A Walk Through Gambling, Insurance, Investments and Probabilities, or Why Investing Isn't Gambling, Although It Can Be (Part 3)

This is part 3 of a 4-part article that begins here, with the previous part being here.

So should we play Black Jack instead?

“With expected values being negative, it is useless to diminish risk as much as we can, because we would only be ensuring a negative result”

With more-interactive games like Black Jack and Baccarat it is not as easy to relate the amount betted with the house's expected profits, if any, because player skill comes into play. Clearly, if Black Jack is played poorly, the house will win quickly. But it would be relevant to know what the odds are if it is played perfectly, namely with all decisions taken so as to maximize the odds for the players, given the information available to them. Calculating that is complex and, to complicate things more, casinos frequently change a few rules here and there, altering the odds. But let me present a non-mathematical argument to be quite sure that, even if a perfect game is played, the odds are still favorable to the house.

In Black Jack and Baccarat, like in Roulette, each player competes in a zero-sum game against the house, even if they share the table with others. If a way of playing that guarantees profits in the long run existed, what would prevent professionals from learning it and earning their living at the expense of casinos? That they would be expelled because of their good game? That would pose a big public-relations problem, to begin with... It is much easier for casinos to adjust the rules so that the odds are in their favor, like it happened with Roulette, even when the players play perfectly. They are probably doing just that.

In these games where we compete against the house, the odds are in their favor or they wouldn't be implementing the game for us

To summarize, in these games where we compete against the house, the odds are in the house's favor or they wouldn't be implementing the game for us. Does that mean we shouldn't play? Not necessarily. Casinos do offer us some things, like thrills, dreams, amusement... We place bets and enjoy the suspense, wondering what we can do with the money we might earn. When we win, we rejoice spending those uncounted-for earnings, even if we had lost more than that in the past. Hence we gamble for the fun of it.

For the possibility to earn money systematically to exist, the zero-sum game would have to involve other players. Only in that case the expected outcome may be positive for us, as it could be based on the losses of other people even if there is a house involved (which always wins in the long run). Nevertheless, if significant money is involved, competition can get pretty tough, up to the point of making any skill advantage almost negligible compared to the high randomness of a game like poker. Better-skilled persons need to play a lot for their ability to reflect in their earnings, and stand many defeats in the process. That if they don't encounter an even-better player in the worst of moments... Therefore, if players are excellent their success is quite uncertain, and if they are not, even worse.

Using the terms we explained in Part 2, we may say that the outcome of a game of poker has a lot of standard deviation compared to the small positive expected value that a better player might have in a highly-competitive league. So, because of the Law of Large Numbers, only after lots of games can that positive expectation become evident.

We can now draw several conclusions of our analysis of gambling. The first is that gambling is done (or should be done) only for the thrills. Not for making money, although perhaps an outstanding player of a peer-to-peer game like poker could, but that is a special, controversial, case. The other relevant conclusion is that, if we spend our money at Vegas playing against the house, the odds will be against us because casinos provide a service that they charge for, almost unnoticeably, by means of a gaming advantage for them. A third conclusion is that although we can shape the risk of your gambling, by putting less money into play and distributing it among many bets, reducing it much doesn't make sense because we would be losing the real reward, which is the excitement, in exchange for the pursuit of an average result which is negative.


The risk/reward profile of an insurance contract, from the insurance company's perspective, is not much unlike a bet viewed from the casino's side. One with a very low probability but a large reward. There is an unlikely but possible event, a house burning down for example (touching wood), which would create an obligation for the company, to make a payment to their customer, just as the casino would have to if a player bet all-or-nothing several times and won. If the improbable events don't occur, then the net income from the customers are positive, because the company collects regular premiums from them. Like the casino, that receives the first chip the player put into play in the recurrent all-or-nothing martingale just mentioned. The insurance company sets the premiums according to the estimated probability of the hazard, so as to produce an average positive outcome for them (when all their customers are considered). Just as the casino did. That positive average is where they profit from, in exchange of the service they're providing. Like the casi... (ok, I know, I'm getting repetitive).

“They are also buying peace of mind

The difference for customers stems from the fact that the improbable payments, this time, are tied to losses, so their total monetary outcomes wouldn't be positive in any cases (unless the insurance company makes the mistake of estimating some asset costs too highly, which is remote). Therefore, people don't buy insurance for the thrills of winning a prize, but to be able to go on if they suffer a loss. They are also buying peace of mind.

To summarize, insurance companies, like casinos, provide a service in which there is an uncertain event that would bind them to reward the customer, and they charge for that service, by means of positive odds (for them) when all their customers' contracts are considered. The difference is that, because of the way their products are implemented, what casinos offer their customers are the thrills of uncertainty, while insurance companies offer quite the opposite: assurance. Both can be worth paying for.

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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