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Science of Roulette Betting

Last updated on April 7, 2019

Understanding the Basics

House Edge

The house edge is the difference between the true odds and the odds that the casino pays you when you win. Though every bet you make has a certain probability of winning or losing, casino games generally provide a predictable long-term advantage to the casino, or “house”, while offering the player the possibility of a large short-term payout.

If you bet on the flip of a coin, the probability of heads or tails is fifty-fifty, and this would be an even money bet. If you bet a euro and was paid a euro when you won, you would be paid true odds however if the casino only paid you 98 cents every time you won instead of a euro, the house edge in this case would be 2%.

The house edge varies from one game to another and special attention must be taken to choose the tables which have the least house edge and the most advantageous game rules.

Bankroll

This is basically the cash you bring to the gambling table. 

My recommendation, even if you’re equipped with the best betting strategy, is never to start with more than you can afford to lose. The idea is to walk away from the table as a winner but bad streaks and very bad luck can happen so before you start betting you must look at your bankroll and think …”This cash is no longer mine!’’

Even Betting

This is when you bet in a way that you can win 1:1 odds. If you play roulette and bet on red or black or high or low you’re betting on an even winning bet.

This is usually the system with the highest probability percentage available (close to 49% depending on the house edge).

Table Limit

This is the maximum amount a casino will let you bet at one go. Table limits can be used to manage, in a limited manner, who plays at tables.

A casino which wants to project a more exclusive image can set the limits higher so that the casual tourist walking through would not be as likely to sit down and play.

Table limits though are usually used so that the casino protects itself from a lucky player that might accidentally, with a stroke of luck, break the bank. Breaking the bank means that a player wins all the available money in the table bank that day. Should that happen, a black cloth is usually placed over the table until the bank is replenished (obviously mechanical tables not online ones).

Roulette at the Casino

Players playing Roulette (French diminutive for ‘little wheel’) have a large variety of betting options.

Placing ‘inside’ bets is either selecting the exact number of the pocket the ball will land in, or a small range of pockets based on their proximity on the layout.

Players wishing to bet on the ‘outside’ will select bets on larger positional groupings of pockets, the pocket colour, or whether the winning number is odd or even. The payout odds for each type of bet is based on its probability.

Normally there are two types of roulette tables; the European with one Zero and the American with an additional Double Zero.  The important difference between the two is the difference in the House Edge.

If a player bets on a single number in the American game there is a probability of 1/38 that the player wins 35 times the bet, and a 37/38 chance that the player loses their bet. The expected value thus is  −1×37/38 + 35×1/38 = −0.0526 (5.26% house edge). 

For European roulette, a single number wins 1/37 and loses 36/37 thus  −1×36/37 + 35×1/37 = −0.0270 (2.70% house edge).

Outside bets will always lose when a single or double zero comes up and the presence of the green squares on the roulette wheel and on the table are technically the only house edge.  

However, the house also has an edge on inside bets because the pay outs are always set at 35 to 1 when you mathematically have a 37 to 1 chance of winning a straight bet on a single number.

Unlike card games luck has a major role in roulette and to increase the odds of winning most gamblers try to predict the next draw either by trying to calculate the probability or else by using betting sequences in which a win makes up for any prior losses or a combination of the two.

The problem with these kind of strategies is that, remembering that past results do not affect the future, it is possible for the player to lose so many times in a row and by increasing his bets he either runs out of money or hits the table limit.

Although it seems hard I made serious money with this game by using sequence of bets that generate winnings fast enough that they absorb the damage of a one-off losing streak. 

Apart from having a good betting strategy before trying to play this game I recommend choosing a European table (or any table with one zero). Ideally try to find a table playing a French Roulette. 

The French roulette game has a special and unique rule called La Partage.

The La Partage roulette rule says that if you make an even money bet, and the roulette ball lands on zero, you lose only half your bet (decreasing house edge by half).

Probability

In reality when gambling on a casino table there is no such thing as an event being due.  An event is not more likely just because it has not happened for a long time.

Many people mistakenly believe that if one colour in roulette has won several times in a row then the other colour is overdue and they should bet on it. While the ratio of reds to blacks will always approach 50/50 in the long term, it cannot be concluded that this will happen in the short term.

It does not matter what the history of past spins is; every trial in games of luck like roulette are independent, and each colour is equally likely to come up every time. While playing roulette in actual fact the probability of on colour coming up is of (18/37) which is 48.64%.

Neither the roulette wheel nor the small ball has a memory so the percentage that an even bet will come out is always of 48.64%. However a streak of the same even bets is not a common occurrence and does have a weight on future bets in a certain way.

If you flip a coin a thousand times then it is mathematically likely you will have a certain number of streaks of different lengths. These streaks are fairly regular, in other words you might expect to have 300 streaks of 2, 200 streaks of 3, 100 streaks of 4, 50 streaks of 5, etc and a certain number of longer streaks, 8 or above.

Therefore the longest the streak the less unlikely it is for that particular pattern to come out. While the probability that a certain even bet will come out is a constant 48.64% the percentage that a pattern of a long streak to come out is much much lower. Actually the longer the pattern the less likely it is.

We can calculate how likely it is for a streak of 20 reds to come out by using the following formula: (18/37)20 which amounts to 1 in 1813779.

We can calculate how likely it is for the same number to come out 7 times in a row by using the following formula: (1/37)7 which amounts to close to 1 in 9 Billion. We can calculate how long is the longest likely streak to come out after a 1000 spins by using the following formula:

Run = (-1/ln(probability of loss))*ln(# spins).

So for us: Run =(-1/ln(0.53))*ln(1,000,000) = 21.76.

So 22 is exactly what you should expect for the maximal run.

An understanding of the law of the large numbers leads to a realisation that what appear to be fantastic improbabilities are not remarkable at all but, merely to be expected.

Let’s imagine a scenario where two players, one with a big bankroll and one with a small one start playing at the same casino table.  If a game is fair it is still true that if it is played until one player loses all his money, then the player who started with most money has the better chance of winning. 

The richer man’s advantage can be calculated:  If one player’s capital is X and another player’s is Z, then the probability that the player who began with X is ruined in a fair game played to a conclusion is Z/(X+Z) and therefore that the probability that he will ruin his opponent is X/(Z+X).

This overwhelming advantage to the player with the larger capital is based on a fair game.  When a player tries to break the bank at a casino, he is fighting the house edge as well as an opponent with much larger resources. 

Even a small percentage in favour of the casino reduces the probability of the player ruining the casino to such an extent that his chance of profiting is minute.

Roulette Betting Strategies

Although some of these systems are specific for the roulette most systems and sequences can be used for any kind of wagers starting from coin tossing to horse racing.

Even if your game is something unique or exotic, testing a betting system on a roulette platform before is quite prudent because in practice roulette is a basic and quick game of betting on a number or group of numbers selected by a RNG (Random Number Generator).  

Most online casinos offer a variety of casino tables that you can test with token money. These are the best training platforms available before trying your luck with real money.

Most of these systems are being sold by people (scamme…’cough cough’) on other websites promising high returns, constant weekly income and unimaginable wealth.

I have acquired almost all these systems and software and never found any that was constantly successful and could beat the house edge in the long run.

Flat Betting vs Progressive Betting

Flat betting is when you wager the same amount of money with each game played while progressive betting is when you increase the bet when you lose a previous game with the intention to make up for it with a consecutive win.

In my opinion unless you have a system that can accurately predict future draws (highly unlikely) flat betting is nonsense.  The following is a quick test to explain the difference. The Flat Better will bet €5 each time while the Progressive better will use a sequence of (€5, €10, €20, €40):

Result of Draws        Flat Betting         Progressive Betting
Lost                                        -5                            -5
Lost                                        -5                            -10
Win                                        +5                           +20
Lost                                        -5                            -5
Lost                                        -5                            -10
Lost                                        -5                            -20
Win                                        +5                           +40
Total                                      -15                          +10        

Obviously this time the player using progressive betting was lucky that he didn’t lose the last bet.

Scatter System

I had a lot of faith in this one when I first heard about it. Even the reason behind it is very poetic in my opinion.

Basically the idea is to focus on the roulette wheel and realise that with time all sections of the wheel will be hit. Like tiles in a yard when it starts raining, the first drop will hit one tile, the next will hit another but after a few seconds all tiles will be hit.

How to use it:

With this system you focus on inside bets. By using a software or printout of a roulette wheel you start marking down the numbers that are drawn until you find a patch of numbers next to each other that have not been hit.

The time when you start betting is referred to as the ‘entry point’ and to be safe these are good guidelines:

Adjacent Number            Entry Point (Spin Number)
12                                           14
11                                           16
10                                           17
9                                              18
8                                              20
7                                              24
6                                              30

If for example you get 9 neighbouring pockets on the wheel and 18 spins have passed its time to bet. Put €1 on each of those 9 numbers and spin.

If you win you get €36 less the €9 you have bet. If you lose you must bet €1 on each of those 9 numbers again.

Keep in mind that each time you lose a spin you’re losing (bet on each number  x  number if adjacent numbers) and if you win you get (bet on each number x 36).

Therefore you must create a sequence of bets so that when you start betting by the time you win, you still get all the money you bet back plus a small profit.

In the case of 9 numbers a successful sequence would be 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16 ….hopefully you’ll win before you have to go further.

The thought behind this system does make sense. In the long run no part of the wheel will not get hit. Probability will convince you that after 30 spins a group of 6 numbers next to each other is due to get hit but from experience I can assure you that ‘due to’ is loser talk and sometimes even if its expected it does not happen soon.

What is annoying about this system is that you wait and wait and when it’s almost time to start betting the section gets hit and you start waiting again. Once you start betting, after a few spins from the sequence you notice how fast the bankroll is going down and unless you have a decent amount put aside you can consume that before your section is hit.

The excessive waiting and steep increase in wagering makes this system very unnerving.

Dozen Bets

A very common system that has been sold for years is this system where you bet either on one of the 3 columns or else on one of the 3 sections (Low, Middle, High). 

The fact that Casinos, these past few years, have been creating e-books explaining this system, and asking people to try it on their online roulette makes you already wonder how successful this system is in the long run.

Since the table pays €2 for every €1 your betting progression is not as steep as other systems and thus gives the player the illusion of being safer. 

How to use it:

Spin in vain without betting until you notice that a certain section or a certain column has not been drawn for 7 spins. When this happens start betting this sequence until you win: 1, 2, 3, 4, 6, 9, 13, 20, 30, 45, 67 …

This system does work for a few times but eventually (sooner than you might think) you’ll hit a streak much longer than your sequence and end up losing all your previous winnings and half your original bankroll.

The more you wait to start betting the safer the system becomes but the more irritating it is because you end up waiting more than actually betting.

Since the progression is less steep than others it can afford to be much longer but as experience will show you …its still not long enough.

A variant of this system is betting on 2 dozens at the same time. Since you’re betting on (24/37) its hard not to win and in fact most of the time you make your money back and get an extra 50% profit.

The issue with this system is that you’re risking of losing 4 times as much as you’re chancing to win.

Software

I managed to acquire the most popular software available. The way most work is that you input the number drawn on the roulette and after a few initial spins the software will tell you where to bet.

One popular program will ask you to put 5 units in different positions per bet (eg. Even, high, black, middle section and 3rd column) and most of the time you do win 2 or 3 of them.

Whether you lose or win the software will always tell you to bet 5units.

While testing it I realised the software is calculating probability and assuming for example that if even came up 3 times in a row now its worth betting on odd. I didn’t trust this system with real money and in fact I lost a 100 token money in less than half an hour.

Another publicised program is very similar but betting is different. If you lose on a certain even bets the software will tell you to increase the wager on the next spin on so forth.

I didn’t like the display much but this proved to be slightly a bit more effective but still a loser and unlike other systems you don’t feel much in control.

Other software I tested where not as intrusive and didn’t tell me when and what to wager but gave me statistics and indications on what will probably will be drawn next.

What was interesting to learn when I analysed the data from most of these software was that in the long run after thousands and thousands of spins the number of red numbers will be as much as black ones, the even numbers as much and the odd ones, the high as much as the low, and even the numbers drawn will almost even out.

The ‘Dopey Experiment’

The idea is to divide one’s roulette session bankroll into 35 units. These units are bet on a particular number for 35 consecutive spins. If the number is draw during these spins, the player makes a profit and can repeat the system.

There is a (1 − (37 / 38)35) * 100 = 60.68% probability of winning within 35 spins on an American roulette and close to 62% on a European.

Biarritz System

Usable only on the Roulette table this system focuses on inside bets.

You basically wait and record 111 spins (37×3) and spot the numbers that have not come out since. You then start a betting progression on those selected numbers depending on the numbers available (similar betting strategy like the one used in the Scatter System.

Differential Betting

Systems using flat bets generally contain long lasting stagnation phases, which make a strategic play uneconomic: expenditure of time and the yield are in no profitable relation to each other.

Based on this realization and the fact that even money chances are ruled by both the law of deviation and the law of balance, it is quite possible to utilize the strategy of differential betting.

Differential betting is not a bet selection or a progression, because it can be used only if two chances are attacked at the same time and it can never be accomplished with flat bets, since all bets would be zero.

Differential betting is only possible if two chances (even bets) are followed with a progression. Here for each chance the respective progression bet size is determined separately, however only the difference is wagered. 

Choose any positive or negative progression you feel most comfortable with and start betting it on both sides of an even bet (even and odds or reds and blacks).

With the first bets you’ll most probably lose and win at the same time, bank roll remaining unchanged, but after that spin you can start differential betting by starting the sequence on the side you previously lost and bet again the first amount on the winning side.

Although you win almost each time, sometimes you encounter a zero and lose on both sides and a long winning streak is also and costly losing streak that’s more prone to happen.

Project 202 for Roulette

System based on analysing a longish wave of flat bets, determining how profitable or not it was and adjusting your bets in the following wave of bets.

The inventor of this system recommends starting with a wave of 40 spins using a very small amount of flat bets.  According to the profit or loss sustained then use the following table for the subsequent wave of bets.

Capital Decrease     Bet Increase      Capital Increase      Bet Decrease

5% or less                       10%                     5% or less                       10%
6% to 10%                        10%                     6% to 10%                        10%
11% to 20%                      20%                   11% to 20%                        20%
Over 20%                         33%                      Over 20%                         33%

Basically after the first wave you decrease or increase your bets in the next wave according to the tables above. You rinse and repeat for 3 waves and if still suffering losses you can now double the percentages of increase but up to a limit of 250%.

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