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That depends on how many combinations the manufacturer programs in to the machine software. Modern "Stepper" machines use a stepping motor and plastic flags on the inside frame of the reel which are read by an optic. This allows the machine to stop the reel on whichever symbol the software says it should stop on allowing the software to use what are called "logical reels". The software can be programmed with an infinite number of possible symbols for each reel. The average 3-reel "stepper" game has 22 physical symbols per reel including blank spaces. 22 X 22 X 22 = 10,648 possible combinations minimum. There are some machines with combinations in the tens of billions. Corrected Answer: If by "one arm bandit", you mean antique, mechanical slot machine, most have 20 symbols per reel, so one BAR symbol per reel should be 8,000 to 1 odds. Many have more than one BAR symbol on at least one of the reels though, so this makes the odds a little more in the player's favor. Modern machines do not use optic readers, they use a computer called a RNG, a random number generator, this tells the motors that turn the reels where to stop. The machine's odds are programmed in to a chip that can only be changed by a select few casino employees, and in most states this is legally done only in the presence of state gaming officials. Slot machines in other countries, and on cruise ships, etc, may be operated in a far different manner, possibly hooked into a master control computer of some kind, where the odds may be changed remotely.

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