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Why you can't make informed choices among slot machines

3 January 2011

Casino gambles are wholly characterized by two pieces of data – the payoff per unit bet and the probability of winning. Everything else that can be known – such as edge and expected long-term gain or loss, the kinds of bankroll swings you can expect to encounter during the action, the likelihood you have enough session money to survive normal cold spells, and the chance you'll reach a profit goal before running into a loss limit – can be determined from these two basic factors. Taken together, directly or through performance measures derived from them, they let you make informed choices about which games to play and the strategies to follow when you do.

You'll always have the payoff figures. Often, they'll be shown on the screens or belly-glasses of the machines or the tops of the tables. Sometimes, they'll be inherent in the rules of the game.

Other than in one class of exceptions, you can also get the probabilities – although you may have to do the math or go to the gurus for the values. The figures will be available because they're based on statistical or physical phenomena – 52 cards in four suits and 13 ranks comprising a standard deck, 38 equally sized and comparably positioned grooves on a roulette wheel, six matched square faces on each of two uniform cubical dice.

The exceptions, for which you won't know the probabilities, are wagers at reel- and matrix-type slot machines. The displays on these devices show payouts for each winning combination. But, unlike other games, the probabilities at each level are assigned arbitrarily and can't be ascertained by any form or deduction or inference. For instance, reels might have 10 symbols on them, each occupying 10 percent of the circumference. But reels don't simply spin and stop under the laws of mechanics, giving each symbol a 10 percent chance of appearing in the window. The positions are assigned chances in proprietary computer programs, totally independent of any statistical or physical effects. One of the 10 might therefore have a one-in-a-million chance of appearing, eight might have probabilities of 100,000-in-a-million each, and the last a prospect of 199,999-in-a-million. Without access to the software, you have no way to determine the chances.

Because the information is incomplete, means are lacking for players to make informed choices of machines that will best meet their personal preferences for gambling. So, maybe aunt Fannie isn't being all that foolish when she looks for a Lucky Ducky machine because she's won on it in the past. Perhaps uncle Egbert isn't picking particularly stupidly by following the theory that the bosses put the hottest games nearest to the doors so they can draw in the suckers. Even your loudmouth brother-in-law may be not be hurting himself looking for a machine that someone who's been losing just abandoned, thinking it's getting due to hit. Such whims have no basis in fact. But, absent facts on which to base more rational choices, no selection criteria are any better.

Some solid citizens think they can draw conclusions about one or another slot machine from jackpot size. One idea is that the smaller the jackpot, the easier it should be to hit, so if you'd be satisfied with $5,000 or $10,000, play on machines that top out there rather than at $50,000 or $100,000. Another notion is that, in order to offer a bigger top prize, which you're unlikely to hit anyway, the casino has to reduce returns at the lower levels, so you have a better shot at a long session and a moderate gain on a machine with a small jackpot. One or another of these beliefs may be true for an individual machine by serendipity alone. But, by the same token, it may be false for another game that otherwise appears identical but is programmed differently inside.

For example, a jackpot of $1,000,000 for a $1 dollar bet may have different probabilities in one machine than another. The difference may arise in numerous ways. One game may have a higher or lower house advantage, or may be easier or more difficult to hit at low or intermediate levels. The games may therefore not be at all alike from the viewpoint of the gambling experience they offer, in such player-oriented terms as prospects of earning modest or large profits or duration of the action a bankroll can be expected to provide. Unfortunately, there's no way to tell.

There's one thing of which you can be sure. If you're bound and determined to invest your stake in a shot at million dollar spin, the probability you'll be successful on a machine with a $25,000 jackpot is zero. Or, as the bettors' bard, Sumner A Ingmark, famously wrote:
If the belly glass don't say,
The jackpot does a million pay,
Then of chance you've not a ray,
A million's just a pull away.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.