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# Does too much focus on edge ignore factors you can control?

11 January 2010

Many otherwise sophisticated casino gamblers focus on house advantage or edge and overlook the trade-off between the odds associated with various results and the accompanying payoffs. The choices here, which solid citizens can control, may have a greater impact than edge on a person's performance in the short term of a session or casino visit.

A more extreme situation than you're apt to encounter emphasizes the effect. Imagine a slot machine that either pays a million-to-one or loses. If the chance of success on any pull is one out of 1,010,102, house edge is 1 percent. Say you start with \$100 and wager \$1 per round. Your shot at winning the million before going kablooie is about one out of 10,102. The other 10,101 out of 10,102 chance is that you'll run dry in exactly 100 rounds.

Pretend another machine also pays \$1 million for a \$1 bet, but has outcomes that return your wager as well as results that lose. This game will give the casino a 1 percent edge if the chance of the biggie on any try is one out of 2,949,820 and that of a push is slightly over one out of two. Your prospects of winning the million before going broke are a bit less than in the jackpot-or-lose game, one out of 10,207. The likelihood you'll eventually bust is the other 10,206 out of 10,207. On the average, you'll get 200 rounds on your original \$100 before this happens.

Here's a third possibility. Picture another win, push, or lose machine, this one with the same jackpot probability per round as the all-or-nothing game – one out of 1,101,102. But the jackpot for a \$1 bet is \$100,000 rather than a million. The casino will still have 1 percent edge if the chances on any spin are just under 89.1 percent that you get your money back and about 10.9 percent, approximately one out of nine, that you lose. Overall, the probability you'll grab the \$100,000 before busting out is one out of 1,108. And, on the average, you can figure on 900 to 1,000 attempts before you bite the dust if you don't luck out.

The differences in these examples arise with the same 1 percent house advantage. It's true, of course, that on particular slots you know neither the probabilities of the various payoffs nor the edge so your choice isn't fully informed. But the return levels are shown with the corresponding combinations so you can distinguish between games with high, intermediate, or modest payoffs. And, absent other data, you can assume the house's edge is about the same in alternate games of equal denomination – getting steeper as the minimum bet decreases. Further, you should realize that a wider variety of payoff combinations doesn't mean more chances to bring home the bacon but lower probabilities that any of them, particularly those of higher amounts, will hit.

There's something else to ponder. Edge is the same 1 percent in all these examples. But, how much money does the casino earn, on the average, from each patron who starts with \$100?

The first machine, that decimates losers in 100 rounds, pays out \$1,000,000 on the average for every \$1,010,200 it takes in; the house earns \$10,200 from 10,102 players – \$1.01 each. The second machine, on which \$1 non-winners with \$100 bankrolls expect 200 rounds, dispenses \$1,000,000 for every \$1,020,600 it collects; the casino make \$20,600 from 10,207 hopefuls – \$2.02 each. The third machine, where \$1 bettors with \$100 pokes average over 900 rounds, pays \$100,000 for every \$110,800 it receives; the establishment nets \$10,800 from 1,108 aspirants – \$9.75 each.

Besides the implications for bankroll longevity, this reveals two common misconceptions about edge. First, bosses who know beans about betting don't try to ravage everyone as rapidly as possible; casino profits rise when players get more action for their money. Second, edge doesn't account for the bulk of the loss particular unlucky players experience; the majority of those in the examples cited dropped \$100 but edge only represented an average of \$1.01, \$2.02, and \$9.75 of each such loss. The rest went to the winners. So much for conventional wisdom. Here's how Sumner A Ingmark portrayed folks who spread spurious speculation.

While self-proclaimed experts are oft sanctimonious, Pronouncements they make may in fact be erroneous.

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Best of Alan Krigman
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.