How UK Bookmakers Use the Law of Large Numbers to Stay Profitable

Bookmakers rely on the law of large numbers, spreading risk across thousands of bets. For example, in a horse race where a 50/1 outsider wins, only a small percentage of bettors typically back the long shot. Most money is placed on the favourites, allowing the bookmaker to retain the majority of losing stakes and still make a profit.

They also build a margin, known as the overround, into their odds, ensuring consistent long-term profitability regardless of individual results.

By balancing their books in this fashion, the bookies are able to take advantage of the law of large numbers: even when a freak occurrence does happen in sport, eventually their conservative odds-making – and built-in margin – will see them profit from the mammoth sample volume of bets that are placed each week.

Defining the Law of Large Numbers

The law of large numbers is a key concept in statistics. It explains that as the number of repeated, random events increases, the average of the results moves closer to the expected or theoretical outcome.

In simple terms for betting, this means uk sports betting sites do not rely on the result of a single match or race. While unexpected or “freak” outcomes do occur, they are balanced out by the thousands of events that unfold in line with expectations.

Because bookmakers apply a built-in margin to their odds, this high volume of betting ensures that short-term fluctuations are smoothed over time. The cumulative effect allows them to withstand periods of variance and maintain consistent long-term profitability.

‘Law of Large Numbers’ - Wikipedia

It's exactly the same when playing online casinos, each spin of a slot machine is independent and it's RTP only tends to the average after millions of spins. Every single game on the casino floor has a house edge, which ensures that after millions of blackjack hands or roulette spins, the casino will win… even if individual players can enjoy profitable sessions.

An even more straightforward example would be the toss of a coin. You could flick a 10p piece ten times and have eight heads and two tails – that’s an 80%-20% split. 
But if you flicked that same coin one million times, you can be sure that the final result would be much closer to 50%-50%... simply due to the law of large numbers.

Implied Risk

There are two ways to overcome the bookmakers’ inherent advantage.
The first is to enjoy a statistically improbable stroke of fortune. Leicester City won the Premier League title in 2015/16 at odds of 5,000/1. If you had backed them to do so – and immediately stopped betting – you would forever be a profitable punter.

Getting on the right side of variance is fraught with risk, however, and you could end up staking a lot in the pursuit of that winning long-odds outsider or huge accumulator. 
This is an okay approach if entertainment is your main goal, but as a source of sensible investing? Perhaps not.

 

Leicester City’ – Getty Images

The other approach is to try and leverage an edge, grinding out an ROI of between, say, 1-5% over the course of a year with carefully selected +EV bets. 

Although finding an edge is becoming increasingly difficult, many betting firms leverage data science and even AI tools these days in the same way an EV punter might; it’s not impossible… particularly if you have an area of specialism that is outside of the standard remit of the average odds compiler, i.e., overseas football, minor tour tennis, or lower league basketball.

With a defined, repeatable edge that delivers consistent wins in a quantity of statistical significance, you might be able to turn the tables on the bookmakers and take advantage of your own law of large numbers.