# Explained: the Law of Large Numbers in gambling casinos

Some would say that being successful in gambling betting can’t be attributed solely to luck and statistical probability. Like the rest of the universe, gambling would also be influenced by laws of physics. This might sound somewhat unrealistic to others, but everyone looking for ways to beat the casino should always consider new theories.

The Law of Large Numbers is one of the theories that has been around for a long time now, still fascinating gamblers ever since it was introduced in 17th century Switzerland. In today’s post we will explain the law of large numbers: how does this law apply to gambling casinos?

## The law of large numbers explained

Don’t worry. You don’t have to know any physics or math, nor be an expert to understand the basic idea. On the contrary, the law of large numbers is actually quite simple and can be tested easily by any player. The law of large numbers (LLN) is part of the probability theory and examines the result of performing the same experiment repetitively. The idea is that the more often you repeat a certain action, the closer the results will be towards the expected value.

To illustrate this:

Imagine tossing a coin. With each time you toss the coin there are two possible outcomes, heads or tails. Theoretically, the chance of both outcomes is 50%. Now if you toss the same coin 10 times and write down the results, it is very likely that the 50% percentage is incorrect. In a ten-fold experiment, the result could even show 10 consecutive heads, hypothetically speaking of course. However, if you continue to toss the coin another 100 times, you will see both percentages move closer to 50% the more you toss it. If you were to flip a coin 1000 times, you would get an even more balanced outcome. The more times you toss the coin, the closer the results are to the theoretical mean of 50% for each side.

This coin toss is the simplest experiment to prove the law of large numbers. This law of large numbers is named after Jacob Bernoulli, a 17th century Swiss mathematician and mechanic. Bernoulli came from a mathematician family and is most known for his law and his derived saying, “Everything in the Universe always balances itself.”

## Overview of probabilities

The example of a coin toss is one of the most practical examples of how probabilities work in the world of games of chances, but it is needless to say that each game of chance comes with its own probabilities. To give you a better idea of how this works per game of chance, we have included some of the most played games in online casinos. The probabilities with which you will end up when implementing the law of large numbers per game of chance are:

• Dice: 16.6%
• Cards: 1.9% (52-card game)
• Blackjack: 4.839% chance of 21
• Roulette: 48.6% (in European roulette), 47.3% (in American roulette)
• Slots: 0.00009% for three of a kind with 22 symbols per wheel, e.g. 3 lemons.

## Northcote Parkinson

As with other theories there were also some criticism on Bernouilli’s law. It was Northote Parkinson, among others, who pointed out some of the main defects of the law of large numbers. According to Parkinson, external matters can play a role in a real life setting, such as expectation, habituation, and psychology — different from a theoretical context which doesn’t take into account these factors. All these additional factors do cause noise however. If only relying on the law of large numbers, without any foreknowledge, the law could be interpreted wrongly and lead to inaccurate expectations. The law itself is therefore invalid as external noise affects outcomes and makes the law…kind of, lawless really. If only relying on the law as promoted by Bernouill, the gambler could blame the dice to be manipulated.

### Parkinson’s law

The British naval historian and author Parkinson also pointed out how his findings can provide useful insight for management teams trying to be as time efficient as possible. Some of these conclusions are expressed in his own laws, with Parkinson’s law being the most known. This law basically suggests that the time that a task takes is equal to the time available. In other words: if you want something to be done quickly and efficiently, you need to give the task to someone who is already busy with other things. This way, that person will speed up the process to get things done as quickly as possible, trying to avoid any failures so that the same process won’t need to be repeated anymore. One of the most important external factors omitted by Bernouill would therefore be time management. In a lot of casino games (think of decision making in blackjack), pressure, and thus time management, plays an important role in the effectiveness of a certain gambling strategy.

## Gambler’s fallacy

The law of large numbers is sometimes referred to as the Gambler’s Fallacy or Monte Carlo fallacy. The opposite is true as well, the gambler’s Fallacy error is often explained by relating it to the law of large numbers. The gambler’s fallacy is the misconception that there is a degree of dependence between independent stochastic events, in such a way that an event that occurred in the past was less frequent than expected, will need to occur more often in the near future as a compensation. For example, when tossing a coin, the gambler assumes that the chance of ‘heads’ increases when ‘coin’ is thrown a number of consecutive times.

### Game of chances don’t have a memory

The error is essentially a wrong, but very common conclusion made from the basics of the law of large numbers: indeed, in the long run, with a pure coin, the ratio between the number of times heads and the number of times coin will approach 1:1, but this is in no way compensated by some sort of natural tendency towards the mean. Also, there is no requirement that the ratio should be about 1:1 for smaller series, as divergences are very common. With every new flip, the chance of heads is 50% once again, independent of the last tosses. After all, the coin cannot remember what happened on the previous tosses. This incorrect theory occurs often in casinos, especially with the red vs. black bet on roulette.

## Conclusion

The only winners of law of large numbers are the casinos and bookmakers. In fact, it is their main revenue model. The house always wins in the end because their revenues are fully based on the idea of the house winning more than the player — at least in the long run . After millions of roulette spins, sports bets, and slot machine spins, the theoretical percentages will always be in favour of the house, to be found in the Return To Player percentage or the house advantage. This percentage is expressed from 0 to 100% and will always be lower than the full 100%. With a RTP of 98% (house advantage is 2%), the return to player for every £100 would be £98 and the house earning £2 of every £100 in bets. This explains the law of large numbers and how this law applies to gambling casinos. This doesn’t mean the player can win, but in the long run — in large numbers — it is always the house that prevails.

## Best Casinos in UK

1.

#### 100% up to £150 with 50 free spins

T&Cs apply
Significant terms: T&Cs apply. New player only 7 days to claim offer and deposit a min of £10 with a further 7 days to wager 35x. Cash stakes only and wagering contributions vary.
Max reward £150. 50 wager-free spins 0.10p each on Big Bass Splash awarded after wagering complete, winnings paid as cash. 3 day expiry.18+ BeGambleAware.org.
2.

#### 100% up to €/£99 with Free Spins

Yako Casino offers lottery, live casino and a bunch of casino games. You won't have a boring minute when you play here. Claim the welcome bonus - a matching bonus plus free spins to start your casino experience at Yako Casino.

T&Cs apply
18 +. Min deposit €20. Wagering 40 x bonus. Live casino is excluded. Valid for 30 days. New players only. Begambleaware.org. 18 +. T&C applies.
3.

#### 100% up to €/£100 with 10% cashback

CasinoCasino is a big brand in the UK and have a lot to offer for their players. Here you have a big selection of games and also a huge welcome bonus. The first impression with CasinoCasino is excellent!

T&Cs apply
New players only. 18 +. Min deposit €10. Wagering 40 x bonus. Max bet €5 with bonus funds. Live casino is excluded from this bonus. 100 % up to €100 on your first deposit. Welcome bonus excluded for players that deposit with Skrill or Neteller. Begambleaware.org. 18 +. T&C applies.
4.

#### 50 Free Spins on first deposit

PlayOJO has been in the industry since 2017 and provides the players with a big selection of games from NetEnt, Evolution, Thunderkick and Play'n GO for example. You get a welcome bonus when you sign up and make your first deposit. It's worth to have a look at PlayOJO - one of the biggest brands in UK!

T&Cs apply
First deposit only. 50 Free Spins on the Book of Dead slot. Min deposit €10. Excl. new players in N.I. Each Free Spin valued at 10p. OJO’s Rewards and Game Play policy applies. Begambleaware.org. 18 +. T&C applies.
5.

#### 100% up to €/\$/£200 with Wager Free Spins

Videoslots casino comes with over 3000 games and a wide horde of online slots. Treat yourself to some exciting casino action, all in one place. With so many games, it means more jackpots and more fun!

T&Cs apply
New Players Only 18+. 1st Deposit Bonus with a minimum deposit of £10. Wagering requirements: 35x bonus. Maximal bet: £20 or 50% of starting bonus value (lower value applies).
You have 7 days to activate the bonus, once activated welcome spins must be used within 24 hours.

Welcome Spins are free from any wagering requirement. No maximum withdrawal limits. A first deposit is required to play these spins. Bonus will be paid out in 10% increments to your cash account. Casino Videoslots gives you a chance to win up to 4,200 Extra Spins on Battle of slots. Full Bonus T&C Apply

6.

#### 100% up to €/£300New players only, min deposit £10, wagering 45x, max bet £5 with bonus funds, 100% up to £100 bonus on 1st deposit, 50% up to £200 on 2nd deposit. No max cash out on deposit offers. Welcome bonus excluded for players depositing with Skrill or Neteller. Full T&C’s apply

Hyper Casino is fairly new in the industry but it boasts of really speedy transactions and responsive a website. Even more interesting is that in the first few months after launching, a Swedish player won a mega jackpot at Hypercasino!

T&Cs apply
1st deposit bonus.100% match bonus up to £/€/\$ 100 on first deposit. Second deposit bonus 50% match bonus up to £/€/\$ 200 on second deposit. A minimum deposit of £/€/\$ 10 is required. Maximum bonus offered will be communicated in the details of each specific promo.

The welcome bonus is available to players from the following countries: United Kingdom, Austria, Canada, Germany, Ireland, Norway, India, New Zealand, South Africa and Switzerland. Unless other rules are specified, bonuses are valid for 30 days and are subject to the X45 wager requirement.

Slots and Other Games apply towards the wagering requirement. Table games, Video Poker and Live Casino do not count towards the wagering requirements. Bonuses cannot be used in the Live Casino. Bonus Terms Apply
7.

#### 100% up to €/£1000plus free spins

Casinojoy promises lots of happiness and bliss for all its players. With the splash of colours, an extensive range of casino games, interesting bonuses and promotions for daily and weekly joy!

T&Cs apply
The welcome bonus is only available to players who create an account and make their first deposit at Casino Joy. As a player, you must deposit a minimum of £10 in one instance. When you do not wish to receive the New Player Welcome Bonus offer, you have the option to opt out upon making their deposit.

Players can only use the Bonus Codes from the New Player Welcome Package once. You will need to wager the Welcome Bonus 40x before you can withdraw the Bonus or any winnings gained from it.

The 20 free spins will be instantly credited upon a qualifying deposit. The remainder will be credited at the rate of 20 per day for 9 days on Starburst.
Casino Joy reserves the right to change the pre-selected free spins game selection at any time, at its sole discretion.

All Free Spins from the New Player Welcome Bonuses are valid for 72 hours upon activation, unless otherwise stated. The maximum withdrawal amount for a player from their Free Spins is £100.

Deposits made via Skrill or Neteller are not eligible for the New Player Welcome Bonus.
The General Terms and Conditions of the Casino Joy website apply.

8.

#### 100% up to €/£300 with Free Spins

This hilarious casino is one of the best known casino brands on the Internet. It's winning awards left and right and has a massive selection of games available from all the leading developers.

T&Cs apply
18+. New UK customers only. Opt-in required. 30 free spins on Book of Dead game upon registration with NO wagering requirements or deposit required for spins AND 100% deposit bonus up to €300: Min deposit €10 and 30x wagering requirements apply on bonus (game weighting applies). Max bet applies. T&C Apply.

9.

#### Level up and get an extra wheel

Rizk is a highly popular and vibrant superhero-themed casino. The mascot, Captain Rizk, fights shady deals and promises “real rewards, no bullshit”.

T&Cs apply
+18, play responsible. full terms and conditions apply.