Rolling the Dice: Harnessing the Power of Randomness

by / 0 Comments / 160 View / August 23, 2014

People usually like to have a plan. We map out our response to all of the possibilities, attempting to control the uncertainty in the world around us. However, across a wide variety of disciplines, research has found examples of how informed but random decision making actually improves outcomes in unpredictable environments.

Take the choice faced by a soccer player trying to score a goal: whether to kick left or right. Any given player is more accurate with one foot than the other. But, if they always kick with their dominant foot, the goalie will know which side of the net to block. Maybe the best bet is to kick to the weaker side and psych the goalie out? But what if they guess? Maybe a double-bluff is in order? Rather than descending into infinite regress, the optimal decision according to the field of game theory to is to randomly alternate between both feet. That way, the goalie can’t formulate an effective strategy. This is exactly what elite kickers do, according to a review of 3 years of games.

 Sometimes, the best strategy involves making guesses that are probably wrong. Let’s say that you’re spending the day betting at the horse races. You have some degree of confidence that each horse will win the race- perhaps you believe that Smarty Jones has a 70% chance, while rival Seabiscuit has a measly 30%. The naïve strategy is to place your bet entirely on Smarty Jones. After all, any money spent on Seabiscuit will probably be lost. However, it turns out that this approach won’t give you the best long-term returns at the racetrack. Betting on Smarty Jones might turn out brilliantly on the first race or the second, but eventually you’ll lose everything when he stumbles at the home stretch. The strategy that maximizes your returns over time is to bet 70% of your money on Smarty Jones and 30% on Seabiscuit every race. This is called proportional betting, where in the general case you bet on each option proportional to your confidence in it. Such a plan can be psychologically difficult to follow through on- after all, you know that most of the time the bet on Seabiscuit is money down the drain. However, acknowledging the randomness of the outcomes is the only way to stave off ruin in the end.

A more subtle example of the power of randomness comes from computer science.   Modern technology depends on breaking problems down into precise steps that a computer can execute. A sequence of such steps is called an algorithm. Algorithms power everything. One essential consideration is how long the program will take to run. After all, a solution does no good if it will take longer than the lifetime of the universe to complete, and such poor performance is entirely possible without careful design. The stakes can be very real. Hackers sometimes exploit the predictability of computer systems by crafting requests that they know will take eons to complete. In the meantime, the system is unable to help legitimate users. To carry out these attacks, hackers have to know exactly how a program will react to any given input. Randomized algorithms avoid the problem by flipping a virtual coin to make their decisions. This unpredictability prevents catastrophic failure when faced with unlucky (or malicious) inputs.

Random strategies may have been discovered by humans, but nature found them first. Organisms use randomness to cope with the uncertain conditions of their environment through a process called evolutionary bet-hedging. Take the unenviable position of a desert plant: its seeds must sprout during a period of time when there is some minimal amount of rainfall in order to survive. The solution produced by evolution is to introduce a degree of randomness into the germination times of seeds. If different seeds sprout at different times, a plant improves the chances that at least some of its offspring will have the moisture they need. There are a number of examples of bet-hedging in the natural world. Many bacteria have genes that are specifically prone to random mutations so that a variety of different responses to unstable environments can be explored. Some frogs stagger the germination times of their offspring in a manner similar to desert plants. In all of these cases, evolution has harnessed randomness to guard against life’s uncertainties.

Across sports, computer science, economics, and biology, there are examples abound of random decision-making yielding surprisingly good results- at times, better than any deterministic strategy.  The next time you play rock-paper-scissors, instead of triple-guessing your opponent, try just picking a move at random. After all, any pattern in your behavior can be exploited. Sometimes a simple but unpredictable strategy wins in the long run.

References:

Beaumont, Hubertus J. E., Jenna Gallie, Christian Kost, Gayle C. Ferguson, and Paul B. Rainey. “Experimental Evolution of Bet Hedging.” Nature 462.7269 (2009): 90-93. Web. <http://www.nature.com/nature/journal/v462/n7269/full/nature08504.html>.

Chiappori, P.-A, S. Levitt, and T. Groseclose. “Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer.” American Economic Review 92.4 (2002): 1138-151. Web. <http://pricetheory.uchicago.edu/levitt/Papers/ChiapporiGrosecloseLevitt2002.pdf>.

Cover, T. M., and Joy A. Thomas. “Gambling and Data Compression.” Elements of Information Theory. 2nd ed. New York: Wiley, 2006. 159-82. Print.

Kleinberg, Jon, and Éva Tardos. “Randomized Algorithms.” Algorithm Design. Boston: Pearson/Addison-Wesley, 2006. 707-94. Print. <http://www.aw-bc.com/info/kleinberg/assets/downloads/ch13.pdf>

Image Credit: “Colorful chameleon on a branch.” Flickr: Creative Commons. Flickr, n.d. Web. 23 Aug. 2014. <https://flic.kr/p/ngtqu1>.