The odds for a random event, like a die toss or a roulette spin, denote the likelihood of this event taking place. To calculate the odds for winning with a given roulette bet, you need to figure out what its probability is. Then you can use the following formula: Odds for Winning = Probability of Winning / (1 – Probability of Winning). The roulette odds on red or black is another even bet. You simply pick the color you think will win and earn your winnings. The house edges are the same as the column bet. The roulette odds on green are different because this only applies to 0 (or 00 if you are playing the American version). The net winnings on a roulette wager can be thought of as a discrete random variable. If we bet $1 on red and red occurs, then we win our dollar back and another dollar. This results in net winnings of 1. If we bet $1 on red and green or black occurs, then we lose the dollar that we bet. That means your probabilities in roulette odds are 37 to one, and this makes it a thrill. Calculate odds with roulette odds calculator online. In order to understand this in terms of money, you must realize that the winner’s payoff is not 36:1 roulette odds because it will be a fair game. It is rather 35:1.
By Ion Saliu, Founder of Roulette Mathematics
This question was posted in mathematical newsgroups (alt.math.recreational, alt.math.undergrad, alt.sci.math.probability): 'Winning and Quitting on Red/Black in Roulette'.
- 'Obviously in roulette betting on in the long run you are going to lose your money but at some point chances are you'll be in profit. To take an extreme example if you had $1000 you could reasonably expect to be up $1 at some point. Is it possible to generalize this? I want to win W dollars at which point I will quit. How much cash C would I need to have probability P of succeeding? Let's say I'm betting on a 37 number roulette wheel (18 red 18 black and one green 0)?'
On the surface, the best probability for the roulette player to be ahead is in one trial (spin): 48.6% to win (versus 51.4% to lose), as far as even-money betting is concerned. I don't agree that it is the best strategy (betting all your bankroll on one spin).
Theoretically, no bankroll will put a player ahead guaranteed, IF flat-betting and playing very long consecutive sessions. There are moments, however, when the roulette player can be ahead by at least one betting unit. Even in even-money bets, the player has a good chance to be ahead by at least one unit after 5, or 10, or even 100 spins. But more than 20 spins are NOT recommended; the probability (odds) to lose go(es) above 50%! Think about it!
The main thing, mathematically, is the number of player's wins in N trials. To be ahead, means the player has won at least one more roulette spin (number of successes) than the number of losses in N trials. The question then becomes:
'What are the probabilities for the player to be ahead in various numbers of trials?'
Everybody can use my probability software SuperFormula, option L: At Least M successes in N trials.
Winning probability: p = 18/37; M must be at least (N/2) + 1.
Here is a number of cases from the player's perspective.
The figures are applicable to all even-money roulette bets: black or red; even or odd; low or high (1-18 or 19-36).
1 trial (spin)
- probability (odds) to win: 48.6%; odds = 1 in 2.05
- probability (odds) to lose: 51.4%; odds = 1 in 1.95
(the probability to lose is 19/37; adding zero to unfavorable cases).
2 trials (spins)
- probability (odds) to win 2 of 2: 23.7% (1 of 2 doesn't mean 'being ahead')
- probability (odds) to lose 1 of 2: 76.3%
3 spins
- probability (odds) to win at least 2 of 3: 48%
- probability (odds) to lose at least 2 of 3: 52%
10 spins
- probability (odds) to win at least 6 of 10: 34.4%; odds = 1 in 2.91
- probability (odds) to lose at least 6 of 10: 41.1%; odds = 1 in 2.43
20 spins
- probability (odds) to win at least 11 of 20: 36.5%
- probability (odds) to lose at least 11 of 20: 46.2%
100 spins
- probability (odds) to win at least 51 of 100: 35.5%; odds = 1 in 2.82
- probability (odds) to lose at least 51 of 100: 56.8%; odds = 1 in 1.76.
It's getting worse for the player...
The roulette strategy (or system) is a totally different ball game! But there are professional gamblers out there, including roulette players! They must have strategies, some roulette systems deduced from some figures like the ones above! The player can be ahead at any point in the game. If so, maybe it's time to move to another (or casino) table: It improves the odds of winning!
Always keep track of the losing and winning streaks. Be strong and put an end to a winning streak. You are ahead, you quit the roulette table. Go to another table and wait until you are ahead. The bankroll is of the essence: It must assure going through long losing streaks. Divide the streaks in 10 spins or 20 spins. Never fight aggressively short or mid-term losing streaks. This is the best approach for those who do not know Ion Saliu's casino gambling systems. A good approach to gambling is the next best thing to a good gambling system! Applicable to blackjack and baccarat, too!
Axiomatic one, everybody knows that the casinos have an edge or house advantage (HA) in all the games they offer, roulette including. The house advantage is created by the payouts in rapport to total possibilities for the respective bet. We can apply this simple formula based on units paid UP over total possibilities TP:
(always expressed as a percentage.)
For example, in single-zero roulette, the one-number (straight-up) bet has payout of 35 to 1. The to qualifier is very important: the casino pays you 35 units and they give you back the unit you bet; thus, you get 36 units. There are 37 possibilities in single-zero roulette: 36 numbers from 1 to 36 plus the 0 number. Therefore, HA = 1 – (UP / TP) = 1 – (36 / 37) = 1 – 0.973 = 0.027 = 2.7%.
Let's calculate HA for the 1 to 1 bets: black/red, even/odd, low/high. HA = 1 – (UP / TP) = 1 – (2 / 2.055) = 1 – 0.973 = 0.027 = 2.7%. There are little differences among bets depending on how many decimal points we work with in our calculations.
The point is, the casinos have an advantage, or the players have a disadvantage. Nonetheless, the players' disadvantage is far better than what they face in state-run lotteries. Yet, most casino gamblers lose big, including at roulette tables. They do not have sufficient bankrolls to withstand long losing streaks.
However, around 45% of the roulette numbers lead the gamblers to profits in a few thousand spins. That is, with a sufficient bankroll, a player has a pretty good chance to make a profit, even if playing a random roulette number, or a favorite number. I analyzed about 8000 roulette spins from Hamburg Spielbank (casino). Quite a few numbers ended up making a profit: roulette systems, magic numbers.
By contrast, the more lottery drawings a player plays, the higher the degree of certainty of a loss. Let's make a comparative analysis to the roulette long series above (spins: total roulette numbers, 37, multiplied by 200). If playing the pick-3 lottery for some 100,000 drawings, it is guaranteed that all pick-3 straight sets will be losers. Some numbers will hit up to 3% to 5% above the norm — but that is not nearly enough to assure a profit. A frequency of 3% to 5% above the norm leads to profits in roulette, however.
Ion Saliu's Paradox and Roulette
Ion Saliu's Paradox of N Trials is presented in detail at saliu.com, especially the
probability theory page and the mathematics of gambling formula. If p = 1 / N, we can discover an interesting relation between the degree of certainty DC and the number of trials N. The degree of certainty has a limit, when N tends to infinity. That limit is 1 — 1/e, or approximately 0.632....If you play 1 roulette number for the next 38 spins, common belief was that you expected to win once. Not! Non! Only if you play 38 numbers in 1 spin, your chance to hit the winning number is 100%. Here is an interesting table, which includes also The Free Roulette System #1 presented at the main roulette site.
The maximum gain comes when playing 38 numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as Free System #1 scares most gamblers. 'Play 34 or 33 numbers in one shot? I'll have a heart attack!' In reality, the Free Roulette System #1 offers a 28.8% advantage over playing singular numbers in long sessions. That's mathematics, and there is no heart to worry about, axiomatic one.
You can also use SuperFormula to calculate all kinds of probabilities and advantage percentages. The option L — At least M successes in N trials is a very useful gambling instrument. If you play 19 numbers in one spin, the probability to win is 50%. If you play 19 numbers in 2 consecutive spins, the probability to win at least once is 75%.
Editor's note
• In an apparent change of heart, the Hamburg casino (Spielbank) offers online roulette results for free. The new link is (for the time being!):
www.spielbank-hamburg.de/spielsaal/permanenzen.php4
• • Real-life roulette spins are also available from the Wiesbaden, Germany, Casino (Spielbank)
www.spielbank-wiesbaden.de/DE/621/Permanenzen2.php: Wiesbaden Spielbank Permanenzen
Roulette: Software, Systems, Super Strategy
See a comprehensive directory of the pages and materials on the subject of roulette, software, systems, and the Super Strategy.- Theory, Mathematics of Roulette Systems, Strategies, Software.
- The Best-Ever Roulette Strategy, Systems based on mathematics of progressions and free-for-all.
- An inventory of free and outrageously pricedroulette systems.
- Software, Systems: Roulette Wheel Positioning, Sectors, Birthday Paradox.
- 'Roulette System that Won Millions!'
~ Ion Saliu's roulette theory, systems, and software were pirated by an Australian gambling group. - James Bond Roulette System for Dozens, Columns.
- Roulette Systems, Threats from Casino Chairman.
- Anti-Gambler Advice from John Patrick, Casino Moleextraordinaire and conspirator.
- Wizard of Odds Had High Praise For Ion Saliu's Gambling Theory.
- Casinos pay troubled individuals to intimidate intelligent gambling system authors.
- Download roulette, blackjack, casino gambling, systems, software.
| Home | Search | New Writings | Odds, Generator | Contents | Forums | Sitemap |
Roulette Zero
The number zero. Is it even a number? Or is it a non-number?
Well, we always talk about the number zero, so let´s say for the sake of argument that it is a number. If you halve something, and then halve it again, and then halve it again, you are going to have a smaller and smaller number. If you did this an infinite number of times, you´d arrive at zero, but of course that isn´t going to happen in the real world. And that´s the thing about zero, much of what we talk about when we talk about the number zero is theoretical- it´s all in the mind.
But back to roulette. The zero is the only green number on the roulette wheel, and it marks the difference between a European Roulette wheel and an American Roulette wheel, as a European wheel has one zero pocket and an American wheel has two zero pockets (the 0 and the 00).
On a European Wheel, the 0 sits between black 26 and the red number 32. Over in Vegas on the American wheels, the 0 sites between black 2 and black 26 and the 00 has red 1 and red 27 as neighbours.
How to Play the Number Zero in Roulette
You can bet on the number zero in the same way as you can bet on any individual number on the roulette wheel- just place a single number bet on the number and you´ll get a 35:1 payout if it comes in (plus your original bet back).
The zero is often seen as an unlucky number (well it is called the zero)- especially in roulette, as many bets will not pay out if the ball lands in this pocket, such as the outside even money bets, the column bets and the dozens bet and so on.
In a way, that´s a little bit unfair on the zero, as if you bet on the red, you´ll lose if a black number comes up OR the zero comes up, but players tend to feel unlucky when the zero lands and they are playing the even money bets. There are ways of insuring yourself against this happening. You could play a roulette variant like Next Gen European Roulette that plays La Partage. This is a rule that forces the casino to return half of your even money bet if the ball lands in zero. It´s a good one to look out for, as it will reduce the house edge down to 1.3% on these bets. You may also find this rule played on many French Roulette games.
You could also lay a small side bet on the zero to cover yourself for those times when the 0 hits. We´d advise against it- it´s better just to run the gauntlet and trust your luck.
The only rule that we suggest you stick to with the zero, is to only play on single zero roulette wheels. Avoid the double zero roulette wheels (the American ones). If you think it´s bad news when the ball lands in the single zero, how bad are you going to feel when it lands in the double zero? There´s a reason that European Roulette is more popular online than the American game. There´s more choice and the odds are better on the former.
A popular way of covering the zero is with the Voisins du Zero bet. This covers the numbers from 22 to 25 including the zero. These are the Neighbours or Voisins of zero.
If you are playing American Roulette (I thought we told you to avoid it!), you could also play the worst bet in roulette, which covers 0,00, 1, 2 and 3. But why would you? The odds are the worst in roulette.
Another neat way of covering the zero on a European table is with a Jeu Zero bet, which is kind of like a mini Voisins du Zero bet. It just covers 6 neighbours of zero with 4 chips.
Let´s Talk About the Zero
Zero is one of those numbers that is known by a number of names including nothing, none, nought, nil, zip, zilch and nada. In cricket, if you are bowled for a duck you scored zero runs and if you are 40 love down in a tennis game you haven´t scored any points.
The zero hasn´t always been recognised- the Ancient Greeks had no word for it and were sceptical as to whether it was a number at all. How can something be something if it is nothing? You can see their point.
The idea of zero is thought to have been fully developed on the Indian sub-continet where it appeared around A.D. 458 in mathematical equations that were spelled out or spoken in poetry or chants. In 628, a Hindu mathematician called Brahmagupta came up with a symbol for zero — a dot underneath numbers.
Free Practice Roulette Wheel
It was through the Arabic world that we came to use the zero as a placeholder and number in calculations. The Hindu–Arabic base 10 system for numbers that we use to this day reached Europe in the 11th century, thanks to the Moors in Spain.
Zero is an even number as you can divide it by 2 without getting a remainder and is the smallest no-negative integer.
Odds On Green Roulette
The number zero really started to come into its own with the development of computers, as it represents the “off state” in a binary system, where 1 is the “on state”.
American Roulette Payout
Summary
So is zero a number? Can you have a number that´s nothing? That´s getting into philosophy, so we are going to say that yes, 0 is a number, at least in roulette. It has its own pocket and space on the betting layout, and there are even 2 of them on some wheels.
Roulette Odds Green
Just remember, the odds of the ball landing in the zero are exactly the same as the odds of the ball landing in any other number!
Comments are closed.