What Makes A Casino Gamble Different Than Making A Decision Under Uncertainty?

We continue with our week of pleasant Thanksgiving topics.

A cop in the police procedural Hell Is A City (start around 54 minutes) discerned one of the bad guys he was chasing would show up at a Tossing School on the outskirts of Manchester.

A Tossing School was a place of illegal gambling, but, I think, in a strange form. Strange because all it consisted of was people standing around making bets on coin tosses. Which are rather simple events.

Two coins would be placed on the tosser’s finger, or a frickin stick in Ireland, and the coins thrown into the air. If they came down opposites, one head and one tail, the tosser continued. If two tails, the tosser lost. Or if two heads, he won.

People would make all kind of side bets, including the number of tosses until win or lose. Any toss could be disputed while the coins were in the air. Once they landed, the toss had to be accepted and the bets were paid off.

There are all kinds of niceties to this, best found in this book. What I found fascinating what the the local brute who ran the school would cover all bets at face odds. Which put him at as much risk as the gamblers themselves. Though I did see another account which claimed the brute took some percentage, but it was vague. Details are scanty. Maybe one of you know.

In any case, these Schools were popular. And very simple. After all, given simple premises, the per-toss chance of winning is 25%, which is the same as the chance of losing, assuming simple win-lose bets. At each toss, I mean.

This bet is slightly up in complexity from a simple single coin toss. You must understand, a coin toss has no probability of coming up heads. Only our uncertainty in the toss, that which is in our heads about it, has a probability. Nothing in the coin has a probability. This video and article explains why.

In a coin toss, the premises are that only one of two possibilities must happen, and in complete ignorance of any causes (besides these), the probability is deduced at 50-50.

Dichotomous bets, those with only two outcomes, are simplest of all bets. And in a dichotomous bet, 50-50 is the point of highest variability. Which is to say, the bet that you might guess that has the most interest. But interest also includes how much can be won or lost.

For instance, the Powerball is also a dichotomous event, at least for the jackpot. You either win or lose. The probability of winning is tens of millions to one against. Yet, as you know, people take a keen interest in the bet when the amount to be won is large, even though the probability of winning is vanishingly low.

Casinos have something close to a 50-50 bet with roulette wheels, but there are usually three possibilities and not just two (red or black or green versus red or black). And the amount to be won is less than that of the Tossing Schools, since the casino takes a cut. Interest is always high, though, at least at the casino’s I’ve seen.

The opposite end of complexity is human behavior, sports being the best example. Since probabilities can only be formed when premises are assumed, the enormous number of possibilities for premises in any human event practically guarantees disagreement in probability. And because people views the gains and losses so differently there is never a shortage of interest in betting.

Well, everybody knows all this. But the curiosity is this. We make uncertain decisions, which is to say bets, on uncertain things almost continuously. Where to place your feet while climbing, whether to buy this or that item to achieve some effect, change lanes now or wait. An endless list. The payoffs are usually not monetary, and neither are the costs.

Mathematically speaking, though, there is no difference between a casino or sports bet and any uncertain decision. Not everything can be quantified, of course, in money or in “utiles”, the stand in for value of satisfaction. But that makes no difference in any formal analysis. Whether it’s a frickin stick toss or you deciding to head down to the store later because you think it might be less crowded then, it’s all the same. On paper.

So why do we see casino betting as different?

It can’t be the voluntary nature of the casino bets, versus the seeming necessity of uncertain decisions. You voluntarily enter a casino gamble, all right, but it’s the same for timing your shopping trip.

You might see casino gambles as a contest or a sport, man against Mr Big, as it were. But you can gamble against Nature when deciding whether to dig out of storage and carry a shovel in the truck (snow later this week, maybe).

Again, there is no difference whatsoever on paper: there is uncertainty in the bet and the amounts. But we all feel casino bets are different.

I think they are, too, though the difference is qualitative and the boundaries fuzzy and permeable.

Because in casino gambles you allow, to the extent you don’t in most uncertain decisions, but far from all, that there might be certain entities or forces, demonic or angelic, Fate even, that are working behind the scenes manipulating the outcomes, and in your favor, with the blessing. Or against you if you have done something amiss.

Which is old fashioned superstition.

You might not name the spirits. This needn’t be definite. The forces at work might be totally unknown to you. But you feel, almost always in casino-like gambles, that these forces are out there pulling levers to balance things out, or lift you up.

You do this too sometimes in, say, waiting for uncertain health results, but here you are more likely to name these forces, and call upon the name of God.

Not knowing the causes of the events is what makes the outcomes uncertain in the first place. So being ignorant of causes is not the difference either. It’s that you are willing to allow the operation of more curious causes when the outcome has more importance. Making money without effort is important, as is your health.

The difference, then, is not in the probability here, but the payment. Rather, the payout.

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