Roulette

Understanding Roulette Probabilities

Introduction to Roulette

Roulette is by far the most popular game in a casino and there are two reasons for this. First, people like to play roulette because it is easy to learn with any complicated rules; you bet on a number, dozen or colour and if the ball lands where you placed your bet you will win. Secondly, it is because you can win a lot of money very quickly and that is naturally a good incentive; who doesn’t want get rich quickly with minimum effort? 

But what is the chance to actually win something at roulette and is there a way to improve those chances? The chance if winning exists of course but in all likelihood it is the casino that will be the winner. There really is no way of improving the probability of winning with a system; the odds are what they are and the casino will always have the edge. 

Albert Einstein supposedly said that the only way to make money from a casino is to steal.  

Basic roulette strategy

The first you must learn is to avoid the tables called American roulette and only play the European roulette tables. The reason for this is that the American roulette table has one extra slot; the double zero. That means that the American roulette wheel has thirty eight slots where the European wheel only has thirty seven. Does this make a difference? Yes it does! 

The chance of winning on the American wheel, if you bet on one single number is 1/38 or 2,63%, on the European wheel it is 1/37 or 2,70%. The 0,07% may not sound like a huge difference but since the payout is the same, 35 times the bet, you are always better off playing the European roulette wheel. 

If you play the even money bets (black or reds, odds or evens) the difference is even bigger; 47,37% on American wheel and 48,65% on the European wheel. The odds are always on the side of the casino anyway so you should always play the casino game that give you best odds possible. 

Roulette odds

Here is a table over the odds of winning at both an American roulette wheel and a European wheel. Even if the differences appear small it is important to remember that even small differences in the odds will have a great impact on the game. Always look for the game best, or least bad, odds. 

American Wheel
Bet	Probability of winning	Payout
Red	47,37%	1:1
Black	47,37%	1:1
1-18	47,37%	1:1
19-36	47,37%	1:1
Column	31,58%	2:1
Dozen	31,58%	2:1
Single number	2,63%	35:1

 

European Wheel
Bet	Probability of winning	Payout
Red	48,65%	1:1
Black	48,65%	1:1
1-18	48,65%	1:1
19-36	48,65%	1:1
Column	32,43%	2:1
Dozen	32,43%	2:1
Single number	2,70%	35:1

 

Never pay for a roulette betting system 

There have been and always will be people who will try and sell you the perfect system; “a system that is guaranteed to beat the casino every time”. Since the odds are on the side of the casino there is no such system that is guaranteed to work in the long run. The people who claim to have made a fortune from these roulette systems are, shall we say, bending the truth. They may have made a fortune selling the system to gullible gamblers but not by actually using the system themselves. 

Every week I get spam from someone who has discovered a brand new roulette system and they want to share this with me (for a small fee of course) because of their kind hearted nature and because they want to see the casino lose. It is a secret of course so shouldn’t tell anyone about it; we don’t want the casino to find out about it do we? 

In nearly all cases the system is this: start betting the minimum bet on either black or red, if you lose simply double your bet until you win and when you do win, change the colour you are betting on and go back to the minimum bet again and start over. They claim this is their own system that they have created and have all sorts of fancy names for it. The only problem is that this is the oldest system in the world and it is called the Martingale system. 

The Martingale betting system 

The idea of doubling your bet every time you loose is the oldest betting system in the world and it can be used not only on roulette but with any game that pays out even money. If you start by betting on dollar on red and loose the next step is to bet two dollars. If you win you will have won two dollars on that bet and since you lost one dollar on the previous bet you have a total profit of one dollar. And that is how it works; you keep doubling you bet until you win and when you do will always be in profit of your original bet. Theoretically it is mathematically perfect, just look at the table below. 

Spin	Bet	If lost	If won
1	1	-1	+1
2	2	-3	+1
3	4	-7	+1
4	8	-15	+1
5	16	-31	+1
6	32	-63	+1
7	64	-127	+1
8	128	-255	+1
9	256	-511	+1
10	512	-1023	+1

In theory it works but in practice it doesn’t. Just take a look at the “If lost” column and you see why. The amount you have to bet eventually becomes too large for any bank roll to handle and even if you had all the money in the world you still wouldn’t be able to put down the bet needed since the casinos always have a maximum bet on every table. 

So the martingale betting system can bankrupt you in a very short time if you are unlucky. But you may think that the odds of losing that many times in a row are too small that it could actually be worth a try anyway.  It is time we took a look at the probabilities. 

The probabilities of roulette

 

What is the chance that red will be the winning colour? What is the chance that there will be two red in a row? What is the chance there will be ten red in a row? But most importantly; does it even matter?

 

I am not going to bore you with mathematics here but the formula for calculating the chances of hitting red a certain number of times in a row is: [pⁿ], where p= the probability the ball landing on red and n = the number of times it lands on read. 

The probability of the ball landing on red (on a European roulette wheel) is 48,65% and that means that the chance of losing on a single spin is 51,35% (1-0,4865) . Here is a little table of the chances of losing if you bet on a single colour (or odds or evens). 

Spin	Formula	Probability
1	0,51351	51,35%
2	0,51352	26,37%
3	0,51353	13,54%
4	0,51354	6,95%
5	0,51355	3,57%
6	0,51356	1,83%
7	0,51357	0,94%
8	0,51358	0,48%
9	0,51359	0,25%
10	0,513510	0,13%

 So if it was possible to double the bet ten times, there would only be a 0,13% chance of losing? That is one of selling points the scam artist use “I mean, how often will it happen that you lose ten times straight eh?” Actually it will happen, on average,  130 times in 1000 (0,13x1000) and that is way too many. But the thing is that this is not the probability that matters; the only probability that matters is the 51,35% you have of losing every times the wheel spins. 

Gamblers Fallacy 

If you think like this: “The ball hasn’t landed on red for nine straight spins. The chance of getting ten non-reds in a row is only 0,13% so I am going to bet all I own on red. I just can’t lose.”, then you have fallen into what is know as gamblers fallacy. Gamblers fallacy is a condition that make casinos and sellers of betting systems very happy.  

After nine spins of the wheel with the ball landing on black the chance that the ball will land on red on the tenth spin is not 99,87% (1-0,0013) it is 48,65%. That means that the risk of loosing the on the tenth spin as well is 51,35%. The roulette ball has no memory. It doesn’t know that on the previous spins the ball has landed on black every time. The probability of 0,13% for ten straight non-reds is only valid before you start the sequence; for each spin of the wheel the probabilities are always the same (black = 48,65%, red=48,65%, zero = 2,7%). 

Conclusion 

Since the odds the favours the casino at all times it is, unfortunately, impossible to beat the casino in the long run. However, with a strategy you can make your bank roll last longer and thereby increase the chance of hitting that winning streak. And that is what you are looking for; because it in short run anything is possible, even beating the casino. 

Don’t be confused by the probabilities; the chance of hitting red is 48,65% on the European roulette wheel no matter if the previous one thousands spins where all black or all red. 

Never pay money for any type of roulette system or any other type of betting system. EVER! If you want to find a betting system for roulette and other casino games you can find them all for free on line. If you want to learn more about a particular casino game then buy a book. Never pay someone in a back alley for a roulette system that is “guaranteed” to work.