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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Multi-line slots don't have to be complex

19 May 2009

Picture a hypothetical old-time three-reel spring-and-ratchet slot machine. The kind with a handle and no computer. Say that each reel has 10 positions and can stop with equal probability at any of them. More, pretend that nine of the positions are marked "x" and one "o." And, posit that returns are 100-for-1 on three x's, 10-for-1 on two x's, and 2-for-1 on one x. Three o's loses.

Chances of the possible results would be one tenth of one percent for three x's, 2.7 percent for two x's, 24.3 percent for one x, and 72.9 percent for three o's. These percentages are no great puzzle. Chances on each reel are 1/10 for an x and 9/10 for an o. So three x's comes in at (1/10)x(1/10)x(1/10) or (1/1,000). One x and two o's is 3x(1/10)x(9/10)x(9/10) multiplication by three because the arrangement could be x-o-o, o-x-o, and o-o-x; this works out to 2.7 percent. Similarly for the other combinations.

Hit rate the average fraction of spins on which bettors "win! win! win!" is the sum of the probabilities for the individual winning combinations, or 27.1 percent. For the return percentage on this game, multiply the chance of each combination by its payout and add the results. Dust off your abacus or trust me. It's 85.6 percent; house edge is the complementary 14.4 percent.

This game is easy to fathom. But nobody would play. The 100-to-1 isn't exactly a life-changing jackpot, hit rate and return percentage are low, and x's and o's are boring.

Computer technology has enabled casinos to extend the same principles to multi-line slots. And these are now all the rage. At first glance, they seem to defy comprehension. To some solid citizens, of course, the magic is in the mystery. Sophisticated players, however, like to know how their favorite games work.

To understand the concept, imagine a tic-tac-toe machine whose display has three rows across and three columns down. The symbols, x's and o's, can appear in each of the nine positions independently of what shows anywhere else. Assume that the chance of an x in any position is 1/10 and that of an o is the other 9/10. Further, make believe that the returns on each row, column, or diagonal match those on the prototype three-reeler.

If the matrix filled with x's, eight equal bets would return 800 units nickels, quarters, dollars, whatever. This far eclipses 100 units, although it would take eight times the bet to get it. Few hopeful bettors would note that the chance of nine x's is 1/10 multiplied by itself nine times, or one out of a billion.

The hit rate would also seem rosy. Prospects of any line winning are only 27.1 percent. Betting eight lines, though, the chance of any return at all on a spin is 61 percent. Never mind that win! win! win! doesn't necessarily pay eight or more units and may actually be a loss. Each row would still return 85.6 percent, as would the whole game, no matter how many lines are bet per spin.

Actual games utilizing this idea have larger matrices, typically three rows by five columns with lines going zig-zag as well as across and up-and-down. And multiple imaginative theme-based symbols are utilized, each with its own probability. But if you follow the tic-tac-toe logic, you grasp the whole genre.

By the way, nothing precludes these games being set up so you could make a single bet -- for instance one-to-five nickels covering all lines. Nothing except casino revenue and player demand for "free" rewards. Covering all eight lines at tic-tac-toe with one nickel wager gives the casino an average gross per spin of a paltry 14.4 percent of $0.05, less than a penny. A nickel on each of eight lines would earn the joint an average of 14.4 percent of $0.40, or almost six cents per spin. Think about 10 nickels per line, a $4 total bet, next time you're scarfing down that "free" buffet meal. Sure, a lucky bettor could realize a nice haul on a game like this. But, at $4 per shot, win! win! win! can quickly drain a bankroll and kill an appetite. Which is why the immortal inkster, Sumner A Ingmark, urged the unwary:

Attend to the basics then, well grounded,
Intricacy won't have you confounded.

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.