# Roulette – Law of the Third

One of the many systems you’ll find among people who play roulette is something called the Law of the Third. While it sounds like some sort of high fantasy novel, it’s actually based in solid mathematics. Solid mathematics, however, does not mean it eliminates the effects of chance, and it takes a strong set of nerves to play this roulette system. I even get nervous playing it in the practice areas at Bodog !

Let’s take a closer look at the roulette **Law of the Third principle**. The roulette wheel itself has 38 number pockets (if it’s American roulette), or 37 (if it’s European or French roulette). Therefore, the chance that the ball will fall into any particular pocket during one spin is, obviously, 1 in 38 (we’re going to use the American system here). If you map out a complete cycle of 38 spins, there are going to be only, on average, 24 numbers drawn. Some numbers will be drawn 1, 2, 3 or more times, while the other 13 numbers won’t be come up at all. Our aim is to narrow down, to include around a third of the numbers.

Mathematically this system is based on a famous probability problem called the Coupon Collector’s problem.

## Playing Roulette Using the Law of the Thirds

Don’t get excited. Yes, this means that, for instance, after 12 spins, your probability of hitting one of the same number again becomes 12 out of 38; next spin, it becomes 13 out of 38. You can keep on calculating to 37 spins and beyond!

So this is at the core of the Law of the Third technique, using the past spins to determine your bets. It’s not an uncommon practice indeed most popular roulette systems and strategies are based on a similar technique of looking at the last spins.

Here’s how it’s done – first of all you need to make yourself comfortable and keep a record of the spins. You then have to write down each number until you have nine different numbers on your list. You can do this on an online roulette game or at a physical casino, neither will mind if you keep a record of results – stick to pen and paper in a real casino though.

After recording 9 different numbers, gather your chips for one spin (although some suggest two spins!) and get ready to place a series of bets. You need to act quickly and make a single unit bet on each of the nine numbers that you recorded for the next three spins.

What should hopefully happen is that one of your numbers will appear a second time – resulting in a win of 35-1 on a single unit stake. You should do this for the next three spins of the roulette wheel, while of course removing any winning numbers from your stake.

### Roulette Law of the Third = Expectation

The idea of this roulette system is that a single win on the first spin pays 35-1 while you are risking a maximum of 27 units (9 x 3). This means you will have obviously made a small profit increased if it happens on first spin by removing the number from the subsequent spins. If you’re lucky then you’ll hit a second number which will improve the profit to 45 chips. The jackpot from this system is all three spins being successful which will return a profit of 81 chips!

A wise move then would be to stop gambling although many system variants determine different options. One popular method is based on the fact that your profit is enough for three more complete sessions (27 x 3 =81) – so your final profit would be the return on these spins following the same system

People can do very well with this strategy, however not because of any mathematical guarantee. What it does instill like so many of these systems is a degree of discipline. It forces financial management to an environment which often promotes reckless risk taking.

## Problem with Expectation Systems like the Law of Third

So what does the ‘Law of the Third’ actually mean? It’s basically the number of unique numbers that you’d expect not to be ‘hit’ after a series of spins. It’s expected to be around a third, so hence the Law of the Third implying of course that numbers are hit twice.

However, there is no way to predict which one of those repeated numbers the ball is going to land on. That is determined by pure, random chance. The roulette wheel has no memory, and statistics are plotted on averages, not absolutes.

Look at the beginning of that last sentence again: **The roulette wheel has no memory**. Any system from Martingale to Oscars Grind or indeed any based on the Law of the Third assumes that, somehow, the previous spin has some sort of effect on the current spin – and we can see for a fact that it does not.

The system has a little more merit if you’re using it to predict groups of spins, but that’s not how most games of roulette work. You bet on each spin, as it occurs, and there is no way to influence that spin. Use this set of statistics to make your play more methodical, if you wish, but be aware that the Law of the Third does not automatically equal increased winnings.

## Success in Roulette Still Needs Luck

That’s the real point with many of these systems or strategies for roulette, if they are followed they make your betting more methodical. The odds in roulette are some of the best you’ll find in gambling and a smart system which is followed properly can lead to some decent winnings. But none of them actually affect the underlying probabilities, so no roulette systems can guarantee that you win.

They may well equal increased heartburn, however. Seriously though, one of the many issues people have playing roulette is discipline using any of the roulette systems can help with this. As long as you appreciate it doesn’t alter the odds they can be useful.

Law of the third states that during 37 spins (one cycle) will on average seem 24 amounts that are distinct (2/3*37) and half (2/3*1/2=1/3 of the amounts of wheel) will be repeaters. On average it’s truth. Now it is possible to try and mistreat because you wait this fact that too many amounts that are different appeared and you are going to wager against this tendency to continue (must be repeated by something) as they have been appearing in a hope or you merely wager amounts.