For many years, researchers were confounded as to why people bought lottery tickets. The chance of winning a Mega Millions lottery ticket is 1 in 302,575,350. At a price of $2, only if the jackpot is larger than $605,150,700 does it make sense to play the lottery because the proportion of that risk you are taking is equivalent to its pay out. This is called the expected value of your bet. To put it another way, the chance of winning is $2 / $605,150 700 = 0.000000001652, multiply this by $605,150,700 = $2. Anything less than the $600 million and you are paying $2 for an expected payout of less than $2. At a $200 million payout, your expected value is just $0.66 for a $2 ticket, so why bother playing?
Eventually researchers came up with an explanation via behavioral economics which tries to study why people make seemingly irrational economic decisions. It has to do with people being more likely to play something with smaller odds but much larger payouts. It’s basically an emotional bet that a big payout can “save” us. This seems to be consistent with surveys that say 1 in 5 Americans believe the only way they can accumulate a significant amount of savings is to play the lottery. When you put it into perspective that the US is the wealthiest country in the world and the salary to be in the 1% of incomes globally is $32,400 this sounds a bit ridiculous. I have pointed out in previous posts that the reason many people don’t have significant savings over the long term has a lot to do with their psychology and bad financial habits they have developed related to that psychology, but I haven’t talked as much about small number compounding which is also important to saving and building wealth.
How Casinos Make Money
Even if you can only save a few hundred dollars every month, over long periods of time saving that money and investing that money in things like the stock market, where your money can compound has huge effects over time.
In order to master this however and take advantage of the compounding, which has averaged 10% over the long term for the S&P 500 over the last 100 years, you have to understand probability and the law of large numbers. Given the recent market volatility and the increased questions I have been getting on the blog and via social media, it’s probably worth discussing how the law of large numbers works and show how this applies to the stock market and other industries by way of an example.
Understanding how casinos make money is a good way to understand this. We perceive gambling as a game of chance. If you walk into a casino and play one game, it is a game of chance for you as a single player. The odds may be 40% in your favor of winning or 30% or whatever but you at least know there is a chance of a payout.
That’s not how the casino owner looks at it though, for her the casino is a game of probability which is oh so slightly tilted in their favor played thousands of times per day. The house edge is the amount of probability greater than 50% that the casino has. For example if the house edge is 5.3% as in the case of roulette, the the casino has a probability of winning any round of 55.3%. The house edge for different casino games is displayed below:
Source: zen investor
At any one time a gambler could walk into a casino and win a $100,000 on craps for example. She might even be lucky enough to do it on the first try. In this extreme example the casino would clearly have a loss right off the bat after that lucky win. Those types of things are rare however and most people would not win a jackpot like that until they have played many times. The more times people play though, the more the wins start to rack up for the casino. This is the law of large numbers.
To give you an example, take a look at a plot of the outcomes for heads versus tails of a coin flip, done on 10 different coins, 1000 times each.
Source: alpha architect
If you look to the left, you will see wide variations in terms of heads versus tails. The more flips are made though, the more the excess of heads over tails or tails over heads, starts to converge towards 0.
The case above is for a 50/50 chance. In the case of a casino, where the odds are slightly in their favor, as the more games are played by gamblers, the return for each game starts to converge towards the house advantage. To illustrate this point, a professor at Drexel University presented the following chart of a data set he runs to illustrate the point. He ran a simulation with a game where the house has an advantage of around 12%. He creates different systems where there is either 1 game played, 10 games played or 100 games played for each trial. The results show that as the more games are played, the outcome starts to converge towards the house advantage. This is exactly what the casino depends on happening and how they make money in the long run.
Source: alpha architect
The Stock Market as Casino
If you invest in the stock market for one day, you are essentially a gambler walking into the casino. You could win or lose, you really don’t know which way it will go. That doesn’t change much for any given month either. It’s one reason that 90% of day traders lose money in the market. If you look at every day as another game played though, eventually you will see that the law of large numbers starts to take over.
In the specific case of the stock market, this will take many years. Over time though, you will start to see your return converge towards that house edge, which for the stock market is about 10% annually in your favor with reinvested dividends. The long term investors are the casino owners. These are people that have the knowledge of things like the law of large numbers and financial coaches such as advisors, to keep their psychology in check when the news is telling you the sky is falling like many are today.
Source: Business Insider
Just look at the above convergence of stock and bond returns as well as that of a 50/50 portfolio over different holding periods from 1950 to 2013. Notice how no 20 year holding period produces a loss. Also notice how this looks somewhat similar to the convergence chart of the coin flip that I showed earlier.
Again, what this shows you is that the long term investors are the casino owners when it comes to the stock markets. The short term investors and the folks paying attention to the media are the gamblers.
It’s your choice which you want to be. The gamblers aren’t just the day traders, they are the people that move their money into cash when the market falls, chase gold, or try to short when the whole market gets volatile. We often are too backwards looking and are so busy crying over what we lost that we discount the potential huge upside that is to come. These psychological factors are the main reason that most people are so terrible at investing. The casino owners know this upside will come and so do the long term investors. So which one are you?
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