## Are you Familiar with the Terms?

No doubt, these terms are familiar to more experienced gamblers, especially those who base themselves online. However, familiarity is only half of the equations; understanding RTP and Variance are the first and most significant steps to informed and reaping the rewards of shrewd wagers.

## What does RTP Мean?

The term payout ratios might sound a bit confusing. We all prefer the term return to player, as payout ratio definitions can differ according to how you are gambling. For example, payout ratios, sometimes referred to solely as the ‘payout,’ is defined as the amount of money that rewarded upon a win relative to your initial bet.

In a particular event, such as a horse race or betting on a roulette outcome, the payout ratio differs with the odds. Let’s work through an example. If an event had a payout ratio of 8:1, then a \$1 winning wager would profit eight dollars.

This means, from my winning wage of one dollar, I would walk away with eight dollars, which sounds promising to a beginner. However, the ratio differs with odds and always gives the casino an advantage. This term, also called ‘house edge,’ is the subject of further discussion in this article.

Online, this relative payout is the long term statistical rate of total money divided by the total money staked. More accurately, we can define payout ratios as the rate of return to the player. These can be anything up to 99%.

The RTP cannot be 100% because this means the house will have no returns, and the casino would be losing money. We can calculate the RTP here much the same as the payout ratios explained above. Let’s use the slot machine as an example.

I’m on a slot machine, which has a return to player rate of 90%. This seems high. But let’s break down the slot machine maths.

Slots work on a simple premise. Play credit and the machine, using a random number generator, will choose a combination of symbols. If the symbols match, you get a payout, which depends on which symbols appeared on your pay line.

Let’s say our imaginary slot machine has three reels with 20 results on each reel. Some results give two symbols that can both be used to make a pay line. Prize money increases with the amount of money played, encouraging you to wager more. These are the basics of our imaginary slot machine.

Now, remember that each reel has different frequencies of symbols on them. The frequency shows how many times each symbol would appear on any given reel. For example, if the frequency is 0 for a coconut on reel 3, the symbol will not appear there. Ever.

So if we want to work out the number of ways to get a particular combination, we multiply the frequency of the symbols for each reel. Let’s take that coconut again – if it shows 3 times on reel 1, 2 on reel 2, and 4 on reel 3, you’ll get 1 x 2 x 4 ways. Are you with us so far?

Now, every slot machine has different payouts for different combinations. Say 3 coconuts have a payout of 200. If we multiply 200 (payout) with the number of ways to win ( 1 x 2 x 4 = 8), we can work out our total return. In this case, our total return is 1600. If we add up all the returns for all winning symbol combinations this way, we can calculate the total return.

Warning – there is now even more maths to come. We need to add up the total ways to win, which depends on what combinations the game favors. Let’s say for argument’s sake that there are 1073 ways to win in on this slot machine.

If each reel has 20 results, then there are 20 x 20 x 20 combinations. That’s a whopping 8 000 combinations. Now we use this and our number of ways to win to work out the expected rate of wins. For our imaginary machine, the probability of getting a line equals to 1073/ 8000, which is 12.41%. You have a 12.41% chance of winning on this machine.

However, this is different from your expected rate of return or RTP. You only receive a payout approximately 12% of the time. In comparison, the expected return is the total return rate divided by 8000 (your total combination possibilities), and your average total return rate is usually around 7500 in most 8000 possibility machines. This mathematics puts the RTP at approximately 94%, meaning \$1.00 would end up being at 94 cents.

Too much maths, we hear you cry! Mathematics is the backbone and skeleton of gambling, so it is worth investigating further!

## Payout Ratio (RTP)

We, as players, want a high RTP for a game to be worth our wager. Although the example above was convoluted and used slots as an example, they aren’t the only way this maths works. You can substitute the ‘total combinations’ for any gambling activities.

For example, in a horse race, bookies calculate odds based on the maths above. Let’s look at some more gambling cases and work through the return to player rates.

### 1. Blackjack RTP

Blackjack is a staple of casinos, though the particulars may differ between locations. It was first referenced in the early 1600’s literature in a text by the author of Don Quixote and has been the backbone of gambling halls ever since. Also referred to as ‘Twenty-One’ or ‘Vingt-et-Un,’ the rules are relatively simple.

It’s all about playing strategically and playing cards with the highest expected return, or RTP. The object of the game is to bring cards closest to the value of 21, but not go over it. You also want to beat the dealer. For a full rundown of BlackJack, check out our Blackjack guide!

While the game itself is fascinating, what about BlackJack’s RTP? Working out this RTP, again, is filled with complicated maths, so bear with us! First, you’d need to calculate the total possibilities of your first, two-card hand. The number of combinations is 1326.

The possibility of getting blackjack is the number of ways of getting blackjack (21) divided by total possibilities. 21 divided by 1326 puts us at around 4.83%. On your starting hand, your possibility of making blackjack with the two cards your dealt is below 5%!

Those odds don’t look favorable. However, blackjack isn’t just the two cards dealt to a player at the beginning of the round. You have to remember that the dealer and all other players also only begin with a 4.83% chance of a perfect score. From there, it becomes a game of skill.

The RTP, or possibility of a win divided by total possibilities, changes with every card dealt because every card dealt becomes a certainty. These changes can be complicated to navigate for inexperienced players. To keep things simple, remember RTP is usually between 95% to 102%.

You read it correctly. The RTP in blackjack can rise above 100%, depending on which cards remain in the deck as the game progresses.

To keep RTP high, you can use basic strategies to optimize your chances within a game. Basic strategy involves memory and maths (again). The rules are as follows and can be read in more detail in our Blackjack basic strategy article. Rules for BlackJack Strategy and RTP optimization come down to four questions.

First, you need to ask yourself. Should I surrender? Most casinos will allow a late surrender after the first round of cards. Rule of thumb for surrendering? If the Dealer has a 9 through to ace, and you have 16 total in your hand surrender. If you have a total of 15 versus the dealer 10?Surrender. Otherwise, it’s up to you.

Secondly, should I split? Basic BlackJack Strategists, such as Derick Warne, say the following: always split aces, never split tens, and always split eights. You can view more splitting strategies in the chart below.

Thirdly, should I double? If basic strategy calls for doubling, you’re RTP is approaching (or crossing) the 100% payout rate! Doubling is a good sign.

Fourth, should I hit or stand? Rules here include: 17 and up always stands; 16 stands against dealer 2 through 6, otherwise hit; 15 stands against dealer 2 through 6, otherwise hit, and so on right through to eleven. If your card value is eleven, then double. Finally, eight always hits. These rules come down to memory.

Why do we rely on the basic blackjack strategy?

A computer simulation derived basic strategy. The computer played several hundred million hands of blackjack through its programs and recorded all the results, and produced a set of ‘best decisions’ for players.

Best decisions here are the decisions that lose the player the least amount of money to the casino over time. The takeaway from this? Using Blackjack Basic Strategy catapults a player’s RTP of Blackjack to around 99.5%, so it’s worth doing your research and referring to the chart below!

### 2. Roulette RTP

The basis of Roulette is that it’s a game of chance. First, you have a wheel where all numbers are either red or black, with 0 and 00 green. The wheel spins, and a ball is released onto it, ultimately landing on a number which becomes the winner.

In roulette, the house has a very minimal edge. However, before we delve into payout ratios for roulette, we need to note the different styles of roulette.

Every style has a slightly different return to the player. For example, American Roulette has both 0 and 00 pockets on its wheel, which increases the house advantage. Your odds of winning are 1 to 38 or 2% here. The average Return to Player is around 94%.

European Roulette is theoretically higher, at 97%. Why is this? Because European Roulette wheels only have 1 ‘zero’ pocket.

These RTP’s are only the starting rates of return and dependent on your wager placement. For example, if you bet on the color black, you have a probability of winning of 18/ 37, an almost 50% probability. In reflection of this high probability, the payout is lower than other wagers, generally set at 2.

Therefore the payout is 2 times the original wager. If we divide 18 by 37 and multiply it by 2, we get out the expected payout ratio. In this case, the ratio would be 97.3%.

RTP in roulette changes with bet placement, which can make it confusing to calculate the return to the player without knowing the move a player is making. For example, a straight bet on a single number would have a lower possibility of winning than betting on a color.

In comparison, if we were to bet on the number 12, then the odds of winning fall to 1 out of 37. That pus the possibility of us winning with a straight bet on the number 12 at 2.7%, significantly lower than our 50% probability when betting on black.

However, the reward for such a bet would be significantly higher as well. That is, there would be a 37 dollar return on a 1 dollar wager if you were to land on the number you picked. If the ball lands on 12, we home with 37 dollars in our pocket. There is one way to win in this scenario and 36 ways to lose.

It’s impossible to lay down a specific RTP for roulette without knowing the way a player engaged with the wheel. In general, play European Roulette for higher odds.

### 3. Slots RTP

Every slot differs in RTP rates, and the best way to work this out is reading reviews and player accounts. As seen in the example at the beginning of this article, payout ratios take lengthy and complicated mathematical equations. We recommend reading expert reviews to find out RTP, like the ones found on this website, to save time and effort and allow you to spend your time enjoying the machines.

## ROI versus RTP

We’ve followed the mathematics of return to player and payment ratios through examples of Roulette, Blackjack, and Slot Machines; however, another term rears its head on gambling forums. Return on Investment, or ROI, is a performance measure used to evaluate the efficiency of an investment.

We calculate this sum by dividing a player’s winnings from a wager by the cost of the said wager. Generally, the ROI is listed on sports betting and online Roulette forums.

ROI differs from RTP, as ROI reflects the percentage of change in a player’s overall bankroll at the end of a period. RTP is the percentage expected to return to the player on a single wager.

## Variance and Volatility

More terms from the gambling forums! Academia is rife with talk of variance, volatility, and dispersion. These terms boil down to very similar definitions.

The variance of a game refers to how quickly your bankroll or table money is changing as you play the game. This change can mean small incremental payouts or prolonged dry spells followed by big payouts.

Games with low variance dish out small winnings reasonably often and games with high variance rarely offer payouts. However, when they do, these tend to be far more significant sums. The term ‘volatility’ refers to how often the game of chance pays out.

Volatility measures how much your money in hand rises and falls throughout a game. RTP is the expected payout, but the variance or volatility level is how often this expected payout actually occurs.

## House Edge

As we delved into definitions and lingo, the term ‘house edge’ came up numerous times. The term ‘House edge’ describes the mathematical advantage that the house or casino has over you as you play. The advantage is the reason the old moniker ‘the house always wins’ rings true.

This advantage results in an assured percentage return to the venue over time. It’s why RTP on slot machines is always below 100.

To work out the House Edge, you take the RTP from 100%. For example, if a slot machine has an RTP of 94.6%, the house edge for that machine is 3.4%. The lower the house edge, the better a player, the chance of winning is.

## Mathematics of Gambling

All this mathematics is impressive and seems to point to clear cut percentages. They prove, in a way, that all players have a chance of winning. But this is mathematics isn’t stand alone. It’s gambling mathematics, which means that there’s a twist.

Say a person plays on a poker machine for five hours. Let’s call him Mark. Mark has \$300 in his wallet. He plays around ten games per minute, totaling in 3 000 games after 5 hours. Mark wagers 1.00 dollar every game. That’s \$3 000 dollars gambled. Yet, he walks away with nothing.

Sometimes he lost, and sometimes he won, always in small increments (this is a low variance example). Every time he won, he put off having to dip into his wallet for a bit longer.

Doing the maths means that by playing \$3 000 from an original \$300.00, the machine operates at a 90% RTP. Yet, all of Mark’s money was gone. Even with a house edge of only 10%, the house still won.

The casino’s never payout all at once. They give drips and drabs and keep the house edge. This variance feeds into the ‘Gambler’s Fallacy.’ This fallacy, also called the Monte Carlo fallacy, is the mistaken belief that if something happens more frequently than average during a given period, it should happen less frequently in the future (or vice versa).

The rules of gambling state that all events are random, so Gambler’s Fallacy is by its nature is made to keep players at the table. This belief contributes to the classic ‘nosedives’ of career gamblers, where gamers raise bets after long dry or losing streaks in the hopes that it will break.

The effect of ‘Gambler’s Fallacy’ on logical and critical thought is a very interest phenomenon, which you can learn more about easily if you’re interested in that!

## Conclusion

Like all things, practice makes perfect, and technical knowledge develops over time. The terms return to player, payout ratio, house edge, and variance seem daunting, but all have simple explanations and meanings.

The longer you immerse yourself in the online gambling world, the more familiar and second nature these terms become. The RTP percentage shows how likely a player is to walk away from the game or table with winnings. However, it doesn’t dictate how or when these winnings are dealt out.

Return to player is one of the most prominent factors gamers consider when choosing a game, slot, or gambling choice. For a good reason! The return to player dictates how often a player gets a payout. A percentage generated by random algorithms and complicated mathematics determines who wins and when.

We have skimmed the surface of this mathematics. Still, without intensive study, memorization of rules (such as BlackJack basic strategy), and a mathematics degree, these theories and calculations can be hard to understand. Easier to understand is this: the higher the RTP, the better your chances of winning.

If you want to know when these payouts will be, it’s time to look at variance! With the knowledge of these terms, you’re ready to go out and play!