Roulette Wheel

 Roulette Wheel

This method selects all individuals to be part of the next generation. This popular selection method is used in a gene algorithm. A roulette wheel is built from the relative fitness (ratio between total fitness and individual fitness) of each person. This can be represented as a pie diagram where the area that each individual occupies on the roulette wheels is proportional to their relative fitness. The sum of relative fit (S) is calculated. A random number between 0 and S is generated. The population is then traversed, and the corresponding relative fitness scores are summed. If the sum is higher than the random number generated the corresponding person is chosen. A person with a higher fitness level will occupy more space in the pie chart. This will increase the chance of it being selected. Fig. 1(C).

Probability

A Scientific Study of Roulette

Roulette wheels outside the United States usually have 37 slots. They are numbered from 0 to 36. There are 38 slots for roulette wheels used in the United States. A spinn ball is equally likely in all slots if it is balanced, fair, and clean. However, some numbers can win more often than others due to imperfections on the wheel.

William Jaggers, an English engineer in the late 1800s took dramatic advantage [4]. He hired six assistants to observe the Monte Carlo Roulette wheels for a month and record the winning numbers. Jaggers noticed that certain numbers appeared more often than others. These numbers were so appealing that Jaggers began to bet heavily and won $325,000 within a matter of days. That's more than $6,000,000 in today's dollars. Then, the casino noticed and started changing the wheel nightly. In Las Vegas, a group a Berkeley students pulled off an identical feat in 1960s. This was while their peers were protesting or studying. To frustrate long-term frequency gamblers, casinos rotate their roulette wheels regularly.

R.H. Riffenburgh in Statistics in Medicine, Third Edition (2012)

Mechanical Generators

The history of gambling has seen a variety of mechanisms: from early dice (Roman bones) to roulette wheels, which gave numbers that were close to random, but with smaller biases. Over the centuries, better manufacturing techniques have produced mechanisms with lower biases. Because gambling dens could not eliminate bias from their machines, they invented machines with adjustable biases that allowed the bias to be reset if the player uses statistical methods to evaluate and take advantage. Flipping a coin with equal weights on both sides has been shown almost to be 50-50. A flip of a coin shows that the side showing after it has been flipped yields relative frequencies closer 51-49 to the side shown at the beginning. Experimental design uses can be made possible by the small bias in dice. You can get dice designed specifically for this purpose. The Japan Standards Association has provided a set three icosahedron dice that can produce unambiguous numbers between 0 to 999. Advanced Math and Statistics

Robert Kissell, Jim Poserina, Optimal Sports Math, Statistics, and Fantasy, 2017.

Uniform Distribution

A uniform distribution refers to an outcome that has the same probability of occurring. A roulette wheel, in which every number is equally likely to occur, is one example of the uniform distribution. The uniform distribution has a constant probability across all values. It can be either continuous or discrete. Roulette - The Importance Of Understanding The Basic Principles