The question “What is random?” descends from the realm of theory into that of practice when we look at how the events which underlie most gambling games are produced. Randomness should be thought of as an ideal that is never really obtained in practice. The gambling devices used by casinos, however, efficiently maximizing uncertainty, and the results produced by these devices are close enough to truly random to be treated as such.
Roulette
The roulette wheel is a very efficient randomizer. Non-linearity is ensured by the combination of friction, gravity, centrifugal motion, and bumps and obstacles. This complexity is magnified many times by the fact that the inner wheel spins in the direction opposite that in which the ball is thrown. Initial uncertainty is introduced into the game by the speed of wheel at the outset, the speed of the ball, the exact position of the ball and wheel, the weight and bounciness of the ball and the air pressure and humidity. The outcome of a roulette wheel would be completely predictable if the ball were always thrown with exactly the same force from the exact same position and the speed of the wheel and all other environmental conditions were held exactly constant. In practice this is impossible; some croupiers, however, can apparently throw the ball with enough accuracy to hit a particular section of the wheel (Bass, 1985). As a result some casinos require that the croupier not look at the wheel when throwing the ball.
Dice
The key to ensuring randomness in dice is the combination of flat surfaces and sharp edges, coupled with the rolling of the dice, which makes it difficult to predict the outcome of a throw. In addition, the house rules for dice games specify that for a throw to be valid, the dice have to hit a bumper on the other side of the table, making it impossible to manipulate the throw’s outcome. Dice used in home board games often have small holes drilled into the dice to mark the numbers. As a result the side with 6 dots is lighter than the opposite side, which has only 1 dot. This produces a slight bias, of 1% to 2%, that 6 and 5 will come up somewhat more often than their opposites, 1 and 2 respectively. In addition, the dice of some home board games we have looked at are not perfectly square and therefore have other biases. However, casino dice have flat sides with no holes, are manufactured to ensure that they are square and are tested for balance regularly by the casino. The bias in home dice may be the source of the belief that energetic rolling leads to large numbers, because a bias will show up more often when a lot of energy is put into the roll.
Bingo and Lotteries
To ensure randomness in bingo and lottery balls, the balls are kept in an enclosed space and moved around by air or the rolling of the cages. Additional bounce may be achieved using a spring at the bottom of the bingo cage. The cage may be made of plastic or wire; the nature of the cage ensures additional variation, adding to the randomness. The numbers on bingo balls are embedded into the ball so that there is no differential weight or drag that would make one ball more likely to be selected than another. While the balls might be entered in the same order, randomness is ensured by tiny differences in the initial position of the balls, the air pressure, dust or smoke in the air, humidity, and the timing of the removal of the balls. Furthermore, the introduction of turbulence through the air jet or rolling adds a great deal of complexity.
Cards
Cards are perhaps the least efficient randomizer currently available. Randomizing cards is a two-step process including shuffling, which mixes up the cards (complexity), and cutting the deck, which ensures uncertainty about how the decks are mixed together. Washing the deck (spreading them out face down and mixing them around the table) is also used to increase the randomness of the cards. With most types of randomizers, past results cannot affect the outcome of the next draw. However, because cards are drawn from a limited pack, each card draw influences the probability of the next card. If, for example, 3 aces out of 4 have already been drawn, the chance that the next card will be an ace is very small. Consequently a skilled blackjack player can make money by card counting (Thorpe, 1966). Most people have some experience of playing cards at home, and this card-playing experience is perhaps a source of the very common belief that random events correct themselves because, with a deck of cards, to some extent they do.
It takes about seven complete shuffles to ensure randomness (Patterson, 1990), but given that games such as blackjack and baccarat often use six or more decks at a time, most casinos do not have enough time to completely randomize their decks. This has given rise to a system called “shuffle tracking,” which is a variant on card counting (Patterson, 1990). Recent advances in computer technology have led to the creation of automatic shufflers, which use a random number generator to determine how to cut and sort the deck. In one variation, after each hand of blackjack, a computer-controlled device “randomly” reinserts each of the discarded cards back into the stack of unused cards so that the dealer never has to shuffle the cards.
Computer Generated Randomness
Computerised games such as video games, electronic slot machines and video lottery terminals (VLTs) use a complex mathematical formula called a congruential iteration to produce “random” events. The formula uses three very large numbers, called A, B and M, which are used over and over again, and a seed value that changes each time. The formula provides complexity, while the seed value provides uncertainty. This system works as follows:
- The seed number is usually obtained from the computer’s clock.
- This seed number is multiplied by a very large number (A).
- The result of Step 2 is then added to another large number (B).
- The result of Step 3 is then divided by a third very large prime number (M).
- The remainder, or “what is left over” after Step 4 is the first “random” number. This “random” number is usually converted into a range that is convenient for the program, such as a number ranging from 1 to 32 (which would correspond to symbols on a slot reel). This remainder is also used as the seed for the next cycle.
- The cycle is repeated as many times as needed.
Because the numbers are produced by a formula, they cannot be considered random and are called “pseudo-random.” However, a sequence of pseudo-random numbers is difficult to distinguish from one produced by pure chance. Like mechanical randomizers, most computerized random number generators are good enough for practical purposes. The sequence produced by this algorithm is limited to the size of the value of M. If M is 4.1 billion, then the sequence of numbers would repeat in the exact same order after 4.1 billion numbers are output. At 25 cents per spin and a 90% payback, it would cost as much $36 million in bets to track the entire sequence.
As stated above, to achieve randomness a system needs both non-linearity and uncertainty. Slot machines add uncertainty in two ways. First, they seed the sequence with a time function so that the sequence will differ depending on the time of day that the computer was turned on. Second, the random number generator in a slot machine runs all the time, but the numbers are withdrawn from this formula only when the player presses the spin button or lever. As such, the numbers drawn depend on the exact millisecond when the spin button is pressed. A millisecond later and the outcome might be different. As a result, the outcomes of slot machines are, in effect, random, and waiting for the cycle to repeat itself is not possible.
The reader might have trouble thinking of a sports game as a randomization process, but just as with dice, coins or computer programs, much of what happens in a sports game follows the rules of chance. How can people be elements in a random number generation system? First, a sports game is a complex system. Successfully playing a game involves a large number of physical actions that when added together result in a great deal of complexity. Second, many elements of a game involve a chance outcome. A highly skilled baseball player may hit a ball only 30% of the time or catch a fly ball only 80% of the time. Third, injuries, health, player composition, weather, time of day, player stress, fans yelling in the stands or even birds landing on the field all add uncertainty to the system. Fourth, the difference between most professional teams is actually very small: even the worst major league baseball team will beat the best on occasion. But this only makes sports games partly random.
If all that people who gamble needed to do to win money was to pick the better team, they could win most of the time by simply betting on the favourites. Unfortunately that prospect is eliminated by the way that racetracks and sports bookies operate. In horse races, the track takes a cut (17%) off the top and distributes the rest of the prize pool to the people who bet on the winners. The chaotic process of the mass betting pool essentially removes the differential ability of the horses. A horse that has a better chance of winning gets more action (bets) and thus less money goes to each individual who bet on that horse. In sports games, the bookies estimate how many points a team will win by. This is called the point spread. A bettor wins only if his/her chosen team beats the point spread. These subjectively estimated lines and odds virtually eliminate the role of a team or a horse’s ability in the outcome of the bet. (See “Part 7: Subjective Probability” in the chapter “Games and Systems” for more information on skill and sports betting.)
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