The Law of Large Numbers

Paul Bradbury a Tennis Tipster on TipsterAcademy. I have been tipping for quite a while on TipsterAcademy and during that time have had frequent conversations with Stuart about various gambling concepts. As I am both a subscriber to tipsters and a tipster in my own right with a reasonably impressive record I was asked to write an article on what people should look for in a good tipster. I thought long and hard about various subjects to cover ranging from the gamblers fallacy, to the concepts of variance and I finally decided the Law of Large numbers is the concept which every gambler should understand. The law of large numbers states that over time, the more you perform an action the more the actual result will regress to the mean, or the expected result. To explain the Law of Large Numbers I am going to turn to the roulette wheel, in my youth I spent 4.5 years working as a roulette dealer in a small casino and it taught me a lot. In a European wheel there are 37 numbers and the odds payable if you hit one are 35 to 1, this gives the house an advantage over the customer, the maths for this is below.

−1×36⁄37 + 35×1/37 = −0.0270 (2.70% house edge)
This is exactly the same as the yield percentage you see for each tipster, i.e. for every 100 chips bet the house expects to win 2.7 chips in the long run, so the house has an expected 2.7% yield. Now 2.7 % does not sound a lot and I know most customers would not touch a tipster with a yield that low. When working at the casino I knew that the casino had an edge, and understood why, it came as a huge surprise to me that the casino often lost, and when I say often I mean often. This is caused by a concept called variance which I will cover in a later article (if Stuart lets me write one). Once I even remember the casino losing every night for a month. However over time the casino always won and over a year the results were about 2.7% of every chip bet. This is due to the law of large numbers. Let me explain. The casino I worked in had 8 wheels running a spin a minute 12 hours a day continuously, that is 12* 60 * 8 = 5760 spins a night over a year 2,102,400 now that is a very large number allowing a very small edge to do its magic. Casinos have been around for centuries and will continue to be around forever because of this edge. The edge is small enough so people win sometimes and so come back and the law of large numbers ensures that the house always wins in the long run – GENIUS. I know you are all bored now and are wondering how this could possibly have anything to do with tipsters, let me explain. I am sure like most people shopping you go for the shiny article in the shop window, you go for the fanciest looking cake with the strawberry on top and ignore the cakes at the back. You will do the same with tipsters, you will look to the top of the yield list and look for tipsters on a good run. You wouldn’t go near a tipster who lost money last month. You would steer well clear of someone who didn’t win yesterday. WHY?  When you now know the law of large numbers, you should look to the large numbers, you should look beyond the last month, or 6 months or whatever timeframe you look into. You should look for the large numbers i.e. the tipster who have been around a long time and consistently make money. The tipster who supplies a lot of tips and works your money hard. They have proven an edge they may be hitting a losing day, or month in the same way as the casino but they have proven they can be trusted to win it back. See the losing month as an opportunity to get in during a negative variance period which I am sure they will recover from and maybe even get a discount and a guaranteed profit sub in the bargain. Remember over 100 – 200 tips you can get lucky or unlucky but over 500-1000s you have proven an edge. I never switch tipsters because they are losing and am currently in very good profit from my BA subs, I do however switch tipsters under other circumstances, which cause me to believe they haven’t got an edge. Those I will cover in another article but believe me when I say I was correct with all but one of them and only one still remains on BA. I am personally now over 500 tips on Tipster Academy and am 99% certain I have an edge, I work hard to keep that edge and spend 30 hours a week running simulations and calculating percentages to decide on what to bet. At the time of writing if you had followed me for the last 6 months you would have turned 2000 into 3700ish far better than investing in a bank. That is with just 5.6 percent yield. If you had followed me in January and February you would have lost over 600. This however has all been recovered with a profit since then as I just kept plugging away with my edge and let the law of large number s do the rest. I am certain I will have losing weeks and months in the future and my yield will go up and down but over time it will stabilise to my expected value due to the law of Large Numbers. So next time you lose a bet with a tipster, stop getting angry they can’t win them all, look at their long term record, check in your own mind that they haven’t changed the way they bet. Check you are getting value for money with the number of tips they produce. Make sure you have a bankroll large enough to cover the inevitable variance and keep following until you recover the money. If a tipster loses there edge BA will clear them off the site and move you to someone who will regain the money. If you are unsure how much bankroll you need to follow a given tipster ask the nice people at BetAdvisor, they can supply this information based on calculations of the tipster’s edge and history. Well that is all for now, please let Stuart ( know if you want any other concepts gone over. Subjects I would like to cover in future articles are as follows:
  • The gamblers fallacy
  • Investment versus Gambling
  • Bankroll management
  • The psychology of losing
  • And many more
You can follow me and track my progress on Twitter (@PaulBradbury13).]]>