Plato had the allegory of the cave. Today, however, the allegory concerns the horse race.

There is a Sheikh in our story who wants to hold a contest among his fine horses. He has sixty such beautiful animals, and he wants to have a race among them as he feels they all have an equal chance of winning as they are all great animals. He, being a Sheikh, wants to open the race up for betting because his Sheikh lifestyle is not going to pay for itself and he does, after all, have these sixty animals to upkeep. He decides to set the purse at around 100 million dollars to attract the high rollers.

Since the race is fair and any horse has an equal chance of winning, the odds on any one horse winning is 1 out of 60. This means that a given horse has about a 1 percent chance of winning. It is closer to 1.6 percent, but the .6 percent does little good should you happen to win because of it. Why? Well it is an irrational .6 percent that repeats. You won’t keep winning, but everyone will argue. Better to stick with the 1 percent, right?

These are not very good odds of winning, so the Sheikh decides to change the terms of the contest. There will be eleven winners, he decrees, with one of those winners winning the grand prize purse of 100 million dollars. The other ten will win 1 million dollars. This changes the odds significantly--as one might imagine. One now has an 11 out of 60 chance to win some money. That is an eighteen percent chance of winning some serious cash! Not bad, for millions of dollars. Depending on the cost to enter, these are probably better odds than one has of getting a million dollars by opening their own business.

Before the race starts, the Sheikh allows the public to see his horses. Not all of them are in the shape that he had portrayed them being. Several of them have a limp. A couple more are overweight. Still another has a jockey who is too heavy to be riding the mount he is assigned to.

This information, to the experienced, influences the odds again. Information, it turns out, can change the odds of a given calculation as Marilyn Vos Savant famously pointed out. This, of course, depends on how you want to look at doing the calculating, but if you are interested in the best odds of winning, and not being right about calculating, then there is a decisive strategy.

Our Sheikh, then, has, it seems, ruled out certain horses as sharing characteristics of likely being possessed by the winning horse. This improves the odds greatly--maybe as high as to a 30 percent chance of winning as certain horses can be ruled out.

There is one enterprising fellow, though, who decides to bet on two horses. He bases this decision on the original odds of his having a 2 out of 60 chance of winning on a single horse. This gives him around a 3 percent chance of winning, but when the new rules are factored in, he has around a 36 percent chance of winning some amount of money. These are good odds indeed, and so long as the entry for each horse is below $500,000, he stands to make something back.

The Sheikh races his horses. When the early results arrive, we find that the man who put in two horses has placed in the top ten! Not only has he placed in the top ten, but BOTH HORSES have placed there! What are the odds? Let’s find out. To discover the odds of both horses the man bet on winning, we have to multiply the probabilities. 11/60 x 11/60 is equal to about three percent. Our handy odds table https://www.ncbi.nlm.nih.gov/books/NBK126161/table/T21/ shows that to be about a 1 in 3000 chance. (This, incidentally, is about the same odds as being possibly killed by a meteorite impact or having your home burn down: https://stacker.com/stories/art-culture/odds-50-random-events-happening-you) Therefore, the man placing with both horses was about as likely as his winning the grand prize purse by entering two horses as per the original terms of the race! Put in negative terms, the man is going to lose his bet on his two horses, 97 percent of the time!

This, of course, makes the horse betters suspicious. At the very least the two horses that have placed ought to be in possession of the top characteristics to horses expected to win the race. It turns out that they are not especially prime specimens. To be sure, they are not bad, but there is nothing at all special about them. They don’t stand out.

The Sheikh goes on to announce the grand prize winner, and indeed, this horse possesses the characteristics that one expects from a champion horse. The problem, though, is that the two horses that placed did so such that other horses that clearly had the characteristics of being pedigreed winners in the contest placed not at all. The incredible thing is not what horse won the grand prize, but the fact that the man who bet on two horses won on both horses--neither of which had the characteristics that the other non-placing horses clearly possessed. One of those winning horses that the man had bet on had a limp, in fact, and looked to be disqualified from racing.

The conclusion that presents itself is something about the contest had some hidden information that the man who bet on the two horses knew. Barring a miraculous intervention, since God does not often seem to get heavily involved in games of chance, what could explain what it was the man who bet on the two horses knew or noticed? In a very real way, despite the grand prize winner winning more money, betting on two not especially stellar horses and winning on both is the real prize. Was the contest fair? Did all horses really have an equal chance of winning? Were the optics of the race manipulated by the Sheikh? Were false reports put out? Is there favoritism in the judges of the race?

The moral to the story is simply this--if you trust a Sheikh to run a horse race you might find yourself poorer--that is--unless you know the Sheikh.