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# Playing It Smart: How to make a mint in the casino on a small stake

30 May 2008

Anyone can get off the casino bus with \$100 and get back on with \$100,000. But few do. This, because the probability is slim. In a "fair" game, no house edge, the probability of this particular feat is one out of a thousand. And the only constraint is that you spend as little or as much time as needed to reach your goal or go bust first.

When edge rears its ugly head, it can still be done. But chances get more remote. And, in addition to the requirement to ignore the clock, the amount of the edge, the inherent volatility of the game, and the size of your bets have an impact on likelihood of success. This isn't necessarily bad, because players can manipulate the last two items.

Roulette offers a good model to study the phenomenon. The game lets players control volatility by choosing bets ranging from frequent small wins to rare big scores; the former giving low volatility and the latter high. Then there's the two versions, single- and double-zero with 2.70 and 5.26 percent edge, respectively. And, of course, solid citizens can bet whatever they please within the limits of each table.

To illustrate the points using conveniently scaled values of probability, posit starting with \$100 and play until you're broke or have \$1,000. With no edge, your chance of success would be one out of 10 or 10 percent. Here's how things change in a real game.

Say you bet \$1 on each of 10 spots. You're risking \$10 to net \$26 per round. Volatility is roughly the same in either game, an average fluctuation up or down (the standard deviation) of about \$16.00 per spin. In the single-zero game, your chance of success is 2.55 percent. At double-zero it's cut to 0.526 percent. Both are far below the "ideal" 10 percent, but hopes are brighter in the lower-edge single-zero case.

Instead, pretend you bet \$2 on each of five spots. Total wager per round and values of edge don't change. You're risking \$10 to win \$62. Volatility is greater standard deviation is about \$24.50 because you'll win larger amounts albeit less often. The chance \$100 will grow to \$1,000 is 5.59 percent at single-zero and 3.21 percent at double-zero tables. Both are still well under the 10 percent for a fair game, but the offset and the relative impact of the edge are less.

Go another step to \$5 on each of two spots. Here, \$10 can get you \$170. Volatility is again higher, with standard deviation approximately \$40.00. And your prospects of success are accordingly up to 7.68 and 6.43 percent for single- and double-zero wheels, respectively.

Changing the size of your wager also affects your chance of success. Betting a greater fraction of your bankroll improves the likelihood you'll achieve a profit goal before going bust. Compare \$2 and \$4 on each of five spots, \$20 rather than \$10. Prospects of increasing your wad from \$100 to \$1,000 becomes 7.20 (from 5.59) percent on single-zero and 5.60 (from 3.21) percent on double-zero layouts.

So, you improve your chance of hitting it big on any given bankroll by betting as much as you dare, at a game with the lowest edge you can find, following a strategy that boosts volatility as much possible.

This is no secret the casino bosses are guarding with their bonuses. And if putting a stake up for grabs to hit some target earnings level is your sole reason for gambling, go for it. But know the downside. The same factors that raise your chance of realizing a monetary goal increase the likelihood you'll go belly-up in short order. And most solid citizens not only want to go home with the gold, but want a lot of action on their stake if they don't happen to strike it rich.

Edge is your nemesis in either case. But higher volatility and larger bets improve your chance for a big score on any given bankroll, while the converse elements enhance the prospects for a long session. So, as in many familiar life's situations, you've got to strike a balance.

Is it a matter of using those bitter real world lessons to enhance your gambling, or of adapting what you learned the hard way in the casino to make your day-to-day comings-and-goings better?

It's an enigma the punters' poet, Sumner A Ingmark, poignantly posed in penning:

We could all our fortunes make,

And our lives of toil forsake,

Were it not for give and take.
Recent Articles
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.