When I was in high school, the probabilities and statistics (“prob-stat”) elective held a special allure. Okay, I admit that it was the only alternative to pre-calc, and that course was way intimidating. So, I pretty much had to take prob-stat. But… we also got to gamble!
We did not gamble with real money, obviously. But our teacher used casino games as examples to teach us important lessons about probabilities. It was an effective and memorable way to get us to ingrain the concepts.
Mathematics is an intimidating discipline for a lot of people. In fact, you might feel the same way about any form of math that I did about taking pre-calculus.
Some of the math involved with gambling can be challenging. A lot of it is not. Willingness to learn about any of it is going to be a huge help to you. Let’s go over how a little math knowledge can help you with strategizing, money management, and more when you play online casino games.
Learning About Probabilities Can Help You Understand Randomness
What the heck is randomness? We talk about it with respect to slots and other casino games a lot, but it is tough to explain what it is.
We have an entire post explaining the concept of randomness. As we explain early on in that post, mathematics—specifically probabilities—helps us to describe randomness.
I am not going to rehash everything in that post since you can read it for yourself. But suffice to say, the better you understand randomness, the more you will understand exactly what is happening when you hit “spin” on a slot game and you win or lose.
- Key Point:
Randomness may be a confusing concept, but you can use probabilities to describe it. This is a big help since many casino games have random outcomes.
You Will Grasp Why “The House Always Wins.”
There is an innate advantage built into almost every game you can play at casinos. It is called the “house edge.”
The house edge is what ensures that the house always wins. Yes, players sometimes win in the short term. But over the long-term, the house rakes in more money, and the players lose.
It is easy to compare the advantage the house has over you with different games by looking at the house edge for each of them. Here are a few examples:
|Game||Bet Type (where applicable)||House Edge|
|Blackjack||Liberal Vegas Rules||0.28%|
|Craps||Pass / Come||1.41%|
|Craps||Don’t Pass / Don’t Come||1.36%|
Higher percentages mean higher advantages for the casino. Lower percentages mean lower advantages for the casino. If you were to see a negative number, that would mean you had the advantage.
Technically, you do not have to learn any math to make use of house edge data! Just check the list for lower house edge games and bets if you want to minimize the casino’s advantage.
But taking a look at how to calculate house edge can be insightful! To offer an example, here is how you can calculate the house edge for American Roulette, which is the type with the double zero.
The American roulette wheel has:
- 18 black slots
- 18 red slots
- 2 zero slots
Added together, that is 38 slots.
Now, imagine you are making a bet on black. Your chances of winning that bet are 18/38 = 0.4736, (18 black slots).
Your chances of losing the bet are 20/38 = 0.5263, (18 red slots plus the 2 green slots).
You need to subtract your chances of losing from your chances of winning:
- 18/38 − 20/38 = -2/38
- -2/38 = -0.05263
That is how we get the result of 5.26% as the house edge for American Roulette.
You can do similar math for European roulette and other games you play at the online casino. Roulette just serves as a particularly good example since the math is so simple and straightforward.
Once you understand mathematically why the house always wins, you are unlikely in the future to make the mistake of thinking you can beat the house.
This is important from the standpoint of managing your time and money wisely at the casino.
- Key Point:
Some basic arithmetic can help you understand the house edge numbers you see for various casino games and bets.
Learning About Math Encourages Optimized Strategies
There is something else about how house edge numbers are calculated that you must know, and that is that they always assume optimal play.
This is not applicable in our roulette example, because betting “red” or “black” is just a simple wager.
But what about a game like Blackjack, where you see a house edge expressed for the game as a whole?
0.28% is a nice low number. But how do you get that number?
As it turns out, there is only one way to get the house edge on blackjack that low, and that is to play the game perfectly.
Playing blackjack perfectly requires making the most optimal decision possible at each and every decision point, no matter how the cards land.
Those optimum decisions never vary. If you are showing a 4-8 and the dealer is showing a 2-6, you always hit. You do not randomly stand or double the next time it happens.
You can find charts of these optimum decisions that you can use as cheat sheets when you play blackjack online. They are referred to as the “basic strategy.”
Once you understand that mathematically, you must make those decisions if you want the lowest house edge for blackjack, you will never have any motivation to play any differently.
But players who do not understand that the house edge for blackjack goes above 0.28% without optimal play might engage in other strategies that cost them more money.
- Key Point:
Knowing that optimal play is used to calculate house edges helps you understand that the house gains an even bigger advantage on you when you play games like blackjack differently.
RTP Will Finally Make Sense To You
As you look for a slot game to play, do you look up its return-to-player (RTP)? If so, that’s great, choosing a slot with a high return-to-player is a smart move!
But exactly what that high RTP means (and doesn’t) is something that is hard to understand without grasping a bit about the math that goes into it.
Players sometimes assume the following:
- RTP represents the amount of your money you personally can expect to get back.
- You can expect to get that money back within a fairly finite amount of time.
- If the game is fair, the actual RTP and the theoretical RTP will be an exact match.
Everything above is inaccurate, however.
There is a good explanation of RTP and how to calculate it over at the Gambling Commission in the UK.
This page gives an example comparing actual vs. expected RTP for a slot using 400,000 games worth of data.
A very large number like this must be used in calculating RTP because of the natural variances in the slot game’s outcomes.
You might be familiar with a concept from statistical analysis called the “clustering illusion.”
Basically, with a random distribution of data points, little “clusters” will form if you plot them out on a graph. When you are playing a slot game, these represent winning or losing streaks.
They look like they are evidence of non-randomness. But that, as the name of this fallacy makes clear, is purely an illusion.
If you only have a small set of data points, the clustering illusion can be very pronounced. For example, you could have a winning streak where you win 10 spins in a row or a losing streak where you lose 10 spins in a row.
If you tried to calculate RTP using these 10 spins, you would get an RTP of 100% in the first case and 0% in the second.
Nevertheless, either or both of these events could occur on a slot with an RTP of, say, 89% or 90% or 92% (or any other RTP).
When there is enough data — i.e. hundreds of thousands of spins — these natural variances start to smooth out, and you get a better representation of the random distribution overall.
But even with large sample size, there is still a tolerance range for actual RTP.
The Gambling Commission states, “If 400,000 games had been played to accrue turnover and win figures of the example then the allowable tolerance will be 1.75 above or below 91.68. The game could return between 89.93% and 93.43% and still be considered to be performing as expected.”
So, based on everything you just learned, you can refine your understanding of RTP. Here are some correct statements about RTP:
RTP is calculated using many, many, many spins of the slot game, so it represents the return over a long period of time — not your hour or day at the casino.
RTP should really be expressed as “return-to-players.” It refers to the money that collectively is returned to players, not to a single player. If the number is 93.43%, for example, it means that the thousands of people who play the slot will collectively get 93.43% of the money back they collectively put in. It does not mean each individual one of them will receive back 93.43% of their own money. In fact, because distribution is uneven (because of jackpots), the average player will get back less than that even over a very long time period.
A perfect match between the theoretical and actual RTP is not always going to happen. But even if the numbers differ, the game may still be working just the way it is supposed to.
That should clear up a lot of your possible confusion about RTP!
- Key Point:
RTP is a useful figure in helping you to select slot games to play, but without understanding how it is calculated, it is easy to misunderstand what it is telling you.
Bonus Terms And Conditions Will Be More Comprehensible
Sometimes, a customer will join an online casino and accept a bonus. They will play for a bit, and then they will attempt to make a withdrawal. When they do, they may run into a snag. They may discover that they are not eligible to withdraw the bonus money. There might be cases where the money they won using it also is locked in their account.
They may then take to the web to tell everyone that they were scammed. They were not, but they believe it because they either failed to look up the rollover requirements for the bonus before accepting it or they simply did not understand what those requirements entailed.
Rollover is also called “turnover.” It is a requirement to tell you how many times you need to turn over the money in your account before you can withdraw bonus funds (and sometimes winnings from bonus funds).
To take an example, let’s say you claim the $3,000 casino welcome bonus at Bovada. The casino stipulates, “The deposit plus bonus amount is subject to a 25X playthrough requirement before the deposit, bonus amount, and any winnings can be withdrawn.”
What does that mean mathematically speaking?
Let’s say you deposit $3,000 and you receive $3,000 in bonus funds. The turnover requirement is:
25 x ($3,000 + $3,000) = $150,000.
…Woah. You can see how failure to do this math before claiming a bonus could leave you feeling very angry and confused!
Rollover requirements may be higher or lower than what you see in this example. A typical range is somewhere between 10-40x.
Using the formula above, you can figure out pretty quickly what a difference the multiplier makes in determining the turnover you need to meet. The lower you can get it, the better.
Now you can understand exactly how and why bonus money serves the casino, not the player.
Clearly, a $3,000 investment by a casino to coax you into turning over $150,000 in funds is good business — especially given that the “house always wins.”
Some people will win big with bonus cash and be able to withdraw it, but most customers will lose.
Some players opt to reject welcome bonuses after doing the math and realizing they do not want their money locked up in their account at all.
Our suggestion is this:
If what you care about most is just having some extra money to play with, go ahead and accept the bonus. Just be sure you really understand what the rollover means for you.
If you want to have full freedom to quickly and easily withdraw any funds in your account at any time, you should skip match bonuses. There are other promos at online casinos you can enjoy (see below).
- Key Point:
Online casino players often fail to comprehend how rollover requirements work for bonuses. Doing the math to find out how much turnover is required to make a withdrawal can help you decide whether to accept a bonus.
You Will Be Able To Determine Which Loyalty Programs Are Best
Online casinos offer comp programs, a.k.a. VIP Programs or Loyalty Programs to provide extra value to dedicated customers.
The concept is simple. As you play casino games, you earn points. You then redeem the points for cash back.
Rather than go over the detailed math of how rewards programs work here, we will point you toward the full post we wrote up on the topic.
In that post, we teach you how to compare the value offered through different VIP programs with a couple of examples.
One thing to be aware of is that rollover requirements can apply to cash-back received through rewards programs as well.
- Key Point:
Comparing loyalty programs requires you to do a little basic math.
You Finally Will Understand Why Progressive Betting Systems Fail
Casino gamblers (and sports bettors, for that matter) cannot seem to get enough of progressive betting systems. There are a number of them out there (see the linked post), but the most famous is probably the Martingale system.
The Martingale system is simple to explain. Every single time you lose a wager, double your next stake.
The theory behind the system is that eventually, a win must happen. The size of that win will outstrip all the previous losses, and you will be back in the black.
Some simple math can rapidly reveal the problem with this system.
Here is an example of how your stake sizes could increase on a losing streak where your first bet is just $10:
Is this a pretty long losing streak? Sure. But is it far-fetched? Not one bit, especially with a high-volatility game.
Plus, if you are someone who is going to start betting with just $10, chances are good you cannot afford to stake $160, $320, or $640. You do not even have to get halfway through this list before you are likely in way over your head.
And do not forget that your losses are adding up all along the way. By the time you have had a losing streak of five bets, you are already down $310. Ouch.
And look how crazy things get if we assume your first bet to be $100:
By the 11th bet, you may as well be staking a modest house!
Basically, if you have infinite money to lose, by all means, go ahead and try using progressive systems like this one. Otherwise, avoid them.
- Key Point:
A little quick addition explains exactly why progressive betting systems are doomed to fail.
You Will Know How To Make Your Bankroll Last
Just as you can use math to figure out why not to bet with Martingale, you can also use some arithmetic to figure out how you do want to manage your stakes.
Let’s say you have $100 in your bankroll. You want to spend significant time gambling today. That means you need to make that bankroll last, not blow it all on several big bets.
You might think, “$10 is pretty modest. How about that?”
Well, just do some division. If you bet $10, assuming you have a severe losing streak, you will only get to place 10 bets before you are done for the day. That will be over in no time!
When you figure that out, you might decide that $10 per bet is too high for you. You recalculate using $5 as the stake size and determine you could withstand 20 losses in a row before busting.
That might sound more palatable. You might even decide to cut it in half again to just $2.50 for each bet. That way, you can really relax and enjoy a nice, long gambling session without worrying about your bankroll running out too fast.
- Key Point:
If you decide how many bets you want to be able to place during a gambling session, you can do some simple arithmetic to pick an appropriate stake size.
You Will Manage Your Budget Effectively
You now know how to use arithmetic to set your stake sizes, but what about the size of your bankroll itself?
Sizing your bankroll requires you to understand how your casino activities fit into your budget.
So many people go through life without keeping a budget at all, but the math involved in budgeting is not hard. It is just a lot of addition and subtraction.
To keep your budget, you just need to do the following at the end of each month:
- Add together all the money you currently have in your accounts.
- Compare it to all the money you had in your accounts last month.
Did you gain money, or did you lose money? If you gained money, great! You budgeted successfully that month. If you lost money, you should try to do better next month if possible.
By tracking your expenses as you go each month, you can see where all of your money is going. Try adding up all of your regular expenses. They need to add up to less than your income. If they do not, you will keep having months where you lose money.
Losing months will happen now and again to everyone — sometimes a big bill comes due. But you need to be profitable overall over the course of each year.
Imagine you have calculated that on a typical month, you are profitable with your budget by $300.
Honestly, that is not a lot of profit, so you probably should be saving or investing most of it. But you have enough wiggle room for some basic leisure expenses.
You need to decide how much of that you are comfortable spending on entertainment. Maybe it is $10. Maybe it is $30. Maybe it is $60.
Whatever it is, that is the amount you can deposit into your bankroll to play online casino games each month.
When you maintain a budget every month, you really understand mathematically how it affects you if you break your rules.
Without budgeting, you might not blink at the thought of sometimes randomly doubling what you put into your bankroll over a typical month.
But with budgeting, you know that doing this could really eat into your income, and maybe put you in the red. So, you are more likely to fund your online casino account responsibly.
- Key Point:
Doing the math with your budget each month can help you gamble responsibly and sustainably.
You Can Better Understand Gambling Psychology.
Here is something you might not expect — some math knowledge may be useful in exploring your psychology as a gambler.
It can be useful to try and understand some facets of your personality and how they affect you as you gamble. To do that, you can take self-assessments.
This activity usually entails answering a bunch of questions to get a numerical score. But on its own, that score only gives you so much information.
What you need to do is compare your score to that of others who have taken the same assessment.
If you are lucky, the provider of the assessment may include information about the average score right there on the assessment. But if they do not, you might need to check some psychology journals to see if there are any research studies with data.
The statistical concept that will come in handy in helping you interpret your results compared to those of others is standard deviations.
To jog your memory of high school math, picture a bell curve distribution of results. The more standard deviations away from the mean a result is, the more of an outlier it is.
If you have information on standard deviations for an assessment you took, you can make more sense of your score. If it is just above the mean within one standard deviation, it is not really a “high” score. But if it is 2-3 standard deviations out, then it becomes more significant.
At that point, it becomes something you may want to pay close attention to. For example, if you are slightly more anxious than the average person, it probably is not going to have a huge effect on your gambling. But if you are 2 standard deviations above the mean, it probably is going to influence a lot of your decisions when you play.
- Key Point:
Understanding standard deviations can help you better grasp how your psychology may impact you as you play casino games.
If you win a life-changing jackpot, you can make the money last.
One more way in which a strong understanding of even basic math can be of great use to you when you are gambling is in that unexpected scenario where you win hundreds of thousands of dollars or more.
You probably have heard that more often than not, jackpot winners fail to make their money last more than a few years. They then find themselves back at square one in their lives.
If you win a massive jackpot, you do not want this to describe your future. You want to stay wealthy.
But the good news is that if you learned the budgeting skills we recommended earlier, you know all the math you need to ensure that happens.
On a related note, you also will be able to calculate the potential impacts on your finances of accepting your winnings as a lump sum vs. installment payments.
- Key Point:
Learning basic financial math can help you plan how you will receive, spend and save your winnings from a life-changing jackpot. That way, it actually changes your whole life and not just a few years of it.
Go Use Your Math Knowledge
If you made it this far, you already learned a lot about math and how it pertains to gambling! Your understanding of house edge, RTP, betting systems and more has increased. You also know some of what you need to study and put into practice to do better managing your money while you play.
We recommend that you continue to research math and gambling, as we have only scraped the tip of the iceberg.
But you should be ready to put what you learned from this post to good use. See our recommended online casinos to start gambling now!
And Be Sure To Take A Look At These As Well!