Why Large Samples Don't Guarantee Individual Results
Gambling, and your success at any game in particular, has a lot to do with statistics. Before you buy dice and start doing some practice rolls, it’s important to note that even the largest sample results may not match the ones you roll on your own…but why is this?
Large samples won’t always match individual results, because often it is impossible to achieve exact results with something as mindless as a die. Not only that, but statistics are based on expected results, never on exact ones. Read on to learn more about why large samples don’t guarantee individual results.
What Are Samples in Gambling?
Statistics refers to samples as a “selection” of tracked outcomes. For example, it can mean simply having a die and stating that you will roll it 100 times and record the outcomes. But it can also mean, during a statistical evaluation, selecting a number of subjects and tracking their outcomes. Either can apply to gambling, however, in this article, we will mostly focus on the first, which is a sample you can take on your own.
Why Large Samples Don’t Match Gambling Outcomes
1. The Law of Large Numbers
The most official reason can be found in referencing the law of large numbers, which states that as the number of trials increases, the outcome should grow closer and closer to the expected outcome. But notice how it does not state that you will achieve a certain outcome—as we mentioned before, even with something as statistically easy to track such as the outcome of a six-sided die, there is always variance, and as such, even if you rolled one million times, you are unlikely to roll a 1 exactly 1/6th of the time.
2. You Are Unlikely to Roll Enough Times
One of the main reasons that large sample sizes don’t help the average gambler is that you need a truly large sample to even achieve results close to exact. We didn’t mention one million by accident, because even with 100 rolls, it is not enough to achieve a statistical outcome.
Of course, just rolling a die at home is possible to do more than 100 times, but in a casino, where you have to pay for each roll and actively participate in play (if your casino even offers something as simple as dice), we highly doubt you will have the time or funds to even roll close to enough times to achieve anything close to what the statisticians have achieved. This means you will likely never experience the same statistical outcomes as professional statisticians simply because you don’t have the time to do so.
3. Each Bet is an Independent Event
We have discussed this topic many times on this blog; however, if you are new, it is important to know that each roll of a die is statistically independent. Even if you have gotten the same result 6 rolls in a row, unless you are rolling loaded dice (which you never will in a casino), your chances of rolling the same number a 7th time are exactly the same as rolling any other number.
Remember, inanimate objects have no memory. Even if you have rolled six 1s in a row, the dice does not remember and does not think that it needs to change to show a different outcome. It is simply a die, and it is just there.
4. Human Influence
One aspect we have to discuss is also the human influence on outcomes. Although we would like to assume that each individual rolls the dice with the same statistically verifiable method, it simply isn’t true. Some may call this cheating (and casinos will kick out individuals they suspect of not rolling the dice well on purpose), but the reality is, everyone rolls the dice a little differently, and this can cause some variance not accounted for by statistics.
5. Expected Average is an Average
Many people become confused about outcomes because they confuse the expected average with the actual average of outcomes. In most countries, casinos must post, or be able to submit, their expected player average to the authorities. This doesn’t mean you will have access to these numbers, but if you do, they may leave you wondering why those aren’t the outcomes you have seen in your play.
Well, this one is easy, because again, this is what the casino expects to give back—but they aren’t controlling the outcomes enough to have any actual influence on it. Most casino games are backed by a random number generator that the casino has no control over. While there are some settings they can affect, that is just the expected average we mentioned above; the reality is, they can’t actually guarantee that this is the return you will experience when you play. This is called variance, and it is expected—so much so that it is called expected variance with the abbreviation EV.
6. Humans Can’t See Randomness
Unfortunately, a lot of this comes from the fact that humans want to search for patterns—it was our evolutionary advantage. As such, it is very difficult, if not impossible, for us to spot randomness and to understand how it works. In fact, if you try, unless you are a mathematician, it may be impossible for you to grasp.
Overall, the takeaway we would like you to have from this article is that you should expect randomness as you gamble. And just because you decide to test something yourself and get one outcome, this outcome has no bearing on anything else during play. We aren’t saying you shouldn’t try your hand at winning—quite the opposite, really, as you may just win. But remember that gambling, while based on statistics, is truly a game of chance, and you should never wager any money you aren’t prepared to lose.
