# The Market is a Casino

The Market's a Casino (If You Set It Up Right!)

Permutations, Combinations and Probability

Historical Analysis and Strategic Discipline

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You've heard it before, and you've seen it in print; "The market is just a casino." It's supposed to be a put-down. When someone calls the market a "casino," they usually mean it's a disreputable institution, needing more and more regulation at best, or perhaps worthy of extinction at worst.

And there's also an implied suggestion that there's no way to trade the market rationally-that logic and strategy are useless.

[The hint of irrationality often comes with a serving of sour grapes. Like when your brother-in-law just lost a bundle in a failed IPO.]

But of course, a casino isn't really irrational. It's a highly rational enterprise constructed to consistently extract money from customers and put it in the hands of the casino operator. And why is the casino such a sure thing for the casino operator? It's because the games are set up so the odds favor the house. The games are rigged!

Not rigged in the sense of being crooked, but rigged in the sense of having the math grinding away in the house's favor. Gambling casinos keep about 4% of every dollar bet. So long as there are many bets, with no break-the-bank monster bets, the operator knows that for every $1,000,000 bet, only $960,000 will be paid out. If the games are set up right, the math just keeps grinding away.

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When I was in high school, I took every math course offered. One course included a section on "Permutations, Combinations and Probability." I loved that unit, and it inspired me to set up a little game for my classmates. (And maybe a few underclassmen.) For this game, I brought to school a sock and six marbles; three black, two red and one white. The game was to draw three marbles and get all three black. I'd offer the other kids to pay me 25c to play. If their three draws were all black, I'd pay a dollar.

There's something about the three black out of six total that makes the game seem like the odds are maybe about 50-50. Or maybe 2 to 1. But in fact the odds are 19-to-1 against drawing three out of three blacks. (The calculation is summarized below.) So if I had 20 players pay me 25c each, I'd collect $5 and expect to pay out $1 to one of them. It was like having my own lunchroom casino!

(I was finally busted by the school administration. I don't think they really minded that much-perhaps they even admired the enterprise-but the operation was thought unseemly, or maybe poor public relations, should it become known outside. Something like that.)

So what about the stock market? In the market there are no 4-to1 payoffs, and certainly no 19-to-1 odds in your favor. But every investment and every strategy has some chance of winning and some chance of losing. And we can't know in advance which is which. (If we could know which is which, we'd only have winning trades.)

What we can do is use analysis and strategy to have more wins than losses, or have bigger wins than losses, or both. We can't create 19-to-1 investment opportunities like my sock game, of course. But that's OK. We can do just fine with 1.04-to-1 opportunities…like the actual casinos.

What's unlike an actual casino is that we never know in advance exactly what are the probabilities of a particular strategy or opportunity. There aren't any "combinations and permutations" tables to look up that answer.

Instead, we rely on history. We define a process, test it historically, and compile statistics on the output to measure just how profitable it has been. More important, we measure how variable the output has been. And of course, we count how often the investment criteria are met.

The "how often?" question is critical because, like the casino operator, we want lots of small bets at all the tables, not a few huge bets at a single table.

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Here's a real-life and current example:

I've been working on a new S&P 500 timing indicator; buy signals and sell signals. The analysis is complicated, but it's essentially based on rate-of-change differences. In the nearly 13 years since 2000, this model has generated 87 Buys and 87 Sells. (One signal every 18 days on average.) Only 58% of the signals are "right," yet the average Buy and average Sell each produces 1.2% gains. And if we can generate 1.2% every 18 days (on average), that compounds to 18% a year!

But that's not enough. When we look at variability, we find the averages can be misleading. The Sell signal outcomes, it turns out, are almost 2x as variable as the Buys. And the successful Sells are dominated by a few very steep and very rare bear market events, while the Buy outcomes are really very consistent over time. So the Sell signals feel more like gambling, but the Buys can contribute to a really attractive "casino" operation; lots of bets at many tables, with the math just grinding out the gains.

Historical analysis doesn't settle everything, of course. Markets are inherently dynamic, and market behavior is subject to change. So we need to keep tracking and testing. Occasionally, a market change will call for a strategy change.

But until that point, it's important to maintain strategic discipline. If your "casino" is set up with care, the probabilities will prevail. The "chips" may move from one side of the table to the other as each hand is dealt, but the inexorable drift will work your way.

Your guide to ETF investing,

Robin L. Carpenter

Editor of *Cabot ETF Investing System*

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Six-marble math note: The first marble drawn has a 3/6 probability of being black. Then there are five marbles left and two of them are black, so the next probability is 2/5. If that second draw is also black, there are then four left, of which only one is black, for a 1/4 probability of getting the third draw also black. So the probability of all three draws being black is 3/6 x 2/5 x 1/4 = (3x2x1)/(6x5x4) = 6/120 or 1 out of 20.

*The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.*

The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.