Slot machines are unlike casino table games in many ways, including the way in which the odds of winning are calculated. Table games like roulette and blackjack offer a relatively small, fixed number of possible outcomes; there are only 38 pockets on an American roulette wheel and 52 cards in a standard deck of cards. Yet the reels of even the simplest slot games can be aligned in tens of thousands of combinations, and those are further complicated by bonuses, multiple paylines, and other special features.
Basic Computations
A three-reel machine with a single payline will commonly feature no fewer than 20 “stops” per reel. Only one of those stops on each reel will be a jackpot symbol. The likelihood of the jackpot coming up on the first reel is 1-in-20, or 5%. The same math applies to the second and third reels. To calculate the odds of all three reels aligning with jackpots on the payline, the probabilities of each event are multiplied together: 0.05 x 0.05 x 0.05 = 0.000125. In other words, this winning combination can be expected about once every 8,000 spins.
A player who bets 25 cents on each spin should expect to spend $0.25 x 8,000 spins = $2,000 before getting a jackpot. It is a certainty that the machine’s top payout will be considerably less than $2,000. In fact, if all of the intermediate winning combinations are taken into account and their probabilities of occurring are added together, the expected total amount of payouts on 8,000 spins will work out to around $1,900~$1,970 or 95.0%~98.5% of the player’s wagers. This difference is the “house edge.”
Unfortunately, even the oldest of mechanical slot machines are not this simple. They might have a single stop associated with each of the jackpot symbols, but there would be multiple stops set up for the other symbols. Instead of 1-in-20, the probability of a jackpot symbol appearing might be 1-in-60 or 1-in-100 for each reel. This especially true for today’s computerized slot machines which employ an unrestricted number of “virtual” stops—typically as many as 256 or 512 per reel.
Electronic Complexities
When an electronic slot machine is designed, a programming process called “mapping” assigns some symbols a higher likelihood of appearing than others. The only way to accurately calculate the odds of a symbol coming up is to know the ratio of virtual stops to actual stops for each symbol.
For example, one very popular three-reel one-payline slot machine is called “Red, White, & Blue.” It offers a jackpot of 10,000 credits for a maximum three-credit bet when a Red 7, a White 7, and a Blue 7 show on the center payline in exactly that order. The payout is 3,333 to 1. With 11 blanks and 11 symbols on each reel, it might seem that a jackpot could be expected once every 22x22x22 = 10,648 spins. However, each reel has 64 virtual stops, and they are unequally assigned among the 22 symbols. The real odds of hitting the jackpot are 1/64 x 1/64 x 1/64 = 1/262,144 = 0.00038%, a far cry from the 0.03% the pay table might suggest.
To makes odds calculations even more difficult, for most slot games information of this kind about virtual stops and mapping is not readily available to the general public. That means players must come up with other ways of determining which slots offer the best odds and how much to wager, such as comparing payouts at “max bet” to those offered for lower levels of wagering.
In the case of Red, White, & Blue, a jackpot pays 10,000 credits for three credits bet, but only 2,400 for a single credit winner or 4,800 for a two credit one. Common sense suggests that this game offers better odds of winning with max bet wagered. Indeed, this is true of almost all slot games with big jackpots, and for some popular slots, such as “Wheel of Fortune,” certain payout features are only available with the maximum number of credits played. For those games, players should bet only one credit or the maximum; intermediate bets only add risk without increasing the odds of reward.
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