Random Chance: Learn About Stats and RTP

Return to Player (RTP)

Return to Player (RTP) is the long-term rate of money won divided by money staked. The opposite of the RTP is the house’s advantage.

That is calculated as 100% minus RTP. So, if the RTP was 95%, then the house edge would be 5%, because 100%-95% = 5%.

Roulette RTP

In European Roulette, the math is pretty simple behind RTP. It’s the number when betting on one color or specific number, divided by all the numbers.So, for black or red, it would be 18, divided by 37 (counting the zero).

RTP here would be 2*18/37 = 0.973 = 97.3. The house advantage would then obviously be 2.7%. 2 is the number used for multiplication because Roulette pays out double.American roulette features much worse RTP and is generally worse for the player due to the double 00.

Blackjack RTP

Blackjack can vary from casino to casino, so it makes sense that RTP will differ widely as well. If you use basic blackjack strategy, that should generally help, and the RTP in that case is usually around 99.5%.

The RTP can change in both online and live blackjack as the dealer hands out cards from the shoe. The RTP can fluctuate from between 95% and 102%. This is all dependent on what cards are left in the decks and can be exploited by those who count cards.

Casinos can usually detect this and prevent them from playing further, but many people are quite skilled at it.

Slot RTP

RTP for slots is usually a little more varied, going between 92% and 98%. This changes by payout table, specific rules for each game, and various other factors such variance/volatility.

Variance (Volatility) Of Random Chance Games

This is an important part of random chance games. Variance, or volatility, determines how rapidly how much money you’re making while playing the game.

If variance is low, you’ll make small winnings, and small losses, regularly. Generally, you’ll lose money as you play due to house advantage, of course, but the losses are small and steady.

High variance, on the other hand, describes a game where you lose a lot, but the winnings are big and happen rarely. It usually boosts your earnings back up to what it was or far past that when it happens.

Variance can also be used to show the statistical distribution of your earnings. These are usually expressed proportionally to the size of your bet, because it’s always a multiple of whatever the amount was that you bet.

For example, in Roulette, all winnings are paid double when betting on a color. When betting a single number, all winnings are 36 times the bet, instead.

Slot variance is more complicated. There are different multiples for different conditions in the same game, and those all affect your bet in different ways. General descriptions are used here, like ‘low’ or ‘high’ variance, which doesn’t really help matters.

Variance of a game has a huge impact on how much money you’ll make or lose at any specific game or machine.

The higher the variance, the better. The reasons for why are the following:

Firstly, it’s easier to win an amount that will let you just walk away with higher variance.

Secondly, because more rounds end in a loss, you don’t bet much from your previous winnings. You lose fast.

Thirdly, you can bet less to have the same amount of a win – because the multiples and amounts are higher. Obviously, this helps you lose less money over the long run.

Expected Returns

You have to remember that payout percentage – or RTP – expresses the normal payout from a single round of a game.

For example, say you had $100 on roulette and you won $1200. That was from one round. If you kept reinvesting your winnings again and again, and kept losing – a normal outcome – those winnings are, of course, decreasing. If you staked twelve more times, in the end, the math would look something like this, with the RTP being used on each round separately:

1300*2.7% = $35.1

Since 97.3% is the RTP of European Roulette, we would use the house edge, 2.7%, to calculate the actual payout average. You need to keep this in mind when trying to figure out the actual returns you may get when you’re doing real gambling.

RTP also does not usually involve a single player. That would be too inaccurate. Instead, many thousands or even millions of players are used to get extremely accurate measurements.

Sometimes, websites may even give a false or misleading definition of RTP, to try and show that players only lose a small portion of what they bet. Of course, this isn’t quite accurate mathematically.

If players use previous winnings to bet, they’re losing more. The RTP, in that case, when you use a bad betting system, can be lower than 50%! That’s really poor.

It’s always most optimal to use a betting system that matches the RTP of the game you’re playing. Don’t place bets using the money that you’ve already won. Stake your whole budget in one round.

Keep betting all-in until you lose or win a good amount of money. You’ll play for a short amount of time, but actually, you will often win a decent amount and be able to simply walk away with that.

Here is another example:

Player 1 and Player 2 both play Roulette. Player 1 bets $10 on a number. Player 2 bets on a color.

They both leave if they win $500 or lose all their money.

If you simulate this, you see this kind of math:

Player 1 has a far better chance of leaving a winner, at about 14.8% of the time. The average amount he left with is about $648, playing 16 rounds on average.

That RTP is about 95.19%.

So, even though he was betting his whole entire budget, he was still winning a decent amount.

Meanwhile…

Player 2 only walked away with the money about 5.15% of the time, with a much smaller bankroll of about $500. Their average RTP was about 21.42%, and they played for about 274 rounds.

It’s not hard to see how variance can affect the payout with an example like this. Player 1 had around a 4.4 times higher RTP than Player 2.

Bet Size Also Affects RTP

The amount you win in a random chance game is figured out using the bet size. This also affects the RTP, of course. The higher the size of your bets, the overall higher the RTP of your betting system is.

That’s of course, assuming, all other aspects of your betting system remain the same: including the initial amount of money you’re willing to use and spend.

Roulette is a very good example for this, and we’ll use it here.

Player 1 and 2 come to a casino, again with $100. They leave if they hit $0 or $500. Player 1 bets $20, and Player 2 bets $5 each round. Both players bet on color, red or black.

If you run the numbers, Player 1 manages to get to $500 10.9% of the time. This is about 48.68% RTP. An average number of 84 games were played.

Player 2, on the other hand, fares far worse. Less than 1% of the time do they manage to win $500, with an average round number of over 700. The RTP is about 3.555 – absolutely horrendous.

The odds are clear as day: if you place low bets on a low variance game, you’re going to lose money.

You may play for longer, but your odds drop significantly. It is not in your favor.

As another example, high variance games with high bets result in some interesting numbers. Player 3 comes to a casino with $100, plays roulette, and all-ins on a single number. Only 2.71% of the time would they win, but the RTP ends up being about 97.4%, due to the wins being $3600 in value.

Our Recommendation For a Gambling System

After reviewing all of this information, it’s clear that the best gambling system is one that has a tradeoff between how much you win, how big the win is, and how long you stay in the casino.

If you want to play for a reasonable amount of time, while having a good chance of winning, the numbers below should help out a little bit with that.

With this data and information, it’s easy to see how important variance is. High bets on numbers can defeat bets on color with ease, even if they’re larger in size. Your stay in the casino will take a considerable amount of time. If you spend a small amount on each bet, your chances of actually walking out with a good amount of money are nearly zero.

If you simulated this a hundred times, you’d still nearly never win.

Part of the goal is to, of course, have fun. And you shouldn’t sacrifice that for efficiency, necessarily, but it’s best to choose a game with high volatility and then try to win big odds with small bets.

So the best betting strategy for roulette, with a $100 budget, is to be between two and four dollars on whatever you think your lucky number is. Fixed bet types and bet sizes are useful in that way.

Conclusions

Finally, here are our conclusions, and what we can take away from all of this information.

How much gets paid out from a game of random chance generally only applies to one round. Your real return will be lowered if you stake winnings.

It’s impossible to not lose on every bet. If you limit your number of bets, however, you’re limiting the profitability of the casino while you are there.

RTP is dependent on things like the variance of the game, how many bets you place and how large they are, and how long you play/when you leave the casino.

Variance itself is simply determined by the multiples of the bet and how much a player can win. The higher you can win, the higher the variance.

Games with more volatility are far more favorable than games with low volatility. It is better for the player.

When varaince is high, you can turn a small chunk of money into a much bigger sum.

When your bets in rounds are large, the RTP of your gambling system is very high, when the money you walk in with is fixed.

If you gamble for fun, then finding games with high variance and betting your money there is the best. A good win or two could get you to the money you want, otherwise you may lose your budget.

Remember that this is a tradeoff system: you’re trading the duration of time you play and the RTP of the gambling system you use.