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Best of Alan Krigman

Gaming Guru

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Don't Quit Your Day Job for the "Full-Pay" Slots

17 March 1997

You sometimes hear about "full-pay" slots. Machines that return 100 percent or more of the money bet in them.

They do exist. The stories aren't all fibs fabricated by casino bosses to beguile believers into betting more. Nor, necessarily, rumors repeated by con artists to sell gullible gamblers dubious inside information, bogus systems, or worthless gee-gaws like space-age opto-digital neural-net hot-slot detectors.

But, don't quit your day job for the full-pay slots just yet.

Full-pay reel-type machines, when used by casinos as promotional loss leaders, are few and far between. And you won't be able to tell them from units with the usual usurious "hold" percentages.


Full-pay video poker machines, in contrast, can be identified. The key is in the payout schedule on the screen or faceplate. You only have to be sophisticated enough to know the probabilities associated with each hand and do the math, read and heed one of the few reliable video poker books where the work has been correctly done for you, or ask the right gambling guru and not argue if the answer isn't what you wanted to hear. Of course, you must follow the optimum strategies to the letter, or the odds will change and the returns will miss the 100 percent mark.

Say you've done your homework. You've found a deuces wild machine having the payouts shown in the accompanying table, which returns 101.1 percent. Not only that, you know the optimum hold and discard strategy for this little puppy and can play it perfectly.

Now, should you quit your day job? Postpone that decision until you learn a little more.

Slots are inherently risky to individual players, even if they return over 100 percent of what's wagered. Why? Payout profiles have large characteristic fluctuations, sharply skewed to balance low-likelihood great gains against high-probability small losses. In the full-pay deuces wild example, solid citizens can expect to hit the 800-to-1 jackpot twice or so in 100,000 tries, losing one bet 55,487 times. Big-buck reel-type slots are far more extreme.

Mathematically, for every dollar bet, the specified deuces wild machine has a healthy long-term expected win of $0.01; however, short-term fluctuation is a severe $7.10 and skewness coefficient is off the Richter scale at 69. In contrast, on red or black at roulette, expectation is a hefty loss of $0.026 per dollar bet but fluctuation is only $0.98 and skewness a mere 0.07.

High slot fluctuation and skewness imply that in the short stretch of a normal session, a bettor's bankroll will typically exhibit a falling tendency punctuated by occasional sharp rises. Recreational gamblers are hoping for one or more of those lucky peaks before they exhaust their day's entertainment budget. "Professionals" would need long playing periods and deep pockets to enjoy reasonable assurance that enough low-probability large jackpots would be hit to offset the frequent small losses.

How long? And, how much bankroll is required for confidence in not being knocked out of the box by a normal downswing?

Assume you want to be 99.7 percent sure your perfect play at the specified machine will break even or yield a profit. An analysis using the statistical properties of the game shows you'd need no less than 3.78 million tries. And your bankroll would have to be enough to support the family while enduring at least a 10,349-bet setback - $12,936.25 in a quarter machine played five coins at a time and paying $1000 for natural royals. Specify some profit level, say $3 per hour, and the requirements get stiffer.

Still ready to quit that day job? I didn't think so. Neither did the bard, Sumner A Ingmark, predicting the predicament poetically in his beloved ballad, "The Brave Who Bet for Their Daily Bread:"


Gamblers trying to make a living,
Find casinos most unforgiving.

TABLE
Payback Schedule and Statistical Properties
of a Representative Full-Pay Deuces Wild
Video Poker Machine
hand
probability
payout
natural royal
0.000022
800
four dueces
0.000209
400
royal with deuces
0.001883
20
five of a kind
0.003098
10
straight flush
0.004236
10
four of a kind
0.062940
4
full house
0.026410
4
flush
0.019500
3
straight
0.055630
2
three of a kind
0.271200
1
loser
0.554872
0
Probabilities assume players follow strategies
specified in "Video Poker -- Precision Play" by
Dan Paymar, Enhanceware, Las Vegas NV 89104

 

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.