C La Roulette Palladienne
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Fitness proportionate selection, also known as roulette wheel selection, is a genetic operator used in genetic algorithms for selecting potentially useful solutions for recombination.
In fitness proportionate selection, as in all selection methods, the fitness function assigns a fitness to possible solutions or chromosomes. This fitness level is used to associate a probability of selection with each individual chromosome. If is the fitness of individual in the population, its probability of being selected is
where is the number of individuals in the population.
This could be imagined similar to a Roulette wheel in a casino. Usually a proportion of the wheel is assigned to each of the possible selections based on their fitness value. This could be achieved by dividing the fitness of a selection by the total fitness of all the selections, thereby normalizing them to 1. Then a random selection is made similar to how the roulette wheel is rotated.
While candidate solutions with a higher fitness will be less likely to be eliminated, there is still a chance that they may be eliminated because their probability of selection is less than 1 (or 100%). Contrast this with a less sophisticated selection algorithm, such as truncation selection, which will eliminate a fixed percentage of the weakest candidates. With fitness proportionate selection there is a chance some weaker solutions may survive the selection process. This is because even though the probability that the weaker solutions will survive is low, it is not zero which means it is still possible they will survive; this is an advantage, because there is a chance that even weak solutions may have some features or characteristics which could prove useful following the recombination process.
The analogy to a roulette wheel can be envisaged by imagining a roulette wheel in which each candidate solution represents a pocket on the wheel; the size of the pockets are proportionate to the probability of selection of the solution.[citation needed] Selecting N chromosomes from the population is equivalent to playing N games on the roulette wheel, as each candidate is drawn independently.
Other selection techniques, such as stochastic universal sampling[1] or tournament selection, are often used in practice. This is because they have less stochastic noise, or are fast, easy to implement and have a constant selection pressure.[2]
The naive implementation is carried out by first generating the cumulative probability distribution (CDF) over the list of individuals using a probability proportional to the fitness of the individual. A uniform random number from the range [0,1) is chosen and the inverse of the CDF for that number gives an individual. This corresponds to the roulette ball falling in the bin of an individual with a probability proportional to its width. The 'bin' corresponding to the inverse of the uniform random number can be found most quickly by using a binary search over the elements of the CDF. It takes in the O(log n) time to choose an individual. A faster alternative that generates individuals in O(1) time will be to use the alias method.
Recently, a very simple algorithm was introduced that is based on 'stochastic acceptance'.[3] The algorithm randomly selects an individual (say ) and accepts the selection with probability , where is the maximum fitness in the population. Certain analysis indicates that the stochastic acceptance version has a considerably better performance than versions based on linear or binary search, especially in applications where fitness values might change during the run.[4] While the behavior of this algorithm is typically fast, some fitness distributions (such as exponential distributions) may require iterations in the worst case. This algorithm also requires more random numbers than binary search.
Pseudocode[edit]
For example, if you have a population with fitnesses [1, 2, 3, 4], then the sum is (1 + 2 + 3 + 4 = 10). Therefore, you would want the probabilities or chances to be [1/10, 2/10, 3/10, 4/10] or [0.1, 0.2, 0.3, 0.4]. If you were to visually normalize this between 0.0 and 1.0, it would be grouped like below with [red = 1/10, green = 2/10, blue = 3/10, black = 4/10]:
C La Roulette Palladienne Slot Machine
Using the above example numbers, this is how to determine the probabilities:
The last index should always be 1.0 or close to it. Then this is how to randomly select an individual:
See also[edit]
References[edit]
- ^Bäck, Thomas, Evolutionary Algorithms in Theory and Practice (1996), p. 120, Oxford Univ. Press
- ^Blickle, Tobias; Thiele, Lothar (1996). 'A Comparison of Selection Schemes Used in Evolutionary Algorithms'. Evolutionary Computation. 4 (4): 361–394. doi:10.1162/evco.1996.4.4.361. ISSN1063-6560. S2CID42718510.
- ^A. Lipowski, Roulette-wheel selection via stochastic acceptance (arXiv:1109.3627)[1]
- ^Fast Proportional Selection
External links[edit]
- C implementation (.tar.gz; see selector.cxx) WBL
On this page:
- 2 Roulette bets
- 4 French roulette bets
- 5 Numbers and colors at French, European and American roulette wheels
- 6 En Prison & La Partage
Once upon a time, a French inventor tried to create a perpetual motion machine. While he didn’t succeed in that, he did invent something that has been spinning every since – the roulette wheel.
Today, roulette is played in casinos all over the world. A ball is spun inside a horizontal wheel which is also spinning (in the opposite direction of the ball). Friction will gradually make the ball lose speed, and eventually the ball will settle in one of the numbered slots located around the edge of the wheel – thereby determining the winning number of that round.
The three main roulette variants is the French roulette, the European roulette and the American roulette. The French and European versions use the numbers 0-36. The American version have added an additional possibility by not just having a zero but a double-zero (00) as well.
If you play roulette in online casinos, you might find more novel roulette games in addition to the three staples.
Roulette chips
If many different players around the roulette just put normal casino chips on the table, it could quickly create a confusing situation where it would be difficult to know who is the rightful owner of each bet. Because of this, the croupier can ask you to exchange your casino chips for special roulette markers. The croupier have access to roulette markers with various color combinations and can assign each specific color combination to a specific player, thus lowering the risk of confusion at the table.
When you don’t want to play at this table anymore, you simply tell the croupier and she will give you ordinary casino chips in exchange for your roulette markers.
Roulette bets
Inside bets
These bets are found in the centre (inside) of the roulette table’s betting area.
Inside bets are suitable when you are willing to take a big risk. The chance of winning is low, but if you win – you get paid well.
Here are some examples of inside bets:
| Name of the bet | Chip placement | Info |
| Straight (also known as Single) | Fully inside the square of the selected number, not touching any of the lines. | A bet on a single number. You win of the ball ends up on this specific number. |
| Split | Across the line shared by the two selected numbers. | Your bet will be spread over two numbers. You win if the ball settles on either of the two numbers. You can only select numbers that are adjacent to each other on the roulette table (their squares must share a line). |
| Street | On the outer line of the selected street. | There are twelve streets on the roulette table, each street consisting of three numbers. The first street is comprised of 1-2-3, second street of 4-5-6, and so on. Select one of the streets and bet on it, and your wager will be spread over the three numbers included in that street. You win of the ball settles on any of the three numbers included in the selected street. |
| Trio | Where the squares of the three selected numbers touch each other. | This is a bet on three numbers, of which at least one is a zero. At a French or European roulette table, two different Trio bets are available: 0-1-2 and 0-2-3. At an American roulette table, three different Trio bets are available: 0-1-2, 00-2-3 and 0-00-2. |
| Corner (also known as Square) | Where the squares of the four selected numbers meet. | This bet is spread over four different numbers. You can only select numbers whose squares share a common point at the table, such as 1-2-4-5 or 16-17-19-20. |
| Basket (also known as First Four) | Two different placements are possible:
| This is a bet on the four numbers 0-1-2-3. This bet is only available on French and European roulette tables. For a similar bet on the American table, see Top Line. |
| Top Line | Two alternatives are available:
| This is a bet on the five numbers 00-0-1-2-3. This bet is only available on American roulette tables, not on French and European ones. |
| Six Line (also known as Double Street) | Across the outer line of the streets, straddling both streets | This is a bet spread over six numbers found in two streets located next to each other. Examples: 1-2-3-4-5-6 (first street + second street) 25-26-27-28-29-30 (ninth street + tenth street) |
Outside bets
These bets are found on the outskirts (outside) of the roulette table’s betting area.
Outside bets are suitable when you want to have a comparatively high chance of winning, even if it means not getting a huge payment on your wager if you win.
Here are some examples of outside bets:
C La Roulette Palladienne Rules
| Name of the bet | Chip placement | Info | |
| First dozen | The field
| Your bet is spread over the numbers 1-12, i.e. the first dozen of numbers. | |
| Second dozen | The field
| Your bet is spread over the numbers 13-24, i.e. the second dozen of numbers. | |
| Third dozen | The field
| Your bet is spread over the numbers 25-36, i.e. the third dozen of numbers. | |
| First column | The field at the bottom of the first column | Your bet is spread over the twelve numbers in the first column, i.e. the numbers 1-4-7-10-13-16-19-22-25-28-31-34. | |
| Second column | The field at the bottom of the second column | Your bet is spread over the twelve numbers in the second column | |
| Third column | The field at the bottom of the third column | Your bet is spread over the twelve numbers in the third column | |
| Red | The field for red, usually marked with the word RED or with the color red | Your bet is spread over all the red numbers | |
| Black | The field for black, usually marked with the word BLACK or with the color black | Your bet is spread over all the black numbers | |
| Even | The field that says EVEN | Your bet is spread over all the even numbers in the 1-36 range | |
| Odd | The field that says ODD | Your bet is spread over all the odd numbers in the 1-36 range | |
| High | The field that says 19-36 or HIGH | Your bet is spread over all the numbers within the 19-36 span | |
| Low | The field that says 1-18 or LOW | Your bet is spread over all the numbers within the 1-18 span |
What can I win?
Below are a few examples of common payouts for common roulette bets, but you should always check the payout schedule for the specific roulette table that you wish to play at.
Examples of inner bets
| Bet | Payout | Example |
| Straight Bet | 35:1 | You bet $10, you are paid $350. |
| Split Bet | 17:1 | You bet $10, you are paid $170. |
| Street Bet | 11:1 | You bet $10, you are paid $110. |
| Corner Bet | 8:1 | You bet $10, you are paid $80. |
| Basket Bet | 6:1 | You bet $10, you are paid $60. |
| Double Street Bet | 5:1 | You bet $10, you are paid $50. |
Examples of outer bets
| Bet | Payout | Example |
| Dozen | 2:1 | You bet $10, you are paid $20. |
| Column | 2:1 | You bet $10, you are paid $20. |
| High | 1:1 | You bet $10, you are paid $10. |
| Low | 1:1 | You bet $10, you are paid $10. |
| Odd | 1:1 | You bet $10, you are paid $10. |
| Even | 1:1 | You bet $10, you are paid $10. |
| Red | 1:1 | You bet $10, you are paid $10. |
| Black | 1:1 | You bet $10, you are paid $10. |
French roulette bets
Examples of French roulette bets
| Bet name in French | Engelish equivalent |
| Premiere 12 (P-12) | 1st dozen |
| Moyenne 12 (M-12) | 2nd dozen |
| Derniere 12 (D-12) | 3rd dozen |
| Pair | Even |
| Impair | Odd |
| Manqué (1-18) | Low (1-18) |
| Passé (19-36) | High (19-36) |
| Rouge | Red |
| Noir | Black |
Examples of French call bets
| Name | Info |
| Voisins du Zero | Voisins du Zero = Neighboors of the Zero This is a bet on zero and the sixteen numbers on the roulette wheel that is closest to the zero: 22, 18, 29, 7, 28, 12, 35, 3, 26, 0, 32, 15, 19, 4, 21, 2, 25. |
| Tiers du Cylindre | Tiers du Cylindre = A Third of the Wheel This is a bet on the twelve numbers that are the farthest away from the zero at the roulette wheel: 27, 13, 36, 11, 30, 8, 23, 10, 5, 24, 16, 33. |
| Orphelins | Orphelins = Orphans This is a bet on the eight numbers that are neither Voisins du Zero nor Tiers du Cylindre: 1, 6, 9, 14, 17, 20, 31, 34 |
| Finales en Plein | This is a bet on the numbers that end with a specific number (of your choice). Example: Finales en Plein Deux (deux = two) is a bet divided over the four numbers 2, 12, 22, 32. |
| Finales a Cheval | This is a bet on the numbers that end with two specific numbers (of your choice). Example: Finales en Plein Deux et Trois (deux et trois = two and three) is a bet divided over the eight numbers 2, 3, 12, 13, 22, 23, 32, 33. |
Chanson C'est La Roulette Palladienne
Numbers and colors at French, European and American roulette wheels
French & European
This is how the numbers are placed at the French and European roulette wheels (clockwise): 0-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-18-29-7-28-12-35-3-26
Number 1-10 and 19-28 are red if odd and black if even. For 11-18 and 29-36 the opposite applies, meaning that red numbers are even and black numbers are odd. The zero (0) is green.
On a traditional French roulette table, the numbers are only red and black on the wheel, not on the table. As a player, you are expected to know which numbers that are red and which numbers that are black without the table telling you.
American
This is how the numbers are placed at the American roulette wheel (clockwise): 0-28-9-26-30-11-7-20-32-17-5-22-34-15-3-24-36-13-1-00-27-10-25-29-12-8-19-31-18-6-21-33-16-4-23-35-14-2
Number 1-10 and 19-28 are red if odd and black if even. For 11-18 and 29-36 the opposite applies, meaning that red numbers are even and black numbers are odd.
The zero (0) and the double-zero (00) are both green.
En Prison & La Partage
En Prison and La Partage are two features that makes even-odds bet a bit more interesting, since they give you a chance to not lose your entire bet on even-odds (red/black/even/odd/high/low) when the ball settles on green.
It is fairly common for French roulette tables to employ the La Partage rule, while En Prison is associated with European roulette tables. Always ask before you start playing; never assume that La Partage or En Prison will be available. American roulette tables hardly ever offer La Partage nor En Prison, but there are exceptions – including a few well-known Las Vegas establishment such as MGM Grand, Wynn, Bellagio and Mirage – where you can find American roulette with La Partage or En Prison.
En prison
- You make an even-odds bet and the ball drops on 0.
- The croupier offers you to let your bet be imprisoned (“en prison”) instead of you losing it.
- You agree and the croupier places a special marker on top of your bet.
- If your bet wins the next round, you get the wager back. If your bet loses the next round, you lose your wager.
So, what happens if the ball drops on 0 again? That depends on the rules of the house. It’s a good idea to check in advance before you start playing.
La Partage
- You make an even-odds bet and the ball drops on 0.
- You only lose half of your bet; the other half is given back to you.
Wheel placement
In the olden days, the standard European roulette set-up would have the wheel in the centre of the table. In the United States, a set up with the wheel placed at one end of the table was much more common. Today, more and more casinos world wide – including casinos in Europe – have adopted the U.S. style, even for European and French roulette. One of the places that still keep with the old tradition is Monte Carlo, where the French roulette tables still have the wheel in the centre of the table.
Table colors
Traditionally, French roulette tables have a red table cloth while European and American roulette tables have green table cloths.
The casino’s statistical advantage over the player
Since the American roulette wheel have both a zero (0) and a double-zero (00), it gives the house a higher statistical advantage than the European and French roulette wheels. With a French or European wheel, the statistical advantage is 2.7%. With an American wheel, it is 5.5%.
Please note that the rules La Partage and En Prison will have an impact lower the casino’s statistical advantage. American roulette tables hardly ever employ these rules. La Partage is fairly common at French roulette, while En Prison is chiefly associated with the European roulette.