The Law of Large Numbers in Betting

There are a number of laws used by bookmakers when creating markets. One of them, the Laws of Large Numbers (LLN) in betting states that the results obtained from a large number of trials will get you closer to the expected value. This means that if you toss a coin in the air a given number of times, it will always show heads and tails the same number of times.

This law is applied on casino games as a theory and according to the law of large numbers (LLN). The average number of results from a large number of trails should be close to the expected value and will tend to get closer to the expected value based on more trails performed.

Large Numbers in Betting

The main importance of (LLN) is that it guarantees a stable long-term result even if the trials performed are more the expected result is still the same and a good example is when a casino is losing money on the first spin of the roulette wheel. The more the trails are performed the possibility of the winning streak coming to a predict end.

The law is only effective if large trials are performed and this may not yield the same result for small trails performed. There is no principle that a small number of observation will coincide with the expected value as in the case of large trials.

The Gambler’s Fallacy

The term Fallacy is defined as a mistake belief and is usually based on unsound arguments or faulty reasoning whereby gamblers or punters place their trust on beliefs and logic.

Also known as the Monte Carlo Fallacy or the fallacy of the maturity of chances and is a belief that if a particular event occurs more frequently than the usual normal during the past it’s less likely to happen in the coming future.

Statistically independent; also referred as historical independence is whereby an established probability does not depend on what has happened in the past. A good example is rolling a pair of dice on a table since we haven’t seen a pair of six’s recently therefore the theory states that there is a good chance for the dice role to six sue to the fact there have been less of six’s.

The gambler’s fallacy can be illustrated by the repeated toss of a standard coin, the toss outcomes is statistically independent and the probability of getting heads on a single toss is usually one in two. The probability of getting two heads in two tosses is one in four and the probability of getting 3 heads in three tosses is one in eight.

After successfully conducting more tosses up to 5 heads in succession the individual may think that the next toss outcome will be tails and not heads again. This is incorrect and this is a good example gamblers fallacy, giving a false belief based on probability.

Another historical example of gamblers fallacy happened in the 1913 a casino Monte Carlo a group of gamblers got interested during the 8th round and started placing money on the Red. As the story goes the white ball landed on black a couple of times and had exceeded its probability possibilities, making it not possible to land on black again but red this time.

As the ball was made to the spin every person at the table was silently watching as the ball made its rounds on the wheel and to their amazement the ball landed on black for the 26th consecutive time with most of the punters backing red they all lost to the wheel.

The gamblers fallacy activated the punters instincts and they automatically forgot about logic, blindly placing their money on red despite believing in their gut feeling they all lost due to faulty reasoning. All the players at that time did not discuss or talk about their wagers they all simply acted on a general belief on punters.

The amount lost during that event is not known but punters really lost a large sum of money to the roulette wheel and this opened eyes to many of them to start to think logically. This tragic event lead to the disowning of the theory on predictions done on probability based on the past event. We punters placing their belief on experience and practice.

How does the law of large numbers apply in sports betting?

On sports betting a different approach know us the progressive draw strategy, this strategy requires a punter to place a stake on a draw rather than a win and if the first match fails we can place on the next match to double or even triple pour winnings, however this only works on champion’s league or Fifa world cup.

It’s unlikely for a Europe champion’s league match to end without a draw or two especially since the match is played on almost the same time and some will always end as a draw after regular time. The bookmakers usually offer an average of 3-5 odds on a draw and can be higher for top teams.

Also it’s important to note that this theory only works based on experience of the punter and it’s more likely to increase the chance of winning it big due to high odds on draws. The strategy mainly works with a large account balance since the first time we try the draw we may loss it so you will need sufficient funds to continue betting on draws and double the wining chance.


Like the theory suggests, it is a base of belief and faulty reasoning. It’s however also important to note that experience is the best teacher. Since this theory has a  tendency to disappoint,we should always use experience to predict the possible outcome and not base our winning chances on past probabilities.

However, despite having a faulty reasoning theory we also get about a 50% chance of winning and the other 50% comes from experience on different gaming styles and strategies used by gamblers worldwide.

Leave a Comment

Your email address will not be published. Required fields are marked *