GAME OF CHANCE: THE WINNING PROBABILITIES OF SLOT MACHINES
The coin-operated slot machine is a pioneering betting device in the beginning of the mechanical age. It was commonly used as a vending machine in the saloons to attract new customers and retain its patrons through wagering in which the prize bestowed to the winner is in a form of cigar or refreshments. Since it was gaining popularity as a betting device in the 20th century, many companies made a lot of varieties of it with differences on their probabilities.
The odds in a game of chance are measured by probability. Probability is a quantifying variable which depicts the degree of occurrence of a certain event or outcome. Its value falls between 0 and 1 in which the former shows no occurrence of an event and latter displays the high occurrence of an event. Probability is expressed mathematically as
Along with this is the expected value which refers to the theoretical amount of return from the waged money of the bettor. Using the winning and losing probabilities of a certain game, the amount of money a bettor could gain or lose is calculated using the equation below
in which a positive EV implies profit over the betting time while negative EV is counted as loss. These two can aid any bettor in waging their money either in mechanical or online games.
WINNING PROBABILITY OF SLOT MACHINES
Before anyone places their bet, one must understand the difference between independent events from dependent events. This is because most betting games are independent events governed by randomness, uncertainties, and complexities. Independent event refers to the irrelevance of a present outcome to the past results. In short, the reflected combination in a slot machine out from presently playing it is not affected by the past rotations. Therefore, the likelihood of winning and losing is the same for all players.
In mechanically and computer-operated slot machines, the probability of the set of combinations is affected by the number of reels, number of symbols used per reel, the time the lever was pulled, and the activation time of the machine itself. It was part of the machine setup to reset the combination series after it is restarted.
Applying the abovementioned information, a three-reel slot machine with 10 symbols each can have 1,000 (10x10x10) probable combinations. To get a jackpot combo, the winning probability is 1 out of 1000 possible combinations (1/1000) and the losing probability is set to zero since other combinations still have their corresponding prizes. Incorporating these values to the EV equation with a prize of $500, the EV is +0.5. The table below is an example which shows the tabulated winnings of a three-reel slot machine with 10 symbols which has a 94.5% payback percentage.
This kind of machine setup allows the game operators to offer larger jackpots that attract more clients just like in Jili. If you’re a slot machine player and you wanted more off from your game, you might want to balance out your chances in these two and see where your luck is.