Casino games and sports betting can be great fun to play and enjoy, but they remain gambling and, as such, will lead to losses. This is the way games of chance work, and those losses should be taken as part and parcel of this form of entertainment. With this in mind, we can hop towards an interesting idea - what about the average loss of a gambling game session? Can one calculate such a thing?
It turns out that yes, you definitely can calculate the average loss of a game or betting session. If anything it’s far more realistic to think about average or expected loss when gambling as opposed to making a profit. This is actually the smart and healthy way to think when placing your stakes on whatever suits your fancy, and we’re going to walk you through it in this blog post.
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What is an Average Loss?
Before we get into how to calculate your average loss, we should first define the term. Average loss is also referred to as “expected loss,” although that is a bit of a misnomer since here we’re referring to the mathematical average you’re expected to go face when playing. Think of this as the true price you have to pay for your games or betting!
A good way to understand average loss is through Expected Value (EV). This is a term borrowed from mathematics, specifically probability theory and statistics, and is the measure of what one can expect to win or lose per bet placed on the same odds time and time again. In other words this is the average outcome achieved through a certain gamble over an indefinite period of time.
Since Expected Value is an actual mathematical term it comes with a formula. Here’s what it involves:
EV = (Probability of Winning × Amount Won) – (Probability of Losing × Amount Lost)
As you surely know, the probability of losing is always higher compared to the probability of winning. Alas, that’s a fact of the game! That is why the EV, regardless of the game or sports you’re betting on, will always have negative results. It’s how the casino or bookie makes a profit, after all. Multiply the EV by your number of bets, and you’ll get your total average loss for the session.
Expected Value Calculation
Expected Value Calculation
Let’s calculate the EV of a bet by using the most simple example out there, a coin toss. Tossing a coin has exactly two results, heads or tails. Assuming the toss is fair, the probability of either heads or tails landing stands at 50% or 0.5. If we’re going to bet £10 on either outcome then we’ll either win £10 or lose that same amount. Let’s put all of this in the EV formula and see what we’ll get:
EV of coin toss = (0.5 x 10) - (0.5 x 10) = 5 - 5 = 0
As you can see this truly fair bet has no expected gain or loss - the EV is simply 0. However no bet is ever truly fair, as the casino or bookie always gets their cut from your stake. So let’s say that we’re betting on coin tosses at a casino that will take £1 from your £10 bets, meaning you’ll win £9 if you guess the result correctly:
EV of coin toss = (0.5 x 9) - (0.5 x 10) = 4.5 - 5 = -0.5
This example shows how you’ll lose an average of £0.5 from every £10 stake you’ll place on the coin tosses at this casino. Or, one can say the casino takes an average of 5% every bet, which leads us to another important concept in gambling, the house edge.
What is the House Edge?
Very simply put, the house edge is the percentage of a stake the casino or bookie takes in order to make a profit. The house edge differs between games, but here are some examples:
- The house edge of slots typically ranges around 4-15%, depending on the game
- Blackjack has one a very low house edge of 0.5-1% based on how good the player is
- The house edge of craps is also low at 1.41%
- European roulette has a house edge of 2.7%
- American roulette has a higher house of 5.26% due to its second zero pocket
The house edge suggests that if you bet £100 in total on a slot with a house edge of 4% you stand to lose £4. However this is an average calculated over many spins; you might end up losing your entire £100, or winning £50 from your spins. This is because anything can happen in gambling over a short period of time, but as the time spent gambling increases then the numbers will gravitate towards the average, and that takes us to the Law of Large Numbers.
What is the Law of Large Numbers?
The Law of Large Numbers (LLN) was devised by Swiss mathematician Jacob Bernoulli in the 17th century. It pairs directly with the calculations of the Expected Value and House Edge we’ve mentioned, as it states that the average result of a series of experiments will get closer to the expected outcome the more times an experiment is done. In a few words, the results of a few spins come down to luck, but once the spins get in the tens of thousands the result boils down to mathematics. It’s how casinos make a profit, and the reason why professional gamblers go for games with a low house edge like blackjack or poker.
What About the Gambler’s Fallacy?
What About the Gambler’s Fallacy
You might be familiar with the Gambler’s Fallacy. This is the mistaken belief that past bets will affect the present. The most famous example of this happened in 1913 at a Monte Carlo casino, where a roulette wheel landed on black for 26 times in a row. As the ball continued landing on black more and more players placed bets on red as they believed these past results will determine what lands next. However each spin of the wheel is an independent event, and each round is separate from the last.
When we talk about the Law of Large Numbers we’re referring to massive numbers of rounds - tens, if not hundreds, of thousands - definitely not the amount one can partake in during a sensible night at a casino.
Why the Average Loss Matters
Ultimately the concept of the average loss teaches us one important lesson - yes, it is the case that the house always wins. Luck might favour you every now and then to bring you a win, but statistically you’ll always end up losing no matter your strategy or the times you play. If anything, the longer you play the closer you’ll end up getting to the average loss, although this is indeed calculated over long periods of time.
So, what are our recommendations? First off, never play to make a profit, as you won’t get to make one. Gambling should be considered as entertainment at the end of the day. Set a bankroll for playing, and stick to it. Make smaller bets if you want it to last for longer, and don’t chase your losses as this will prove to be a fruitless affair. With this and knowledge of your average loss in mind you’ll be all set to play smarter while having more fun doing so.
