That is, indeed, how game theory would present the problem; yet, intuitively, this approach seems to depend on the game’s being repeatable. Professional poker players bluff about as often as an optimal mixed strategy would suggest—but that’s because they play game after game. What if everything depended on one hand? Could you really justify taking the low-probability route on the basis of a random choice?
Equations combine variables and constants. In scientific experiments you control only the variables, but in human affairs the constants may also be open to attack. The Allies chose the Normandy invasion route despite (or, perhaps, because of) its lower probability of success—this was the apparent constant. They then set about adjusting that constant, while at the same time keeping it unchanged in the minds of the defenders.
It was, of course, impossible to hide the invasion forces gathering on the coast opposite Normandy, but it was not impossible to disguise their relative importance. A huge phantom army, the “First U.S. Army Group,” was created—complete with canvas landing craft and inflatable tanks—and billeted in southeast England, convenient to the Pas de Calais. Normandy’s lack of secure anchorage and difficulty of supply were brilliantly overcome by technology: the floating concrete Mulberry harbors and PLUTO, the first underwater fuel pipeline. Counterintelligence adroitly finessed German expectations: the double agent GARBO (Juan Pujol) warned Berlin of the Normandy invasions hours before they began—that is, just a little too late. He then exploited the credibility this warning gained him to convince the defenders that Normandy was merely a diversion and the real attack would be at the obvious point: the Pas de Calais. Twenty-one German divisions were kept out of the battle for two months in expectation of an invasion that never came.
How far have we come from Earl Waldegrave’s card table? In many ways, we have never left it. Every negotiation, from the divorce courts to the United Nations, still involves accepting the least bad as a substitute for the best. Every leader, from parent to president, knows that leadership often simply means willingness to make the random choice required by a mixed strategy. If the winning choice were always determinable, we could leave government, like chess, to the computers.
Modern game theorists deal routinely with matters that even their RAND predecessors would consider incalculable: prior belief, imperfect information, irrationality. Just as with formal probability, it has become necessary to include in their equations a Bayesian term—something to represent the mind we came with, the game we thought we were going to play. In a way, therefore, Tolstoy was right: winning or losing is a thing we find within us.
Tolstoy probably came to this conclusion during his own experience of fighting in the Crimean War in 1854. In all that long account of individual courage and collective incompetence, nothing reads more strangely than the battle of Inkerman, the Russians’ great attempt to break the siege of Sebastopol. On paper, their plan was perfect: 40,000 troops, divided into powerful attack columns, would sweep up the Inkerman heights, where a British force one tenth their number was lightly entrenched. Meanwhile, a mobile Russian army would threaten the position from behind, dividing the defenders’ attention and getting ready to scramble up the steep cliffs on their side the moment they saw the attackers’ standards reach the old windmill that marked the British camp.
It was a morning of thick fog. The Russian troops coiled out of the town in a dense, dark, overcoated mass. On the heights, the defenders were aware of something happening, but the vagueness and confusion that marked all command in the Crimea prevented special preparation for an attack. By the time any British general realized that a major assault was being planned, it was already under way.
What happened next was as unpredictable as it was effective: all over the hill, individual British units, groups of twenty or thirty men, realizing that attempting to hold a waist-high pile of stones against the force of thousands was a hopeless job, decided instead to attack. Without command, without coordination, these companies leaped up and plunged into the looming mass, each man swimming through it with sword or bayonet like a scarlet fish in a great gray ocean. What was still more remarkable was the effect on the Russian columns: designed for irresistible forward momentum, they began to collapse on themselves once the enemy was in among them. The attack that had looked so perfectly organized on Prince Mentschikoff’s map table dissolved into pointlessness and confusion. The standards never reached the old windmill; half the Russian force stood by and watched the defeat of their brave but baffled comrades, driven off the mountain by tiny groups of darting red figures.
The battle was won and lost by prior beliefs: the Russians believed in the power of numbers applied through a system of unquestioning obedience. The British believed in the power of technique applied, in an emergency, through the initiative of the individual. This contrast in assumptions determined the game, not any choice of strategy—indeed, the British command never got around to having a strategy for Inkerman.
The spirit of battle moves in an incalculable way, but a cannonball moves in a parabola and a man-of-war obeys the combined vectors of wind and current. Mathematics entered warfare through gunnery and navigation: Cardano’s rival Tartaglia published the first treatise on algebraic artillery; contemporary mariners’ handbooks gave captains the trigonometry they needed to circle the globe. Here, at last, we can feel at home in classical physics, projecting force over distance; and it was in the branches of military thinking most dependent on physics—particularly in the navy—that warfare came closest to being a science.
One of Leibniz’s hopes had been that naval fighting could be studied on a tabletop, and here, at least, he would not have been disappointed. A remarkable Scotsman, John Clerk of Eldin, was obsessed by seafaring—although he himself had never sailed farther than the forty miles from Glasgow to the isle of Arran. He was connected by birth and marriage with most of the sparks of the Scottish Enlightenment, which gave him, in addition to many excellent sources of information, an unwillingness to accept anything purely on authority. Having mastered the mathematics of navigation and ship handling, he saw no reason why naval tactics should not be reduced to similar principles.
Starting around 1775, Clerk took his protractor, parallel rule, compasses—and his fleets (represented by small pieces of cork)—and restaged on his table after dinner the unsatisfactory recent performances of the Royal Navy. The fundamental problem was that the British wanted to bring the French into a full-scale battle and the French had little wish to cooperate. The British fleet would typically bear down on the French from the windward side and then attempt to maneuver into a neat line, bringing their broadside batteries to bear. It was a complex but time-hallowed procedure; indeed, a commander who attacked in any other way might well face a court-martial. The French, however, would not play the game: instead of holding their position, they would pour fire into the leading ships of the approaching fleet and then turn downwind and escape. It was very frustrating.
Clerk’s cork squadrons revealed the answer to this vexing question: a simple, daring maneuver called “breaking the line.” Instead of arranging themselves parallel to the opposing fleet, hoping to pound things out in a fair upright fight, the British should use their downwind momentum to cut right through the opposing line of battle, aiming their powerful broadsides against the poorly defended bows and sterns of the French and then rolling them up before they could break away. It was a plan very close to the tactics later adopted on land by Napoleon.
Clerk tested his idea in many tabletop engagements under different simulated conditions of wind and wave. Once he was certain of its efficacy, he briefed those he felt could put his discoveries to best use: the friends and advisors of Admiral Rodney, then (in 1780) about to sail against the French in the Caribbean. In the following engagement, the Battle of the Saints, Rodney put the new technique into effect with complete success. Clerk got the usual reward for an amateur who meddles successfully in someone else’s profession: denial and oblivion. Rodney’s partisa
ns vehemently repudiated the idea that their hero would ever have needed the assistance of some landlubber and his bits of cork.
Clerk deserved better: he had shown the fundamental difference between war at sea and war on land. Naval warfare is Newtonian. Small but powerful units move purposefully through a uniform (if dangerous) space, exploiting the laws of classical mechanics to gain advantage over other, equivalent units. One ship may differ from another in armament, speed, or efficiency—but once these factors are known there is bound to be a best way to deploy it, which you can determine by calculation and simulation. In this simpler universe, models and war games can have the predictive power that Kriegspiel promised but failed to deliver.
This may explain why the Vatican of war simulation is in Newport, Rhode Island, at the U.S. Naval War College. The first school of naval theory in the world, it was founded in 1885 with high hopes and a very low budget. Fortunately, Newport had in Alfred Thayer Mahan one of history’s greatest theorists of naval power, and in William McCarty Little an ingenious deviser of war games, simulating naval battles from single-ship duels to hemispheric fleet actions. Soon, the checkerboard linoleum “deck” of Pringle Hall became famous as the training ground of future admirals.
Between the world wars, the Naval War College fought 130 strategic war games, 121 of which represented war with Japan. Looking through the records, what is fascinating is how the Navy’s assumptions changed as a result of these simulations. The traditional view, based on Mahan’s theories, was that a single conclusive engagement of massed fleets would determine the fate of the Pacific—Mahan may indeed have inspired the thinking behind the Japanese attack on Pearl Harbor. Game experience showed, though, that the war would be long, that sea and land operations could not be separated, and that victory would not come until mainland Japan was completely isolated—and perhaps not even then. “Nothing that happened during the war was a surprise—absolutely nothing,” said Admiral Nimitz, “except the kamikaze tactics.”
In strategic terms, Nimitz was right—but in fact, almost everything that happened tactically was a surprise, because the War College’s tactical games were designed in a different spirit from its strategic ones. Here, all was precise data: exact armor thickness, ship by ship, deck by deck, the aim being to reproduce every nuance of technological warfare—in which, for example, the rotation of the Earth is a crucial variable in the gun-aimer’s calculation. The danger with this obsessive approach was the same as with Kriegspiel: precision in executing a game emphasizes every inaccuracy in its assumptions. These games assumed long-range battles between big fleets in daylight. In reality, most tactical engagements in the Pacific were like weasels fighting in a bag: close-range, confused, vicious, nonstop. The game had allowed players three minutes per move. The enemy did not.
Today, Newport boasts a great blank specialized building to house its war-game facilities. The checkerboard floor and celluloid models have been replaced by chilled, windowless rooms where simulations run on supercomputers. Purely naval combat has been extended into games incorporating all branches of the armed services, at scales from individual Special Operations teams to carrier task forces. The largest games can involve hundreds of participants and include many more than just the military: simulated politicians hesitate and fret, while simulated CNN runs constantly in the background, revealing and second-guessing strategy.
Even the nature of winning has changed. In the Cold War, game designers often gauged success by attrition, determining how large a force with what firepower was needed to destroy a given number of the enemy. With the relaxation of nuclear tension, military historians realized how few battles, perhaps fewer than a fifth, are actually won purely by attrition. The equations of Kriegspiel have given way to the acronyms of qualitative utility: MOEs (Measures of Effectiveness) in pursuit of an RMA (Revolution in Military Affairs). The distinction between strategy and tactics is increasingly blurred on a battlefield where every private is part of an “information battlespace.”
John Bird’s job is to make sure that war games do all they reasonably can, but no more. He is a designer and assessor (“white team,” in game jargon) for Navy, Army, and Air Force games. A civilian used to working in a charged military environment, he is a careful man, speaking with the slow, precise manner of someone whose mind has a lot of classified content. “The armed forces come up with strategic concepts or new forms of operational art; we explore them, we discover, we develop. If at the end we’ve knocked the whole idea into a cocked hat, that’s OK, too.”
Game theory still rules games, but it is a theory far removed from the certainties of von Neumann. “It’s not always zero-sum; all parties are trying to achieve what’s best according to the objectives of their own side—but that might not include foiling the other side. Politics is always part of the equation; otherwise, you lose sight of the objectives, winning the game but not the war.”
The assessor’s role splits the difference between slave of the dice and omniscient analyst: “Where small forces are important—like Special Operations—we’ll take one or two typical engagements and look at them in detail: individual lives, minute-by-minute schedules, probabilities of remaining undetected. If that gives us a clear picture, we can aggregate data for the other operations. It’s like weather forecasting; if one area is critical to the whole system, you look at it in greater detail. The results are generated using techniques like Monte Carlo analysis and then combined, throwing out the random outliers—which means we’re assuming the enemy will do the smart but not necessarily the brilliant thing. In a sense, it’s a kind of Bayesian approach: if something comes out against expectations, if it contradicts accepted wisdom, then it’s worth studying further.”
How close can the model be to real life? “Low-intensity warfare is hard to model; urban warfare is hard. And then you have psychological forces—we have a hell of a lot of difficulty with that, and not just in gaming. In the Iraq war, the U.S. ran a psychological operation to try and get enemy troops to desert. We had some experience with this and some ideas about how it would work. Well, it was effective: we had a desirable outcome in that we reduced the probability of combat between major units—but we had the undesirable outcome of a bunch of armed guys heading back into the population where we couldn’t find them. In game design, you’d say we suboptimized the desired outcome.
“It’s hard to quantify exactly what the military does. You want the opponent to give up—but what does ‘give up’ mean? Unconditional surrender, change of regime, cease fighting, stop invading neighbors? Every country has a different relationship between its population, its government, and its armed forces; as you go into it, you may find that psychological parameters change in a way that improves your probability of success—but what success, exactly?”
We may never know to what degree simulation influenced the conduct of the Cold War; certainly, as the rivalry wore on, pure game theory played less and less of a part. Instead, the Cold War, in its purely military aspect, was eventually won not by military skill or strategy but by expenditure. The total cost to the United States of its nuclear deterrent over the forty years of tension had been nearly $5.5 trillion—a burden, but one easily borne by the richest nation on earth. The Soviet Union simply could not match that effort, ruble for dollar, over so many years. The true model for victory proved to be none of the clever strategies developed at RAND, but rather something that dated back to the Bernoullis: Gambler’s Ruin, the discovery that in a game of matched bets, the deeper pocket always wins.
Charles Kinglake, chronicler of the Crimean campaign, said: “The genius of war abhors uniformity, and tramples upon forms and regulations.” Yet the civilian eye sees forms and regulations as the stuff of military life. All conflict is ultimately conventional, not just for convenience but because victory is so difficult to define. How, then, should the successful commander behave—as a rational player or as the genius of war?
Millennium Challenge ’02 was a $250 million joint forces ex
ercise, one of the most elaborate ever undertaken. The scenario involved a U.S. action to neutralize a rogue military strongman in the Persian Gulf area—someone not entirely fictional. The Joint Forces Command, anxious to measure American capabilities against a worthy adversary, brought in retired Marine Lt. General Paul van Riper to lead the opposition. A decorated combat veteran, ex-Commanding General of the Combat Development Command, he is known for his aggressive and unconventional thinking.
Van Riper took to his role with evident gusto: knowing his radio traffic would be insecure, he sent orders by motorcycle to be broadcast as part of the evening call to prayer. He set his air force and navy circling, apparently aimlessly, in the sea approaches to his unnamed country—but when the invasion fleet concentrated in one spot, his forces suddenly swooped in a precoordinated attack, and sank it. The ships had to be “refloated” for the exercise to continue. But by the end of the first week, van Riper says, he found his orders were being countermanded: “Instead of a free-play, two-sided game as the Joint Forces commander advertised it was going to be, it simply became a scripted exercise. They had a predetermined end, and they scripted the exercise to that end.”
The Joint Forces Command countered, perhaps reasonably, that the point of an exercise is to test untried systems and concepts; if an opponent exploits loopholes in the rules to gain an advantage, this negates the wider purpose; it becomes a matter of winning the game, not winning the next war. Van Riper, though, would have none of this: “You don’t come to a conclusion beforehand and then work your way to that conclusion. You see how the thing plays out”—including, presumably, how it plays out against someone whose game is very different from yours. It was a new example of the old problem: what if the enemy doesn’t agree with your definition of victory?
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