The Role of Variance in Gambling: Why Winning Streaks Happen

Variance is the key ingredient that gamblers need to make a profit and an essential part of casino games. Understanding how variance works, and allowing it to play its course is crucial for making a betting system and trying to turn a profit. To get a better understanding of how it works, we will dive deep into the science behind casino games, analysing frequencies, patterns, and tendencies.

Players tend to misunderstand how variance works and buy into beliefs such as winning or losing streaks. While they can occur, they are not scenarios that you want to rely on or make any dangerous assumptions about. Here, we will analyse how variance works and how you can work it into your game.

Defining Variance

Variance is a measurement of how much the real results differ from the statistical probability. This deviation can occur if, say, you bet on red in roulette and win 2 or 3 times in a row, or if you go without a win for the same number of rounds. Before playing, the mathematical odds of the ball landing on black 3 times in a row is 1/8, meaning there is a 7/8 chance of a red landing anywhere in the first three goes. Variance is usually more prominent when you have played fewer rounds.

When you play more outcomes, then the anomalies and variance should balance out, and theoretically, the ball should land on red nearly 50% of the time. The Monte Carlo method uses hundreds of thousands of simulations to determine the odds, and frequency of winning. The more outcomes you have to analyse your results from, the closer they will be to the theoretical odds.

However, it can also mislead players into making wrong assumptions. For instance, if you have played 3 rounds and not hit red yet, it doesn’t mean that the odds on landing red in the following round will be greater or smaller. This is a common cognitive bias that gamblers can form, and something you need to steer clear of.

Significance of Variance in Casino Games

Casino games are designed to produce random results, whether it is drawing a card, spinning the reels on a slot machine or any other mechanism. Even though we have the technology and software to analyse the statistics, we cannot accurately predict what will happen. The likelihood of winning a straight number bet in roulette is 1 in 37 if you are playing either French or European roulette.

So, therefore, in a statistically perfect world, you should win at least once in 37 rounds. But while probable, it is not always the case. In baccarat, the statistical odds of winning Banker bets are approximately 45% of the time, but there are no guarantees that you will win 9 times out of every 20 rounds you play. Especially when you only play a few hands.

Why Winning or Losing Streaks Happen

A winning streak is a prime example of variance doing its magic. You win consecutive rounds in a game, beating the odds and pulling in sizable returns. This is just a product of variance and has no foreboding on what will happen in the next round. Winning streaks are simply a part of the natural ebb and flow of probability, just like flipping a coin and landing heads 5 times in a row. It is just as much a part of the game as a losing streak.

Variance can occur in all types of bets, no matter how likely or unlikely they are to win. Let’s say you play straight numbers in roulette, with a chance of 1 in 37 to win. Should you play 37 rounds and win 3 times, variance has given you a great helping of luck. In theory, you would have won only once if there was no variance. But you have won triple the number of times that you would have by laws of averages. It may not be a winner streak by definition. But it is a streak of good luck that will undoubtedly send your dopamine levels through the roof and motivate you to play more.

However, you must always be prepared for any eventuality in which variance works against you. Just like winning streaks, losing streaks can come at any time, without warning. You may find that after winning at a higher frequency, suddenly, your rounds end in losses one after the other. The statistics point out that over a longer period of time you can reduce these anomalies, but even then, that is not good enough if you want to build a profit.

Why You Need Variance to Turn a Profit

We have talked about the probabilities of winning casino games, but not how the house takes its cut. Casinos don’t design the games intentionally so that you will lose. Instead, they take a small cut out of your potential returns to create a house edge. This means, that even if you win the mathematically perfect number of times, you will still be at a loss.

For example, in roulette, a red/black bet is priced at 1:1, but you only cover 18 of the 37 segments on the wheel. The zero does not count, and therefore your odds of winning are slightly less than 48.64%. To break even, you will need to win 50% of the time, meaning you will need to win more times than the odds suggest.

This is the same in all casino games you play, as the house must make a profit to keep running its business. It is a well accepted fact, but it does mean that if you want to make a profit, you will need luck and variance to play on your side.

Where Variance Can Differ in Casino Games

Each casino game has its own bets, pay tables, mathematical odds, and game rules. The aspects that unify them all are that there is uncertainty about what may happen and that you have to beat the real odds to make a profit. Where there is randomness, there is room for variance to play a part. There are no casino games with “more” variance than others, as this is just a measurement of how much the outcomes are different to what is mathematically sound.

But there are different degrees to which you may feel this variance, and that is where you need to stay alert. For instance, when playing games where you have a close to 50% chance of winning each hand, it is easier to notice bigger discrepancies. In blackjack, Banker/Player bets in baccarat, 1:1 bets in roulette or various other casino games, the effects of variance are felt greater. You don’t really expect to win 4 times in a row playing Banker bets in baccarat, it is a welcome winning streak that is an obvious example of high variance.

Multi Tier Payouts and Paytable Structured Games

In video poker it is a bit more complex, as there are numerous ways to win. The complex paytable structures can make counting the variance very difficult. At a lower level of variance, you can win consistent smaller hands, with a fair share of losses in between. It is the most likely outcome, based on the design of the game. But then you draw a Royal Flush, and suddenly the variance shoots up. You will feel the effects of the high variance immediately with a big win, especially if you made the big hand relatively quickly.

In that regard, slots are quite similar to video poker. They too have structured paytables, and 1 spin can either win nothing or go as far as to trigger a bonus round and make tremendous returns. Slots that have partial payline payouts can reduce the feeling of variance, as they can produce consistently smaller wins. You won’t really feel whether you are in the profit or not without looking at your bankroll. That is, unless you suddenly trigger a bonus game that will flood you with huge winnings.

Optimising Your Gaming Strategy

While variance can be frustrating, but it is important to factor it into your gaming strategy. Especially if you are looking at the bigger picture, and want to build your bankroll in the long run. Before playing your game of preference, you must create a bankroll that can handle a good amount of variance. You shouldn’t be relying on getting any returns. Never mind how likely it is that you pull in some smaller wins to maintain your bankroll.

Draw out a plan for your gaming session, approximating how much money you want to spend, and how long you are going to play for. Then, you can start thinking about realistic goals and markers to hit during your gameplay. To ensure you don’t end up chasing losses or go bust, you should also make markers for your loss limit. Namely, how much you are prepared to lose before calling it a day.

Making Space for Variance, and Taking Advantage of It

An optimal budget is one that can sustain a good long gaming session. The hope is that there will be some variance during your session, and for it to work in your favor. You may experience fluctuations in your bankroll during gameplay, but it is important to stick to the plan. When you plan for variance, you are planning for both winning and losing streaks. Should you come into a winning streak, you can cash out while you are ahead, and finish on a high. Losing streaks can be frustrating. However, if you weather the storm, the variance should diminish and your returns/losses should balance out.

We can’t assume whether there will be high or low variance, or whether it may be favorable or not. But by calculating for all possible scenarios, you are best equipped to optimise your gameplay. Think of the bigger picture, and how your actions can make a profit in the long run.