Exploring Casino Game Mathematics: House Edge, RTP, and Variance

Introduction

Casino games are designed to be thrilling and engaging, often keeping players on the edge of their seats with the promise of potential winnings. At Stake, this can be even more so with the Stake Originals – older titles that have stood the test of time and continue to be popular among its users.

The secret sauce behind the intriguing lights and sounds and effects that are all part of the excitement probably lies in the world of numbers that defines the outcomes and profitability of these games.

In this article, we take a look at the essential concepts of casino game mathematics: namely, the  House Edge, Return to Player (RTP), and Variance. 

These components together help you understanding the dynamics of casino games and strategising your bets wisely.

House edge: The casino’s advantage

You might encounter this term a lot in crypto casinos, and you’ll see chatters in Stake talk about “HE” a lot.

The term "House Edge" or HE refers to the statistical advantage or edge that the casino has over players in a given game. This edge ensures that, over time, the casino will make a profit, regardless of individual wins or losses. The House Edge is expressed as a percentage, representing the average amount a player is expected to lose relative to their initial bet.

For example, in a game of Roulette, you will find many variations on Stake. Each variation has a different HE. American Roulette is probably among the highest, with an average of around 5.26% (compared to 2.7% HE on European Roulette). This is because there’s an extra panel on the wheel – the 00. That means there are two, not one panel, outside of the regular panels 1 to 36.

This simply means that over time, for every $100 wagered on American Roulette, the casino expects to make $5.26. This is almost double that of European Roulette, where the casino expects to make $2.7 for every $100 wagered.

So it does make sense for the gambler to choose a game with a lower house edge – always pay attention to the variables offered with unique games. At Stake, the house edge is as low as 1% on Stake Dice!

With an optimal strategy, Blackjack HE can be as low as 0.5%.

Understanding the House Edge is crucial for players as it allows them to make informed decisions about which games to play and how to manage their bankroll. It’s important to remember that the House Edge is a long-term concept; in the short term, players can and do win. This is because of the volatility of results or variance, which we’ll cover in the last section.

Return to Player (RTP): the player’s perspective

Return to Player (RTP) is the inverse of the House Edge and represents the percentage of wagered money that a game will pay back to players over time. If a slot machine has an RTP of 95%, it means that, on average, the machine will pay out $95 for every $100 wagered.

RTP is particularly relevant for slot machines and other games where the outcomes are determined by random number generators (RNGs). While RTP gives a good indication of how generous a game might be, it’s important to understand that it is calculated over a long period and many game rounds. Individual gaming sessions can deviate significantly from the stated RTP. Once more, this is called variance, and covered in the next section.

For instance, you might play a slot with a 95% RTP and either lose most of your bankroll quickly or hit a lucky streak and walk away with a profit. The key is to look at RTP as a guideline for long-term play rather than a guarantee for short-term results.

Variance: the measure of risk

Inexperienced gamblers often complain that they’re losing money even at a low HE game, or they busted their bankroll playing slots in just a few hours despite the high RTP.

This is because HE and RTP are only accurate in a large sample size – just like in statistics. You need tens of thousands, if not many, many more plays, to witness the House Edge or RTP coming closer to its average.

In a small sample size of perhaps just a handful of plays or even just several hundred spins, variance could result in an extremely lucky, or unlucky, streak.

Variance, also known as volatility, measures the level of risk associated with a particular casino game. High-variance games offer larger, less frequent payouts, while low-variance games provide smaller, more regular wins. Understanding variance helps players choose games that align with their risk tolerance and gaming style.

High-variance games are suitable for players who enjoy the thrill of chasing big jackpots and are willing to endure longer losing streaks. These games can be exhilarating but require a larger bankroll and a strong understanding of bankroll management.

On the other hand, low-variance games are ideal for players who prefer consistent winnings and a steadier gaming experience. These games might not offer massive payouts, but they provide more frequent wins, which can be satisfying for players who prefer a less risky approach.

Practical applications and strategic considerations

Armed with knowledge about House Edge, RTP, and Variance, players can make more informed choices about which games to play and how to approach them. Here are some practical tips.

1. Choose Games with a Lower House Edge: Opt for games like Blackjack, Baccarat, or certain types of Poker that have a lower House Edge and offer better odds for the player. Make sure you also follow the optimal strategy – there are plenty of Blackjack guides out there to tell you whether to hit, stand, or even double down your wager. Of course, some players enjoy games with a higher house edge -- where the maximum returns are sometimes more exciting.
2. Consider RTP: When playing slots or other RNG-based games, look for those with higher RTP percentages. This increases your chances of winning in the long run.
3. Understand Variance: Select games that match your risk tolerance. This is especially true with slots. Slots titles at Stake will often indicate the level of volatility associated, so make sure to pick the slot that suits your style!

Remember, staying rational and keeping yourself informed ultimately enhances your gaming decisions and increases your enjoyment on platforms like Stake.

Disclaimer: This article is for educational purposes only. Always game responsibly and seek professional advice if needed.