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What can falling apples and feathers teach you about casino gambling?

1 November 2010

The laws of science generally say – in effect – "do this to get that." The laws of probability tell you what outcomes that are possible and the prospects each will occur. Gamblers might prefer the second type was more like the first. Of course, in this case, there wouldn't be any gambling. Still, laws of the two kinds aren't as different as they may first seem. And, it's not what's known that ties them together; it's what's unknown.

Newton's law of gravity indicates that if you drop two apples of different weight at the same time from a height such as 100 ft, they'll hit the ground together. You could profit betting on this, were you to find anyone willing to wager that the heavier an object the faster it falls. But what if one of the objects is a feather, not an apple? The apple will normally land first. And if you dropped two feathers you thought were identical, they wouldn't necessarily land at the same time. This doesn't violate the law of gravity. Rather, it calls for considering an additional effect – the frictional force exerted by the air on objects passing through it.

At the speeds in question, the influence of the air is negligible on apples but significant on feathers. And, without rigorous monitoring or control, you can't know enough about the state of the air along the path or the key features of the feathers to account for the phenomena. Worse, you can drop feathers repeatedly but can't apply past results to future trials because conditions aren't necessarily constant. This leaves no option but to view the impact of the air on falling feathers as random and to give up trying to augur reliably when they'll reach the ground.
In casino games events have well-defined finite sets of possible outcomes. Examples are 36 combinations forming integral totals from two to 12 on a roll of two dice, 38 grooves on a double-zero roulette wheel, and 13 ranks of four suits in a standard card deck or shoe with no jokers. You know in advance precisely what can happen and the associated chances. You can't predict the specific outcome of any particular trial. The reasons for this uncertainty and your inability to dependably anticipate when a feather dropped from 100 ft will reach the ground are identical. The unknown but significant influences that manifest themselves as random factors.

To reliably foretell where a roulette ball will come to rest, you'd have to know about – and how to evaluate – such details as tilts in the wheel, conditions of the bearings that could cause the rotation not to be perfectly smooth, differences in the grooves that make the ball more or less apt to bounce out of one than another, surface imperfections in the track around the wheel that could divert the ball, the position of the wheel and the rate at which it was turning when the ball left the rim, and the motion the dealer imparted to the ball when releasing it. In practice, you'd be unable to determine information like this to a useful degree of accuracy, let alone process it.

This doesn't mean that the laws of probability can't be helpful in the casino. If not in determining how to win the upcoming round, then in planning your gambling strategy.

In many games, the probabilities alone tell you the chance you'll win or lose an individual coup. At double-zero roulette, the chance of winning on one spot is one out of 38. Are you patient enough to endure a string of failures while betting this longshot and fantasizing about a big score? Going further by including both chance and payoff, the laws of probability can tell you how much edge the bosses are enjoying. Something you won't notice on a single round but that can take its toll over extended play. You'd be surprised how many solid citizens prefer bets on the four to those the five at craps because they pay $9 rather than $7 for $5 at risk and ignore the chances. Accounting for both shows the bosses withhold $1 on the four and $0.50 on the five relative to "fair" payoffs, and this boils down to house edges of 6.7 and 4.0 percent, respectively.

At an even higher level, the laws of probability can help you decide how much to bet per round, given the stake you're willing to risk, the level of profit to which you aspire, and the importance you place on getting time in the fray for your money. Say you have $200 and are at a blackjack table with four total spots in action. Assume you follow Basic Strategy somewhat loosely. At $5, playing until you doubled your money or busted out, you can calculate that your chance of success would be 38 percent and you'd have 97 percent chance of staying in the action for three hours. At $10, your chance of earning $200 before losing the same amount improves to 44 percent but your prospects of surviving for at least three hours decreases to 71 percent.

You could keep covering the four at craps and make more than someone on the five. Or, you could wager $5 at blackjack and earn $200 handily, while another player bet $10 and never got close to this goal. Random influences can't be discounted, but this doesn't mean you have to put yourself wholly at the mercy of chance. As the punters' poet, Sumner A Ingmark, slyly scrawled:

Though random factors may affect you,
Using knowledge helps protect you.

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.