, break even and make no profit.

A casino pays even-money odds to a gambler who bets on red on a roulette wheel. The gambler who bets a $1 stake wins $1 if the ball lands on red. The gambler loses $1 if the ball lands on black or green. There are 18 red pockets, 18 black pockets and 1 green pocket.

Question No. 1

How many ways can the gambler win if he bets on red?

Question No. 2

How many ways can the gambler lose?

Question No. 3

On average, what is the ratio of the moneys that will end up with the gambler and the house respectively?

Question No. 4

How would you express the gambling operator's advantage as a percentage? This is the same as saying - on average, how many extra wins would the gambling operator expect per 100 plays?

Discussion

If you examine a roulette wheel you will see that the roulette wheel (in use in Australia) has thirty-seven spaces. Eighteen are red, eighteen are black and one is green. Suppose the gambler bets on red:

· the ball lands on red - the gambler doubles his money.

· the ball lands on the black or the green - the player forfeits his bet.

Answer to Question No. 1

There are eighteen chances that the ball will land on the red and the gambler will win.

Answer to Question No. 2

There are nineteen chances that the ball will land on the black or green and the gambler will lose.

Answer to Question No. 3

The odds are thus 18:19 against the gambler. Another way of looking at it is that the gambler is paid out at less than the true odds. The true odds are 18 to 19. That is, if a gambler stakes $18 on the red and wins, the gambling operator should pay $19. In fact, paying out at even money, the gambling operator pays $18, one dollar less than payout at the true odds.

To find the true odds against the gambler one counts all the possible outcomes and sees how many of those the gambler will win. In a right bet at craps, there are 1980 different results of which 976 are winning results for the gambler and the others (1980 - 976) 1004, are losing results. The odds are thus 976/1004 against the gambler.

Answer to Question No. 4 

Another way of expressing this is that the house has a margin. This margin is expressed as a percentage. In the case of a red or black bet on roulette this margin is 1 in 37. That is, in every 37 spins the casino can be expected, on average, to win one more bet; 18 to 19. To work this margin out as a percentage we ask, if the casino wins one more every 37 spins - how many more will it win every 100 spins. The answer is, of course, 1*100/37 = 2.7%. The house percentage on a straight black or red bet on roulette is thus 2.7%.

Looking at it from the gambler's viewpoint, if the house has a 2.7% margin, the return to the gambler will be 100% minus 2.7%, a 97.3% return. On average, for every $100 bet on the wheel by the gambler, the house gets $2.70 and the player (the gambler) retains $97.30.

With gaming machines, the house percentage cannot exceed the maximum 13% allowed by Victorian law. [ Source: Gaming Machine Control Act 1991 (Victoria) section 135] To take another example, in one type of bet at craps (a casino dice game) known as a "right bet", there are 1980 different results of which 976 are winning results for the gambler and the others (1980 - 976) 1004, are losing results. The true odds are thus 976/1004 against the gambler.

To work out the gambling operator's percentage we ask, on average, how many extra bets will the gambling operator win per 100 bets. In every 1980 results the house on average wins 28 ie (1004 - 976) more bets than the gambler. Thus every 100 results the house wins 28 x 100/1980 = 1.41%

Modern "pokies" are called electronic gaming machines and they are run by computers but they simply emulate early machines which were developed last century called gaming machines or reel machines. These machines have a number of reels in them which generate a number of combinations - say a total of 1000. The way to work out the house percentage on a poker machine is to see how much would be paid out if the machine stopped at each possible combination in turn - from 1 to 1000. You add up all the possible prizes that can occur if the machine stops at the first position, second position, third position ... up to the 1,000th position and these prizes might total perhaps 900, 900 coins out for every 1,000 coins in. Thus the true odds for the gambler are 900:1000 against the gambler. The gaming operator wins 100 extra coins for every 1000 coins put into the machine so to work out the house percentage we ask how many coins can the house expect to win for every 100 coins put in. The answer is 100*100/1000 which gives a house margin of 10%.

Take win bets on the horse-betting totalisator. The totalisator forms a win pool into which all moneys are paid. Then, when a horse wins, the totalisator deducts taxes and profits of, say, 15% and divides the remaining 85% amongst the winning bettors in proportion to the amount of their bets. Thus, if the gambler can expect to get, on average, $85 back for every $100 he bets, the odds are 85:100 against the gambler. The house percentage is, of course, 15%.

Bookmakers try to adjust their payout odds so that no matter which horse wins, they will have received, say, $115 in bets for every $100 paid out in wins. Take a very simple example. Imagine a race with 6 equally matched horses and one bettor for each horse wanting to bet $20 to win. The bookmaker could fix odds of 4 to 1 on each horse. Thus the bookmaker would take in 6 bets of $20 ie $120. No matter which horse won, the bookmaker would pay the winner (at 4 to 1 odds) by returning the $20 wager and paying an additional four times as much, $80. Thus, no matter which horse wins, the bookmaker takes in $120 and pays out $100 for a profit of $20. The odds against the gambler are 100:120. That is, for every $120 the gamblers put in, they get back $100.

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Quotation No. 1

[Source: Old computer programmers' saying - see George Skarbek - Age Newspaper 3 October 1995]

Quotation No. 2

"One of the most striking and fundamental things about probability theory is that it leads to an understanding of the otherwise strange fact that events which are individually capricious and unpredictable can, when treated en masse, lead to very stable average performances."

[Source: Warren Weaver "Lady Luck - The Theory of Probability" Dover Publications Inc NY 1963 at page 361

Quotation No. 3

[Source: John Scarne "Scarnes's New Complete Guide to Gambling" by Simon & Schuster 1986 at page 19]

Discussion

Although randomness implies the absence of certainty, randomness itself is subject to its own laws.

The principle law is popularly known as the law of averages (the law of large numbers). Simply stated, this means that where a large number of events occur truly randomly, the occurrence of the events will, though random, be very close to the result which one would expect in theory.

In other words, the greater the number of events, the greater the tendency for the actual result to accord with the theoretical result.

Look carefully at the above table. It is a computer-generated simulation of a coin being tossed increasing numbers of times.

Question No. 1

What happens to the percentage variation between heads and tails as the coin is tossed more?

Question No. 2

Is there an exact correlation between the increasing number of throws and the percentage variation?

Question No. 3

Does the difference between the actual numbers of heads and tails thrown tend to increase or decrease with the increasing number of tosses?

Question No. 4

If a coin has been tossed ten times and it has come up heads each time, what are the chances of it coming up heads on the eleventh toss?

Discussion

The purpose of this exercise is to educate about the way randomness behaves. We have already considered ways in which randomness might be generated.

This was recognized at least many centuries ago. The odds that certain events would occur in card games was first documented in a book titled: "Book on Games of Chance" written by an Italian scholar, Giralamo Cardano, in 1564. [Source: David Parlett "The Oxford Guide to Card Games" Oxford University Press 1990 at page 52] This predated Pascal, who is normally regarded as the father of probability theory, by more than a century!

Answer to Question No. 1

The more the coin is tossed, the greater is the tendency for the percentage variation to approach zero. This accords with the law of averages which states that where there is a large number of truly random events, the actual result should approach the theoretical result. In this case, the theoretical result is 50% heads and 50% tails which gives a percentage variation of zero.

Answer to Question No. 2

It can be seen that the correlation is not exact. At times the percentage variation increases with increasing numbers of tosses. Note that the law of averages describes a tendency.

Answer to Question No. 3

With increasing numbers of tosses, the actual difference in the number of heads and tails tends to increase. It is the percentage variation that tends to decrease. From the point of view of the gambling operator, it is the percentage variation that is important.

Answer to Question No. 4

The law of averages does not apply to small numbers. [Source: David Spanier "Easy Money - Inside the Gambler's Mind" Penguin 1987 at pages 152 and 153] Take tossing a coin. Each event is separate. Each time we toss the coin the chances of it coming up heads or tails is 50:50. If the coin has come up ten heads in a row, the next time we toss it, the chances of it coming up heads is 50:50. The coin has no memory. The odds of a coin coming up ten times in a row is 1 in 1024 and the chance of it coming up eleven times in a row is 1 in 2048. However, the fact that the coin has come up ten times in a row is past history at the time of making the eleventh throw. The law of averages only works on large numbers and it is a tendency, not a strict rule.

Further Discussion

In the short term the player can bet and win against the odds. (He is more likely to lose.) However, the longer the player plays, he is increasingly likely to lose and increasingly likely to lose more. [Sources: Bob Sehlinger "Unofficial Guide to Las Vegas" Macmillan Travel 1995 at page 266. "Although 1% doesn't sound like much of an advantage, it will get you if you play long enough": Sehlinger (supra) at page 270. "However, I must remind the reader that any gambler must lose in the end if he repeatedly takes the worst percentages in any game, whether his disadvantage is a low of 1 percent or a high of 10 percent or more.": John Scarne "Scarnes's New Complete Guide to Gambling" by Simon & Schuster 1986 at page 296. For an excellent discussion on the law of averages read Sehlinger (supra) at pages 265 - 282.]

Just to clarify this point of losing more, let us say a gambler is placing $10 bets on even money bets on the roulette wheel. On average the gambler should be down 2.7% of moneys bet. Suppose after 1000 spins ($10,000 in bets) the gambler is down 5% ($500). The gambler says the wheel should "come back" to around 2.7% over time and he is probably right. But suppose the gambler sticks with the wheel for 10,000 spins and suppose it does come back to 2.7%. The gambler is only down 2.7% of the moneys bet but the gambler has bet $100,000 and thus he is $2,700 behind. The result is set out in the table below:

It should also be pointed out that the law of averages applies to a person's total amount of gaming whether it is conducted in one session or spread out over years, whether it is conducted at one casino or venue or carried out in casinos or venues all over the world.

Gambling against the odds is a little like running a cross-country race against an evenly matched competitor (the casino) over undulating country when you both start off at the same level and take different paths of equal length. However, your competitor finishes at a lower level than you. At times, when you are going downhill you will run faster than your competitor (you will have a run of cards, the dice will be "hot" etc) and at other times, your competitor will be going downhill and running faster than you (the cards will be running against you, the dice will be "cold" etc). However, in the long run, your competitor will get more downhill running than you because his finish is on a lower level. Over time, your competitor will slowly draw ahead.

One other matter which should be considered is the matter of "volatility". The law of averages states that where there is a large number of truly random events, the actual result should approach the theoretical result. Our senses would tell us, however, that while we may need to toss a coin only thirty or forty times before the law of averages started to manifest itself, in the case of the roulette wheel with 37 numbers, we would need to have a larger number of spins before each single number started to approach the same percentage as the other numbers. This is correct. Betting a single number on a roulette wheel will tend, in the short term, to bring about larger fluctuations of wins and losses than betting on even money propositions such as red and black; this tendency to wide swings is known as "volatility". An extreme case of volatility is to be found in the lotteries where a bet of a few dollars may win hundreds of thousands. Betting at volatile games increases the player's chances of large wins but correspondingly increases the player's chances of large losses. The player is always, of course, fighting the house percentage.

The law of averages applies to a person's total amount of gaming whether it is conducted in one session or spread out over years, whether it is conducted at one casino or venue or carried out in casinos or venues all over the world.

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Quotation No 1