© 2011 Harvey Gillis What do you do when you have a lot at stake and your choices are complicated or unclear? Ordinarily, your goal is to maximize a profit or minimize a cost or elapsed time — for example, when you try to select the best route to drive to a destination for something of significant consequence.
The simplest decisions of this kind are called “deterministic,” because they do not include the uncertainty of unknown factors like traffic, actions of opponents, weather, dice, dealt cards, economic issues. An example would be the problem of getting a patient to a hospital where the shortest route involves some traffic lights. A longer route (without the lights) may be more predictable. If your passenger is losing blood, how should you trade off the shorter distance against the possibility of a long delay when it is too late to call 911?
Let’s complicate our decision. What if we have someone that wants to prevent our reaching the hospital? Now we have to take into account what our adversary may do before we make our decision, or, in a more convoluted circumstance, what our adversary may do as a result of our decisions. This is real-time action, just as it occurs in sports, war, head-on business clashes, or board game tournaments. There is no time to use fancy computer models or theoretical decision platforms like game theory. These rapid-fire selections could involve outcomes with grave consequences or mortality! And to make things even more obscure, what if there is a major factor involved that is rather unpredictable, like traffic, weather, dice, emotions, or technology? The introduction of such probabilistic (or stochastic) factors makes these decisions incredibly vexing.
Just imagine if Germany, in WWII, had not made the decision to invade Russia during winter or the United States had not been the first to develop the atomic bomb? What if Khrushchev had not pulled the USSR’s ballistic weapons out of Cuba? Imagine if Apple had not embarked on a strategy to invent a disruptive product to download music or roam the Internet? And what would have happened if the politicians had not bailed out Wall Street on the heels of their own poor decisions to make non-documented mortgages of questionable quality prior to 2008? For something closer to home, what if you had bought stock in Google rather than Washington Mutual several years back? Is there a way to clear some of the smoke for decisions that involve a myriad of choices in an uncertain environment complicated by an opponent that is concurrently making his/her own decisions?
Before you rush off for an aspirin, let me assure you that a methodology exists for evaluating decisions of this kind; but it requires some ingenuity and discipline. It has different names in various contexts. In business, it is often called risk/reward, benefit/cost, sensitivity or boundary analysis. Some people refer to it as “what if” analysis. In medicine or war, it may be categorized as scenario analysis or contingency planning. For our purposes, we will call it upside/downside analysis. What is involved, under any name, is a disciplined process of constructing the possibilities of potential outcomes (combinations of the roll of the dice and decisions by our opponents), the upside/downside of our decision for both of the combatants involved, and the discovery of what improbable occurrence may destroy you or your adversary. Before we become too arcane, let’s provide a framework for the “science” that will help us make these life-determining decisions.
What we want to construct is a methodology by which we maximize the range of beneficial outcomes for ourselves; protect ourselves from catastrophic outcomes; and make life as treacherous and miserable for our enemy as possible. “Fancy pants” mathematicians known as “game theorists” (I must admit that I am one) call this strategy determining technique, “MiniMax.” Its mathematical intent is to minimize the chances of your worst outcomes while maximizing the chances of your minimum gains. Hence, the technique was termed MiniMax. In baseball, for example, your best course of action is generally to go for singles, doubles, or sacrificed flies or bunts rather than swinging for home runs, as long as you are not overly timid or conservative when opportunities present themselves, or, far behind in the score. Conversely, Indiana University scientist and backgammon player Chuck Bower helped design a computer model for football that shows it can often be worthwhile going for it on fourth down at mid-field even when there is plenty of time left in the game! Backgammon, by its very strategic nature and the uncertainty of two dice, exquisitely reflects this decision analysis methodology.
Backgammon is a board game that captures the very essence of making choices from a strategy point of view and manifests the crucial elements of what makes a great game: easy to learn, but difficult to master. Backgammon has rich analogies to many real-life choices and decisions which make it a tremendously productive vehicle for learning upside/downside analysis skills while providing an exciting opportunity to enjoy some character-building jousting. So, let’s develop our upside/downside analysis talents while learning how the mastery of backgammon transfers to other valuable life skills as well. Backgammon is a strategy, analytical territorial game where you engage your opponent in combat as you attempt to move your “men” past his/her men, after which the first person to bear their men all off of the board wins that specific game for the points at stake (one point at the beginning of each game). The game is realistically made more complicated and exciting with a doubling cube (every “raise” in ante is a double of the amount of prior point(s) that were at stake) and with the rule that a roll of the two dice that results in doubled numbers (e.g., 66, 55, 44, 33, 22, & 11 – a roll of two dice x and y are designated as “xy”) is taken twice by the person that rolled the double.
A Backgammon “match” consists of a series of games to a set number of points, for example nine. The games are played by engaging your opponent in a territory where one route to a game win is achieved by maneuvering your “men”(each side has fifteen) past his/her men and then over your goal line before your opponent does it to you. Another route to winning a game is to achieve a commanding position, offering your opponent a “Double” – the opportunity to resign the game and lose the point value of the game or play on and risk losing double the initial game point value or more.
Interaction and conflicts arise as an outcome of navigating your men through the territories. You decide within the confines of the dice that you roll, meaning the distance you are compelled to travel, and the limitations imposed by the forces marshaled against you, where you end up after each move.
“Land” which neither side is in possession of at the outset is up for grabs, subject to being possessed, either temporarily, or more permanently. Two or more men are needed on any given piece of land to own that “point” and to avoid the risk of being displaced when the other side is within striking distance. Displaced men are sent back to the very beginning point of their territory to move forward from there.
Each move constitutes one side’s playing out of its Game Plan (“GP”). Game Plan choices are complex, often needing to consider both strategic and tactical components that apply to both sides. The common threads that connect choices made in backgammon are score, timing, race and positional features. Typically, the decision making process compares candidate plays from the perspective of their upside/downside. For example, you may need to choose between taking possession of a valuable piece of land and sending an opponent back to the starting gate. If you decide on sending your opponent back you risk having the land you could have possessed co-opted by your opponent, or left without occupancy. Such an occurrence would increase the danger of an assault on your men, by lengthening their path to safety. Determining quantitative estimates of such potential positive and negative outcomes is the kind of challenge the game poses. An excellent introductory book is Paul Magriel’s, Backgammon. This entertaining text takes you to advance concepts and principles in just one quick read.
Essentially, you must first categorize the possible outcomes (roll of dice or competitor’s choices) for every type of choice you have to make and mentally simulate a truncated summary of the ramifications. This involves a number of steps to complete an upside/downside analysis,
1) First of all, what is the nature of your and your opponent’s game given the current scorecard and board (i.e., battlefield) position? In sports, war, business or medicine, you would also have to take into account the amount of time remaining. The scorecard matters because of the desirability of your decisions changes if you are close to a determining victory, far behind, or neck and neck coming down the stretch (risk versus return). If you are the leading candidate for the Presidency with a few months left until the election, you should not agree to ten debates. All you would be doing is providing your adversary with multiple opportunities to change the game by delivering a knock out punch over the public media. If you are ahead in a minimal contact race, why take risk that entails the chance of contact. If you are behind, then complicate your opponent’s path by maximizing contact. When decisively behind, you have to disrupt the situation. When desperate you must take desperate steps. Once you have concluded what each of your games or needs are from a helicopter view, you can evaluate your range of options for making the game more expensive for your opponent (turn the doubling cube) and moving your men after you have rolled the dice. Remember one of Kit Woosley’s rules, every turn requires a doubling decision, no matter how obvious in its appearance.
2) Within the framework of #1 above, what are your practical options? Now it gets complicated. First of all, you need to count the good and bad roll percentages for one or two rolls of the dice, no matter who is rolling. Even for considerable upside, often you cannot flaunt your advantage by giving your enemy a measurable chance of turning the game around with a lucky, or, “Joker” roll of the dice.
3) Keep in mind, for every cube decision or move, you must keep an eye on what you have to gain and lose from an overall match point of view (“match equity”). This optimization of decisions’ impacts on the war over the battle is referred to by backgammon enthusiasts as “match equity.” It is one of the more clear elements to learn and memorize. To be a top player, you must maximize the match over the game, even when the decision is a risky one! Since human beings are involved, you may find that a worrywart will make a mistake if you throw a little aggression or risk his/her way.
4) Now you must go through the laborious practice of evaluating the outcomes, upsides, and downsides of your choices. Some players, like Neil Kazaross and Art Benjamin, do this quickly. Others, like Perry Gartner, Bob Koca and I are more deliberate and slow. Please note, however, that Bob, Perry, Neil and Art are all some of the top ranked backgammon players in the world. How and when you allocate your time can be critical for a clocked match or combat with limited time. More often than not, decision-makers rush their decisions to save time too early in a game or match. Regardless, a reasonably thorough evaluation of your options is mandatory and must be done to conclude what the best option(s) are for pursuit. Gut instinct, heuristics, or karma are rarely good substitutes for evaluative scenarios and memorization of past situations (“reference sets”) for possible implications.
5) Keep in mind the impact on, or, the reaction of your opponent from your choices. Your opponent is the human first and the dice second. You may be playing a worrier or an overly aggressive player. Also, if you have a game-changing move, do not avoid it because it has some tolerable risk. One, who takes no risk, takes the greatest risk of all especially if your chances of winning are slim to none.
6) Don’t forget to analyze the upside/downside for your opponent! Half of your job is to make his life as wretched, uncomfortable, and tormented as possible. Search for the dice number or combination of numbers that may destroy him when it is his roll. Call this brittleness or inflexibility, but it can be hidden by your focusing on your probabilities. For example you may have gotten a great roll that gains you some valuable landscape, but overlooked a move that is nearly as productive for you and destroys your opponents board (battle position) if he rolls any six! It is surprising how often a defensive position like this arises. Another example is to check doubles to see if they can produce a game-changing roll for your opponent. If it costs little to block double sixes, fives, fours or threes, give it a look-see in a close race. Similarly, look at the possibility of making a large roll of 65, 64, 63 or 54 uncomfortable.
7) Also, keep in mind the next roll. Should your strategy work or not work, what is the chance of you or your opponent forcing each other out of the game (“cashing”). This is true of any other engagement as well. If your competitor in business has a lower gross margin than yours because your costs are lower, you might want to lower prices to the point that they would lose money if they match your price drop. This becomes a Hobson’s choice between bad or worse for your competitor, losing money, or, giving up market share. The same is true of backgammon, war, or sports. In basketball, if the player you are covering cannot go left very well, then over cover him on his right, pushing his choices to his weak side. In BG, as with any other engagement, if you see an upside that will kill you if it does not work, should you risk it if your enemy can turn the game with a reasonable chance of a hit?
8) Lastly, look at your prerogatives if you do not take a risk. If you are behind your enemy’s lines (away from a five or four-point prime), you may have to move up a man to establish a path of extraction even if it means “coming under the gun,” a phrase originated by Paul Magriel.
Well, we cannot go over every element of combat or backgammon. Our purpose here was to establish the framework, concepts and ramifications of upside/downside analysis particularly, through the lens of backgammon. It can be viewed as the torture and beauty of analytical, decision-making games (e.g., see the movie, A Beautiful Mind about game theorist John Nash with the talented actors, Russell Crowe and Jennifer Connelly). In backgammon, life, medicine, war, careers, or business, the evaluative requirements are the same especially, in the face of uncertain factors. You must chart your landscape of outcomes to maximize your opportunities and minimize the chances of your opponent getting the jump on you. Backgammon is a dimensional vehicle by which to master critical decision analysis techniques in a real-world environment of uncertainty. As with any competition, contest or conflict, you want to have your adversary end up very unhappy. Therein lays the joy of intellectual combat. The thought processes that makeup backgammon decision analysis skills and techniques can make a difference in many of life’s challenges.