A Cursory Look At Gambling And The Laws of Probability

A Cursory Look At Gambling And The Laws of Probability

One tool useful in evaluating the financial feasibility of projects is the sensitivity or responsive analysis. This process permits posing the question – what if? What if the room rate in a hotel was such and such, what if – the interest rate on borrowed capital was higher or lower and so forth. Sensitivity analyses identify and quantify variables that impact on the project and specify the consequences. The method differs from that of a risk analysis which provides an indication of the likelihood that an event will occur.

The latter involves the laws of probability, laws that casino operators know very well. They know, for example, the odds against getting any one of four possible Royal Flushes in a hand of poker are 649,739 to 1; they are aware that the odds of drawing any one of 624 possible hands of – four of a kind, that is four 2’s, four 10’s, etc., are 4,164 to 1; that in a roll of two die, the odds against a single roll of 2, (snake eyes) are 35 to 1. They know if you throw a six faced die once, the chance of getting a 1 or 6 is 1/3; getting an even number is 1/2; less than three -1/3 and less than 5 -2/3. How does a poor ol’ country boy know that? I looked it up in the World Almanac.

One of the cornerstones of the theory of probability is the “law of great numbers” which states, in simplified terms, that the larger the number of tries the closer the ratio of hits to misses will approach chance expectation and, conversely, the larger the number of tries, the greater the odds against persistent deviations from that ratio. Economists and professional gamblers are not statisticians, nor are they mathematicians, but they use a smattering of both tools and know, or should know, that a paradox exists in the fact that probability theory is able to predict with uncanny precision the overall outcome of processes made up out of a large number of individual happenings, whether the issue involved is gambling, the annual number of divorces or dog bitings, each of which in itself is unpredictable.

In other words, both observe a large number of uncertainties producing a certainty, a large number of chance events creating a predicted outcome – generally that is. Seems a little weird doesn’t it? What it means in terms of gambling is – the more money you have to wager, and if you pace yourself in betting, the longer you can stay in the game and thus the greater your odds for winning. The less money you have, and the larger your bets, the shorter the length of time you can play and thus the greater your odds for losing. All professional gamblers know this, but I’m not certain they all know why they know it. The lesson to be learned being that if you must gamble, and have a small amount of money, wager small amounts so you can stay in the game longer and thereby improve your odds of winning. The striking thing about the probability theory is that it leads to an understanding of the otherwise strange fact that events that are individually capricious and unpredictable can, when treated totally en mass, lead to very stable average performances.

Citing an example, unrelated to gambling, the circumstances which result in a dog biting a person seriously enough to be reported to the health authorities would appear to be complex and unpredictable. Yet in a report cited in the New York Times ”in New York City after the first year of study there were on the average 75.3 reports per day of dogs biting people; in year two – 73.6; by year three – 73.2; and in years four and five – 74.5 and 72.6 respectively. Mathematical probability can therefore be said to be proportionate possibility. The mathematician’s definition of what is probable is concerned with what may happen, and is relevant to calculations of practical value only in so far as circumstances warrant the belief that events occur with corresponding frequency in real life. For example, in the game of roulette, the odds of a bet on black winning as opposed to red is 50 – 50. This leads to a paradox in the theory of probability resulting from the fact that the outcome of a croupier’s throw is not causally related to the outcome of previous throws. The longest series of black coming up was 28 straight times in a row. Never-the-less the chances of black turning up on the 29th roll was still 50 – 50. And how does the roulette ball know that in the long run zero must come up once every 37 times? So much for the laws of probability. Returning to the subject of sensitivity analysis, there has been quite a bit in the news lately relative to the pros and cons of casinos in the Commonwealth and while I’m not a gambler, I became interested in the impact such facilities might have on only one issue, that being the generating of Business Gross Revenue Taxes, (BGRT), and undertook my own sensitivity analysis to ask, what if the following occurred?

Assuming that it takes two years to construct the facility, tourist projections indicate that we can expect 893,00 tourists in 1998 assuming, of course, the hotel rooms are available to accommodate this number of visitors. If fifty percent of the tourists visit the casino only one time and spend (lose) one hundred dollars each, the revenue generated by gaming activity alone after the payout to those that had winnings would be $44.6 million. The five percent business gross revenue tax thus generated if levied on the casino’s net gaming income would equal $2.2 million. This is a very conservative estimate since it is likely those visitors with a propensity to gamble would visit the casino more than once and spend (lose) more than one hundred dollars each. Consider that two players are seated at a table, the first one bets $1,500 and loses, the house takes possession of the money and has grossed $1,500. The second player wins $500. Should the gross revenue tax be levied on the initial house take of $1,500 or the house net of $1,000? Of course, the casino operator would obviously prefer the latter, but would that figure be considered gross? I don’t know. One thing is certain if and when casinos get off the ground, the latter is a greater incentive for investment than the former.

The annual amount of money mention above is only the tip of the ice berg. A full service, first class casino will earn additional revenue from room sales, food and beverage income, space rental and revenue from ancillary services such as stage shows. One analysis indicates that a 350 room hotel with competitive room rates operating at an 80 percent annual occupancy can generate approximately $23.1 million in gross revenue annually and pay $2.9 million in room and business gross revenue taxes. It should be realized, however, that any measure of the profit potential of a new project is nothing more than an elaborate combination of estimates, the calculations of which rest upon the estimated cost of the project; estimated operating and marketing costs and estimated earnings from sales. To the extent that any of the above are in error, then the final estimated profit (or loss) will be in error. Hazardous as it is, it is an improvement over the intuitive method which some would employ without any attempt to measure the factors involved.

Estimating the number of visitors likely to visit the casino is the subject of a marketing study and not a financial feasibility study. It is very difficult to determine the multiplier effect of casino gambling within the economy since there is both a positive and negative effect on the amount of money in circulation. Obviously money spent (lost) on gaming is not directly available for other discretionary purchases by the individual at play. On the other hand, the casinos will employ people, make local purchases, pay taxes, etc., and possibility be an additional incentive for some to select the island as a vacation destination. Casinos provide another attraction to enhance the area’s “overall” tourist plant and negate any advantage that a competing tourist destination might have in offering this activity for the enjoyment and challenge to this particular segment of the visitor market.

Casinos in some countries do not permit residents to gamble but they can enter and enjoy the restaurants and stage shows. Personally, I don’t have an opinion one way or the other about the existence of casinos in the Commonwealth, but I find it interesting to write about. The safest way to double your money is to fold it over and put it in your pocket.