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Best of Alan Krigman

Gaming Guru

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Staying in the Game Helps Get that Shot at a Hot Streak

29 August 2000

Winning in a casino often seems to boil down to being in the right place at the right time. Is it all a matter of luck, or are skill, knowledge, and a knack for the numbers somehow involved?

Solid citizens who are serious about gambling, who assimilate experience and respect arithmetic, will be happy to learn that expertise is indeed a factor. Not in the sense of ability to predict when a machine or table will get hot, deduce combinations of wagers that magically eliminate the house advantage, or vary bet sizes in a way that guarantees a profit. These aren't marks of proficiency, they're signs of fantasy and flawed logic.

Genuine gambling aptitude starts with an understanding of how to size bets relative to a bankroll. It's arguably the most critical talent distinguishing adept gamblers from casino patrons who had a good time anyway, not to mention three desserts at the fabulous all-you-can-eat buffet. Proper bet sizing yields earnings big enough to satisfy players' goals while also improving chances of "being there" by surviving normal downswings.

Playing time is important not simply because participation is inherently exciting. More, it affects the likelihood of encountering profitable situations. In sessions of reasonable duration on slot machines or other jackpot-oriented games, chances of a big score rise roughly in proportion to the number of tries players' bankrolls buy them. That is, 200 bets offer a whisker under twice the chance of 100 bets. At non-jackpot table games, where good earnings usually imply encountering a run of winning rounds, the situation is similar but more complicated.

As an example, say you make Pass and Come or Place bets at craps. Your vision of valhalla is a long roll involving only box numbers -- four, five, six, eight, nine, and 10. The chance that one of these numbers will show on any roll is 24 out of 36 or 66.7 percent. The chance of seeing one or another of these numbers on 10 throws in a row is about 17 out of 1,000 or 1.7 percent. Similarly, the chance of getting a box number on 15 successive throws is about 2 out of 1,000 or 0.2 percent.

If you play craps for six hours with moderately-paced action, you'll experience roughly 360 throws. What's the chance that within this time span, you'll encounter at least one streak of 10 or more successive box numbers? It turns out to be about 49 percent, meaning that you can expect it to happen in almost half of all six-hour sessions you play. An unbroken run of 15 or more box numbers has a probability exceeding 8 percent, such that it can be expected in eight or nine out of every hundred six-hour stretches.

But, if you allocate six hours for craps and tap out prematurely, your shot at encountering a long series of successive box numbers drops dramatically. The effect is shown in the accompanying list for runs equal to or greater than 10 and 15 hits in a row.

Chances of runs of at least 10 and 15 successive
"box numbers" in sessions of various durations
     
hours per session at 60 throws per hour
chance of a run of 10 or more box numbers
chance of a run of 15 or more box numbers
1
9%
1%
2
19%
3%
3
28%
4%
4
36%
6%
5
43%
7%
6
49%
8%

Don't err, however, by thinking that after a marathon cold session, a hot roll is due. Although the chance of encountering a streak of box numbers increases with playing time, you can never assume you're in the middle of a long-awaited hall of fame run.

Whether you've just bellied up to the rail, or are ready to retire after six hours of hooting and hollering, the probability of the dice showing a box number on any try is always 24 out of 36. Regardless of what's recently been rolled. And you should keep this firmly in mind when you bet. The beloved bard, Sumner A Ingmark, captured the quintessence of the quandary like this:

Though gamblers' wishes and denials,
May strongly hint of other things,
In games of independent trials,
No past tells what the future brings.

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.