Many old books will report that the
odds of a particular combination of symbols coming up on a slot machine can be calculated from the layout of the
symbols on the reels. In modern times, this is certainly not so. The combination of symbols that comes up is determined by a computer.
The old method might have been something like this: The jackpot symbol is three sevens. Each of the three reels has 20 symbols, including one seven per reel. So there are 20 * 20 * 20 = 8000 possible ways the reels can stop, one of which is the jackpot. Therefore, the probability of a jackpot is 1 in 8000.
Fallacy: The machine's internal computer decides what comes up. If the casino decides that the jackpot odds are 1 in 2,000,000, so be it. This is perfectly legal, I think.