When do you cash in?

July 11, 2001 12:15 AM
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A celebrated school of gambling thought, promulgated primarily by people who wouldn’t know the inside of a casino from the canasta corner at a cushy country club, says to quit when you’re ahead because the longer you play, the more apt you are to give it back. Like many musty maxims, this banal bromide isn’t really wrong. But it glibly glosses over an inherently intricate issue.

It’s true that the house has an edge on every bet. This is what ultimately keeps the casinos in business and subsidizes those all-you-can-eat buffets. But the phenomenon is a manifestation of the law of averages. Each patron is apt to do better or worse than forecast by edge and handle, but the bosses book enough action so these deviations essentially cancel each other out.

Say that a person has adequate bankroll and sufficient discipline to ride through the inevitable downswings of a or machine (two conditions not often met, by the way). Then, playing longer but within ordinary limits of human endurance still leaves the individual in the realm where the volatility of the game dominates the edge. This improves the chance of attaining any specified earnings goal, while unfortunately raising the likelihood of falling to any loss level as well.

The effect is evident in the accompanying list. The figures are for blackjack played with perfect Basic Strategy and the same amount bet on a single spot every round. Trends would be similar although details would differ for other situations, and would be less promising as games have greater house advantage or put more of their return percentages in large but infrequent jackpots.

Chance of reaching 10-, 20-, and 25-unit earnings peaks at blackjack during sessions comprising indicated numbers of rounds

Round

10-Unit

20-Unit

25-Unit

peak

peak

peak

50

20%

2%

1%

100

36%

7%

2%

200

51%

19%

11%

300

58%

28%

18%

400

63%

35%

24%

Reading down the columns of the table shows how chances of soaring to 10, 20, and 25 bet units ”” for instance $100, $200, and $250 wins for $10 wagers, respectively ”” improve as a session stretches from 50 to 400 rounds. To illustrate how to interpret the data, a $25 bettor has 19 percent shot at getting at least as high as $500 within 200 rounds, and 35 percent likelihood of achieving this 20-unit objective within 400.

The chart shows something else worth noting. Reading across the rows reveals that for any length session, increasingly high peaks become progressively more perverse. For example, a solid citizen betting $5 per round has a 63 percent chance of earning $50, but only 35 percent of hitting $100 and 24 percent of grabbing $125.

Is there some catch to this? Or should you just keep playing until you reach whatever earnings objective you set for yourself? If you’re asking this question ”” or, worse, keeping it entirely off your radar screen ”” you ignored three factors you didn’t want to believe were significant.

1) Longer sessions increase the prospects of hitting any given loss as well as any particular profit level. And, the edge causes an imbalance, such that penalties tend to be greater than rewards for equivalent numbers of rounds and probabilities.

2) Players must be able to ride through any valleys that come before the crests. While casino buffs often have their heads in the clouds when musing about wins, their feet are usually on or close to the ground with respect to what they’re willing to lose. 3) In the long run, edge swamps volatility. Then, profit is only possible with a rare high jackpot in games having this feature.

Stay? Quit? There’s no one right answer. Once again, we’re at an impasse where inquiring minds have the facts and have to face the awful prospect of actually making a choice. It’s arguably less a question of gambling than of philosophy. And, for this, it may be propitious to ponder the profound poetry of Sumner A Ingmark:

Winning’s grand and losing’s dreary
So, of risking,
folks are leery,
That’s why there’s
decision theory.