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Do You Have a Better Chance with More Ways to Win?

2 July 1996

By Alan Krigman

When it comes to bait for the hook of easy money, no premise or promise can be too preposterous. And don't think the only fish who nibble on nonsense are naive or nitwitted. Consider all the college presidents, museum directors, and ministers who sent seed money to the Foundation for New Era Philanthropy.

To some folks, of course, easy money is the whole point of casino gambling. Give it a try, they think. If you're lucky, you win. If not, it didn't cost much more than a night at a pro ball game - and you got a free buffet, free drinks while you were playing, and free admission to a classy lounge show.

But, even solid citizens who understand the games and the odds can get fooled. Take slots that offer "more ways to win." These machines create a compelling illusion that players somehow have a better shot at that pot of platinum.

Video poker furnishes an example. Purists can still find ordinary five-card draw machines with simple pay tables. But they're not as common or popular as games which provide more ways to win with features like wild cards and bonuses for selected hands. The extras, though, are accompanied by three drawbacks.

1) While it's easier to "make" high-valued poker hands with wild cards, comparable results are worth less. For instance, draw poker usually returns one bet unit on a high pair and two units on two pairs. With deuces wild, you might not get paid unless you have triplets or better.
2) Bonuses for hands like "sequential" rather than random-order straights are balanced by lower payback on other results.
3) Strategies that maximize the expected value of a final hand are more complicated and less intuitive when wild cards and bonuses are mixed in the stew. As an illustration, say you're dealt two pairs - fives and eights. At straight draw poker, you'd hold them and hope for a full house. What if the game is joker-wild, bonus for five eights? Do you still keep the two pairs? Or, only the eights, fantasizing over the five-of-a-kind? How would your answer be influenced by various alternate payoffs for two pairs, triplets, a full house, or four-of-a-kind? What about the size of the bonus?

Reel-type slots with multiple "pay lines" for more than one coin similarly suggest more ways to win. Do three pay lines really triple your chances for a hit on every pull? The computers inside modern slot machines use programs based on random numbers to determine whether and how much you win on each spin. A single-line machine might show the computer's decision with side-by-side Liberty Bells. A three-line machine might display the same decision with golden eagles positioned along one diagonal. The extra pay lines didn't provide more chances to win. You still had one chance to win but the machine had three ways to present it.

Maybe you've seen the new four-reelers with the "nudge" feature. If the machine stops on a "near miss," you can touch the glass and nudge one reel to the next position, creating a winning line-up. Does this really offer a second chance? Say the computer decides that a particular pull is a winner. It may show four stars across. Or three stars side by side, and the fourth where you can nudge it into line. One chance to win, two ways to show it.

Overall, bet the same dollar and get more ways to win less or as many ways to win as much. To improve your chance to win more, you have to bet more on more bets - raising new issues altogether.

None of this necessarily says to avoid certain slots. Lest I spoil your fun, if you like a "more ways to win" machine, and are playing with recess and not lunch money, go for it. While these slots are no better than their plain vanilla twins, neither are they worse. Anyway, what's wrong with picking a machine because of an illusion? Isn't illusion what casinos are all about?

The immortal Sumner A Ingmark, whose poetic genius has also been labeled an illusion, put it thus:

The more the ways your bets can win,
The more you've stretched your dollars thin.

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 were focused on those interested in gambling probability and statistics. He passed away in October, 2013.