Slot Odds

Published: 25/02/2012

Unlike casino table games, which feature a relatively small, fixed number of possible outcomes, the possible combinations of symbols on slot reels are huge. Even the simplest slot games can have tens of thousands of alignments, and calculating the odds of winning is further complicated by bonuses, multiple paylines and a variety of special features.

Take, for example, the basic three-reel slot machine, which has a single payline. It will typically have no fewer than 20 positions per reel where the symbols can come to rest. These positions are known as “stops.” Just one of the stops on each reel is a jackpot symbol, so the probability of seeing it come up on the payline for the first reel is 1-in-20, or 5%.

The same calculation applies to the jackpot symbols on the second and third reels. The odds of all three reels all showing jackpots on the payline is the probability of each of the three events multiplied together, which is exactly 0.05 x 0.05 x 0.05 = 0.000125. That means this winning combination comes up about once in every 8,000 spins.

Now consider a player who bets a penny on each spin. His/her expectation is to spend $0.01 x 8,000 spins = $80 in order to get a jackpot. Of course, the machine’s jackpot payout will be considerably less than 8,000X, so even if the win comes within the allotted number of spins, the return will surely be less that $80.

What’s more, if all of the lesser winning combinations are considered and their probabilities of occurring are combined, the anticipated total payout on 8,000 spins will work out to about $76~$78 or 95.0%~97.5% of the player’s investment. The difference is known as the “House Edge.”

In reality, most slots are far more complicated. For one thing, the number of stops usually exceeds the number of symbols on each reel. Although there might be a single stop associated with each jackpot symbol, other symbols can have multiple stops. That means instead of 1-in-20 odds for the jackpot symbol on each reel, the true probability might be 1-in-50 or 1-in-100.

This is particularly true of computerized slot machines. They can employ an unlimited number of “virtual” stops, frequently on the order of 256 or 512 per reel. A process known as “mapping” assigns some symbols a higher probability of appearing than others. The only way to accurately calculate the odds of any particular symbol being displayed on a payline is to find out the ratio of virtual stops to actual stops for each symbol.

In the popular three-reel one-payline slot machine called “Red, White, & Blue,” a jackpot of 10,000 credits is offered for a maximum three-credit bet. The payout is therefore 3,333 to 1 and it is awarded only when a Red 7, a White 7 and a Blue 7 are displayed on the center payline in exact order.

Because there are 11 blanks and 11 symbols on each reel, one might expect a jackpot once every 22 x 22 x 22 = 10,648 spins. But that is far from the case. Each reel has 64 virtual stops, which are unequally mapped to the 22 symbols. The true odds of hitting the jackpot are 1/64 x 1/64 x 1/64 = 0.00038%, or once every 262,144 spins, which is not even close to the odds suggested by the paytable.

Complicating the odds calculations even further, information regarding virtual stops and mapping is not publically available. Players must therefore come up with other ways of identifying which slots offer the best odds and what constitutes a reasonable wager. One of those is to compare payouts at “max bet” to those offered for winning combinations at a minimum bet.

As noted above, Red, White & Blue pays the top jackpot of 3,333-to-1 only when three credits are wagered. When a single credit is wagered, the maximum payout is just 2,400 credits. Common sense indicates that this game offers much better odds of winning for max bet, so slot players are well advised to wager the maximum; betting less simply has the same risk at worse odds.

Published on: 25/02/2012

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