A Walk Through Gambling, Insurance, Investments and Probabilities, or Why Investing Isn't Gambling, Although It Can Be


“Is investing the same as gambling?”

Today I would like to share some views regarding a question that many new or to-be investors make: Is investing the same as gambling? The point is not to discuss semantics, but to address a doubt that many people have when they are presented with the possibility of investing in the financial markets: Wouldn't I be risking my savings as foolishly as if I gambled with them in a casino or at a poker table? I guess I won't be throwing away much suspense if I advance you that my answer is no, but it is the reasoning behind that answer that I consider worth sharing, and the concepts that will be applied to the argument, which have an important role in investing. For suspense, it remains to be seen how I will introduce insurance into this picture.

As I was saying, the point is not to discuss the semantics of investing, gambling and insurance. That would take us to endless arguments. For example, if we say gambling involves a game, some may state that for professional gamblers it is not or that investing can be fun too, and so on. So lets keep dictionaries aside and analyze each practice.

Gambling & Probabilities

If we are playing a game of chance that requires skill, such as poker with friends, then we might win money systematically if we play better than the rest. Our gain would be equal to the sum of our friends' losses, because gambling is a zero-sum situation. Needless to say that, if we take that to be a money-making mechanism, it doesn't look rewarding nor sustainable...

Lets say that, after we have taken so much from our friends that they don't want to play anymore (that is if they still speak to us), we go to a casino to play Roulette. Although there may be others playing at the table, it is a zero-sum game between us and the house only, because we are not competing with the rest. But the casino is not like any kind of player. They are a company, with costs to cover and revenue to make in exchange for the service they are providing. Therefore, to make sure they have income, they set the rules so that they win more, in average, than their customers.

The Casino wins that small fraction of the sum of all bets, and it doesn't matter what betting system we use

The roulette has 38 numbers if it includes a double–zero (U.S. style) or 37 if it doesn't. If we bet on a color, only 18 of those numbers favor us. So our chances of winning are 18-in-38 (or 18-in-37 but lets use double–zero roulettes in our examples from now on), which is slightly less than a 50%, but the house will only pay twice our bet if we win. For our chance of winning money, in the long run, to be exactly the same as the casino's, they should pay us 1/9 more of what we bet (or 1/18 of what they are paying, which is the same), because 18/38 times 2 1/9 equals 1 (if you don't understand the reason for this multiplication it doesn't matter, just take my word that 1/9 more would even the odds). That bit that they're not paying is their profit.

Betting on single numbers leads to the same. Only one number in 38 favors us, but the reward is 36 times our bet, when it should be 38 times if things were to be made even. If we bet a chip, there are two chips "missing" from our reward, which equals to 1/18 of what they pay to us, just like before.

Some people may think that its ok if they charge like this, only when we win, since we can give away part of our profits and our result would still be positive. But it is a fallacy. There'll be lucky spins and unlucky ones, if we are given less money during the lucky ones and we are taken the normal amount on the unlucky ones, then our net result will be negative. We need a "fair" return in the lucky spins so that we can stand the unlucky ones. There is an analogy with investing, when some professionals and companies charge too high a fee for investing other people's money. During bull markets (that is, markets on the rise) their customers may be ok with the fee, probably unaware of it, as they are having profits anyway. But on bear markets the high fee shows, as customers lose their assets' value plus the high fees that they are charged with. In the long run, their return is lower than reasonable, as lower as the unreasonable portion of the fee.

The last paragraph can be illustrated with the Roulette example. The casino keeps 1/18 of every prize. Isn't that the same as keeping 1/18 of all money that is bet? Of course it is. Think of it. Imagine there are a zillion bets being placed in a magical ideal casino that has no profits, because the rules don't contemplate a small reward for the casino (e.g., its Roulettes have no zeros). Some players will win their bets, others will lose, but the total amount of money on the tables before and after the spins will be more-or-less the same, since the bets are plentiful. I mean, if you toss a coin a thousand times, very close to half those times it will show tails (this is due to what they call The Law of Large Numbers in the theory of probability). So the sum of all players' money, after the spin, will be practically what they had before, because the odds were even. What if the magical casino charges a 10% fee on those receipts? Wouldn't that be the same as charging a 10% on the money that was bet? For the same reason, keeping 1/18 of every prize is like keeping 1/18 of every bet.

If we are given less money during the lucky spins and we are taken the normal amount on the unlucky ones, then our net result will be negative

In average, the house wins that small fraction of the sum of all bets and it doesn't matter what betting system we use, because each spin is uncorrelated. What if people retire after winning one dollar? It won't work, because the time they lose the first bet and spend the whole night without recovering will cancel all their previous (meager) earnings. It's just that each bet is a bet, no matter if it's done by the same person or another one, the same day or the next or whatsoever. If people bet double-or-nothing each time they lose on a spin? It won't work! When players bet insane amounts because of that system, the house is more than happy to see so much money being put on the tables, as they are bound to win a fraction of all money being bet.

If we apply the previous math to roulettes with no double zero, where our chances of winning are slightly higher (18-in-37), the result is that the house keeps only 1/36 of the sum of bets. That is only half of what the casino earned before, so one might be tempted to conclude that the single-zero roulette makes roughly half the profit. That wouldn't be necessary true, since the money being bet would probably be less if they were double zero, because casino profits have more to do with the quantity of visitors, their wealth and their behavior. Anyway, that was a side note, what is important here is to notice that in a game like Roulette, the rules are such that there is a profit for the casino, because they wouldn't be in that business if it weren't so. No wonder there are no roulettes with no zero, where casino profits would be nil.

Proceed to the next part of "A Walk Through Gambling, Insurance, Investments and Probabilities, or Why Investing Isn't Gambling, Although It Can Be"

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