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# How Volatility Improves Your Chance of Winning Big

10 May 2006

Recreational gambling gets the adrenaline flowing and adds more excitement to life than alternatives like buying a few rounds at the corner tavern or going out for dinner and a movie. But not too many solid citizens visit the casino chiefly for the rush. They go to make money. Typically, to start small and finish big.

Sadly, the more by which a bettor wants to multiply a bankroll, the dimmer the outlook for success. Even if the bosses had no edge, hope of winning would be mathematically limited by the ratio of the amounts involved. So, say you begin with \$100. The chance you'll board the bus with \$100,000 is 100/100,000 or one out of a thousand. With \$1,000, it's 100/1,000 or one out of 10.

These figures are ideal limits. Actual probabilities will be less. Inquiring minds will naturally want to know how to keep the actuals from falling any further below the ideals than need be.

The edge matters, of course. All else being the same, gamblers should look for the games in which this is the least.

Assume you're a blackjack buff. You start with \$100, bet \$5 per hand, and will go for broke to run for the door with \$1,000. In the limit, your chance is 100/1,000 one out of 10. You find a table with liberal rules and follow good Basic Strategy, giving the house half a percent edge. Your toss is a one out of 22 proposition. Maybe you don't always split or double when "the book" decrees these moves, so you give the house 1 percent. This decreases your shot at reaching the \$1,000 mark to one out of 60.

Instead, make believe your passion is jacks-or-better video poker. Again, you start with \$100 and hope to head home with \$1,000. You now know that your chance tops out at one out of 10. You find one of those mythic 9-6 games and play like an expert, so edge like that in the good blackjack example is only half a percent. Betting \$1.25 per round, your chance of victory is one out of 12. You're more apt to be on an 8-5 game in which edge is roughly 2.7 percent; in this case, expert strategy at \$1.25 per round would cut your risk level to one out of 33.

Bet size also has an impact. In the blackjack situations, pretend you bet \$10 rather than \$5. Your chance, fighting half a percent edge, rises from one out of 22 to one out of 14; versus 1 percent edge, your shot improves from one out of 33 to one out of 22.

Similarly for the video poker alternatives. Upping your bet from \$1.25 to \$5 strengthens your chance in a 9-6 game from one out of 12 to one out of 10.5, near the ideal. At an 8-5 machine, your prospect brightens from one out of 33 to one out of 13.

Volatility is a third factor. To see the effect, compare the half percent blackjack and video poker games each at \$5 per round. Your chance of reaching \$1,000 before losing \$100 was one out of 22 at blackjack and a superior one out of 10.5 at video poker.

The primary difference between these options is volatility. In terms of "standard deviation" think of it as the average number of bet units your bankroll fluctuates per round volatility is 1.13 for blackjack and four times as much, 4.40, for video poker. High volatility, which characterizes games with moderate and large returns for relatively rare outcomes, enhances the probability of hitting your target before biting the dust.

By driving down the edge, raising your bets, and finding games with high volatility, you can approach the theoretically maximum likelihood of hitting your profit target before busting out. Approach, but never quite reach. And certainly not surpass.

There's something else to consider. Bet size and volatility work for you when your criterion is earnings. However, they militate against you when your objective is to survive for a reasonable period of time before a bankroll downswing sends you packing. Trade-offs are in order because you can't have it both ways. It's as the immortal muse, Sumner A Ingmark, so eloquently elucidated: