How To Win Games And Beat People Part 2

"It was Jeff Murphy." Murphy is head of surveillance at Cosmopolitan. "I answered and said, 'How the heck did you know I was here?'?" Already, he would soon learn, in Murphy's office they had taken a screengrab of the CCTV footage of his arrival, printed it out, and written "Public Enemy Number One" beneath it.

Murphy knew it was Mike for the same reason that every casino in the US knows when Mike walks in. Mike is probably the most famous card counter in the world, and if casino surveillance guards- the shadowy security teams hiding behind their CCTV cameras and two-way mirrors-have any purpose at all, it is to make sure that he never again gets to sit at their blackjack tables. That does not stop him from training other people, though."It's the only casino game you play against the house which has a true element of skill," he says.

"The reason why, is that what happened in the past has an impact on current probability." In a typical blackjack game, the dealer uses six packs-312 cards-shuffled together. This means the probability of getting a king, say, may start off as 24 in 312, but if half the cards are gone and no kings have emerged, that probability doubles. "Ninety-nine percent of blackjack players have no idea what the odds are at any point in time," says Mike. "Card counting is a means of knowing where you stand at all times."

These days Mike provides blackjack tuition. In the past, though, he was head of the Ma.s.sachusetts Inst.i.tute of Technology blackjack team. For two glorious decades in the 1980s and '90s, this team of mathematicians and scientists took most of the casinos in America for all they were worth. Their secret? "We were not gamblers."

Before joining the MIT team, Mike had never played blackjack. "Why would I gamble? Why play a losing proposition? Gamblers are not rational." His only understanding of card counting came from the film Rain Man, in which an autistic man wins in Vegas by recalling all previously played cards.

"I thought you had to have a photographic memory." He would learn it was far simpler.

Before that, though, the first thing members of the MIT blackjack team were taught was not how to count cards, but what is known as "basic strategy" (see diagram on page 60). This is the set of optimal rules for how to play in whatever situation presents itself. It tells players when they should stick with the cards they have, fold to get another, or-a more advanced technique-split equal cards into two hands.

"The reason basic strategy is so important is that it reduces the house edge compared to the average player by about 75 to 80 percent." The house edge is the expected casino winnings for each hand. In blackjack a crucial factor of the game is that the dealer only plays after everyone else has been dealt all their cards. If the player goes bust, he or she loses-even if the dealer also subsequently goes bust. "That means that for most players, including professional card counters, you will never win more hands than the dealer."Learning basic strategy means that for a typical player the house edge drops from 2 percent to 0.5 percent. With the addition of card counting, in blackjack-uniquely among casino games-the advantage goes the other way. The dealer might still win more games, but card counting tells you which ones those are likely to be, enabling you to bet big on the others.

Unlike the scene depicted in Rain Man, the technique does not involve memorizing each card; it simply involves keeping a rough idea of how many high cards remain. The more high cards there are as a proportion in the pack, the greater the chance of getting blackjack-an ace and a high card- which pays out extra. Since the dealer is obligated to fold with any hand below 17, more high cards left also mean that he or she is more likely to go bust.

Strategies for card counting vary (see the following page), but typically the player keeps a running total, subtracting 1 for every high card dealt, adding 1 for every low card, and keeping the total the same for a 7, 8, or 9. When the total exceeds a certain number-10, say-that implies a lot of high cards are left and the house no longer has the edge. That is when Mike Aponte would bet high. Until, of course, he got banned from every casino in the US.

BASIC STRATEGYCARD COUNTING.

For every card dealt that is of value 2 to 6, add 1.

For every card of value 10 or a picture card, subtract 1.

The resulting total, which you add and subtract from throughout a game, is called the running count.

The importance of the running count value depends on how many cards are left to be dealt.

Therefore, you can divide the running count by an estimate of the total number of decks left to give the true count. A high true count indicates you are more likely to receive cards of value 10. This means the dealer, who sticks only on 17 or above-whereas you can choose to stick below that-is more likely to go bust. It also means the player is more likely to get blackjack (ace and 10), which pays out at a higher return.SCRABBLEWHAT'S IT ALL ABOUT?

Do you know your zo from your za, your yo from your ya? Then you are already ahead of the casual Scrabble player, who might call "fy!" or utter an "od" at their bo's use of esoteric two-letter words.

HOW DO YOU PLAY?.

Scrabble is about words in the same way that stamp collecting is about delivering mail-in other words, it isn't. Forget about making pretty words, start looking for ways to get a Q on a triple letter score.

HOW DOES IT END?.

With a polite impa.s.se (11 points, plus 50 for using all seven tiles) about whether or not od is a word, precipitating a somewhat socially strained visit to the bookshelf for a dictionary, which is then slammed shut with a "Fine, tell me what it means then." The answer, not that it matters, is: "a hypothetical and omnipresent natural force."

a.n.a.lYSIS.

There are two answers that Brett Smitheram gives when he is asked how he got into Scrabble. The first is that it was because of the "love of language." The second is that the Under 16 national champion at the time "was my nemesis. I really hated him. I thought that the best way to get at him was to be better at the thing he was best at, and really p.i.s.s him off."

There can be few better ill.u.s.trations of the sort of strategic thinking and dedication that has made Brett one of the finest Scrabble players in the world-or of the contradiction at the heart of the game.

For some, Scrabble is a pleasant word game, a gently taxing way to end an evening with friends and family. For others, it is a game of tactics and mathematics in which words are simply a tool-a tool that can be applied without any knowledge of their actual meaning.

"When you play Scrabble with linguists they get caught up in the loveliness of the words," says Brett. As far as he is concerned, this is like enjoying the aesthetic sweep of a Samurai sword when your opponent has an Uzi. "You might be able to play, say, disjaskit and have a 5 percent chance of winning, or kid and have a 100 percent chance. I would always play kid, but I've seen it time andtime again, people play the nice word and get stuck and don't a.n.a.lyze the strategy." For Brett it is not just about the word, or even the score he can get from the word, but what effect playing that word will have on the board, on his opponent's next available moves and on his next available moves.

Before you can learn all that, though, you need the basics. "Everyone starts by learning the two- letter words." These enable "parallel play," meaning that you can have a word going horizontally that also adjoins several letters vertically along its length to make a whole series of words. The next step, says Brett, is to notice how the board works. "Premium squares are generally four or five places apart. So make sure you are stronger in four- or five-letter words, then you can reach from a triple- letter score, say, to a double word." He trains by using computer programs that generate words in the order of their probability of appearing in Scrabble tiles, and learning them.

"My third piece of advice would be to understand the relative value of tiles. Blanks are not worth anything, but are the most prized tiles in the set. You shouldn't really play a blank for less than 50 points. Similarly, S is only worth one point, but simply by using it for pluralization you maximize the chances of a seven-letter word." If those tiles are underappreciated, with others the reverse is true.

"Q is a cla.s.sic example. A lot of players will hold on to it waiting for a U-thinking it is worth lots of points. The problem is, when you are finally able to play it the opponent has been scoring 30 or 40 points every go and you've been hampered by only having six usable tiles. Usually, unless there's something on the immediate horizon, it's best to get rid of it." In most cases, by "getting rid of it" he means just playing it alongside, say, an "i" to spell "qi" for 11 points. Sometimes it is worth actually losing a go to change tiles, though.

"W and U-those two tiles together are appalling. The worst three-tile combination is v, u, w."

Although those three are so bad together that every serious player has learned the strategies to use them. "Vrouw (used in Afrikaans instead of Mrs., since you ask) can get rid of them all at once."

To demonstrate the power of these simple techniques, Brett was once challenged to play a game in French, with a native speaker whose vocabulary vastly exceeded his own. Importantly, though, Brett ensured that his vocabulary in very specific areas was superior.

"Beforehand I learned the French two-letter words, and the highest-probability seven-letter word -which also makes four anagrams." This word is aligote. "I spent the whole game playing two-letter words and waiting to play this word."

He won, naturally, and afterward his enraged opponent stole the book he was using to practice.

Such reactions are common. He doesn't play against non-tournament-level players these days, because they "become too despondent." When he plays online, he says people often call him names and accuse him of cheating. "I always say, if you go out for a race with Mo Farah you wouldn't expect to win. So why do you with me?

"People lack an awareness of their capability when it comes to language; people think they are alot better at it than they are. This causes a lot of rage, not just online but around the kitchen table. I've lost count of the amount of times I've heard people have fallen out with their granny because of a dispute over whether something is a word."

And what of his nemesis, how did it go with him? Was there a rapprochement? "He beat me the first time, then I won all the games after that and he gave up Scrabble. It was a victory in every possible sense." Among Scrabble players, that counts as a heartwarming tale.

See a list of two-letter words in Appendix 2 at the back of this book.THUMB WRESTLINGWHAT'S IT ALL ABOUT?

Float like a b.u.t.terfly, sting like a bee; the thumb can't hook if the knuckle stays free.

HOW DO YOU PLAY?.

First, lock fingers. Then position your thumb in front of your opponent's and let the two thumbs face off, impa.s.sively, like Mayweather and Pacquiao squaring up at a weigh-in. Would that pair be man enough for what follows though?

HOW DOES IT END?.

While boxing is a rigidly coded contest, where the victor has to leave his opponent alone when he hits the mat, thumb wrestling has no rules. It is more like a dirty street brawl. If, admittedly, both partic.i.p.ants in the brawl have no arms, one leg, and can only hop around vigorously and then lie on top of each other.

a.n.a.lYSIS.

When grizzled veterans get together to compare war stories and reminisce about the old times, one fight is still spoken of. A clash of t.i.tans, an epic struggle between dogged technique and brute power.

Think David versus Goliath, but with bigger stakes. It was 2001, and in contention was nothing less than the annual San Francisco thumb wrestling champions.h.i.+ps.

"I only exaggerate a little," says Oscar Villalon, recalling what has become his own Rumble in the Jungle; a contest that would echo in eternity. "My opponent was maybe nine feet tall. His hand completely enveloped mine. He was blond and a huge human being-he looked like he sailed with Erik the Red."

Ordinarily, Oscar admits he would have thought it was surely the end. But, as happens with all the greatest champions, in that moment something inspired him and gave him an inner force to try and to believe he could overcome. Specifically, in this case, that "something" was alcohol. "I'd had a few beers."

"I went for him a bit like Mike Tyson. While he was whopping his baseball batsized thumbs around I was ducking and bobbing, weaving on the inside. You go for where the web of thumb begins, try to pin him there, from that knuckle back there." What you don't go for is the nail-you slip right off. "The nail is nature's linoleum."

Oscar is a three-time thumb wrestling champion. Now retired, these days he is a grandee of the sport rather than a compet.i.tor. "It's a young man's sport. By the end of a tournament your forearm is pretty numb," he says. He realized that his third t.i.tle could well be his last. "After three wins I just wanted to go out on top; the last contest was brutal, absolutely brutal."

Even if his flesh is weak, however, his tactician's brain is still as strong. Oscar has a theory: he believes thumb wrestling has a lot in common with another sport of pugilism."I don't mean in any way to diminish the sport by making this comparison, but it's pretty much about employing the tactics of boxing," he says. The sport he is concerned about diminis.h.i.+ng through this comparison, by the by, is thumb wrestling, not boxing.

In one respect, though, he maintains they are the same. "You have to take leather to give leather."

"The crux of thumb wrestling is in the counterpunch-the counterthumb. You need to set up your opponent so that he or she keeps stretching their thumb out to get you." It is when their thumb is extended, unguarded, that you strike. "If you are quicker than they are, then you get in over the top and pin."

Equally, just as a good boxer doesn't look at the opponent's gloves, so the same principle applies in thumb wrestling. "It's not about the thumb. Do. Not. Look. At. The. Thumb," he says, enunciating each word. "One of the things I do to unnerve my opponents is I look at the ceiling when I thumb wrestle. Just as in boxing, you do it by feel-you feel them out with your jabs. If you look at the thumb you will lose."

Eventually, though, you have to accept that tactics will only get you so far. For Oscar, his most fearsome opponent was arguably not the nine-foot Viking, but someone with an even more insidious advantage.

"Just occasionally you get someone with inordinately sweaty hands, and you just can't get a purchase on their skin," he says. "It is the thumb wrestling equivalent of fighting a southpaw. They have ample opportunity to get you because they can come over the top really easily-they are slick with sweat. And your hands are normal because you're a normal human being.

"Personally, I think if the sport goes big they should regulate that sort of thing. Your opponent should be forced to wear a latex glove." While that may be the goal, and we can all agree he makes a good case, even now there is yet to be a proper regulating body for thumb wrestling. So Oscar had no choice but to fight.

"It was really, really hard. It was an ugly fight. I just had to rely on technique and cussedness."

And, he admits, an occasional bending of the rules about how much you're allowed to bend your wrist. "There was maybe a little tilting of the wrist on occasion. But if the referee didn't see it, it didn't happen."Ultimately, it was the same dogged determination that won the day against his blond giant. After fifteen seconds, the fight was over. The Viking was vanquished-brain had triumphed over brawn.

Either that, or-Oscar concedes that it is an unlikely but just possible alternative-"he just didn't care that much about thumb wrestling."OPERATIONWHAT'S IT ALL ABOUT?

Cavity Sam is ill. So ill, in fact, that he needs all his organs taken out slowly, one by one. This makes him better until, eventually, he dies. Good family fun.

HOW DO YOU PLAY?.

A knowledge of anatomy sort of helps, a shaky hand definitely hinders. Just like real surgery.

HOW DOES IT END?.

Badly, if you're Sam.

a.n.a.lYSIS.

When Roger Kneebone, Professor of Surgical Education at Imperial College, sees a good surgeon in action, he says it is "like a miniature ballet. . . .?There's a kind of ch.o.r.eographic beauty to it. The most impressive surgeons are the ones with the most fluidity, who just slowly, efficiently make single movements with no apparent rush."

As with lifesaving operations, so with board-game operations. "Success in Operation-whether the board game or the real thing-is about the relation between the instrument, the hand, and the job,"

says Professor Kneebone-and that really is his name. Surgeons long ago learned that steadiness requires different grips from those we would more naturally use in our daily lives. "For really delicate work, don't hold the tool like scissors. It helps a lot to grip with your thumb and ring finger, then use your index finger for supporting it. If real exactness is required, you might even want to support with your other hand."

R. M. Kirk's canonical handbook, Basic Surgical Techniques, has other advice. "Surgeons do not usually have extraordinarily steady hands," it says, noting that what abilities they do have diminish with age. With that in mind, the handbook explains, "If you hold instruments at arm's length, the tips magnify the tremor, and anxiety exaggerates this. Do not feel embarra.s.sed. The further the distance from a firm base to the point of action, the less steady are your hands." So, instead, it advises, "Stand upright with feet apart, arms and fingers outstretched." This is, admittedly, somewhat complicated as a technique if the Operation board is on the living room floor.The next suggestions are potentially more pertinent. "Press your elbows into your sides and you should find your hands are steadier. Sit, or brace your hips against a fixture, to become even steadier.

Rest your elbows on a table; also rest the heel of your hand or your little finger on the table." Finally, it says, "If you need to carry out a smooth movement, try practising it in the air first, as a golfer does before making a stroke." Which might make you look like a total pillock, but you'll be a pillock who wins, rather than someone with dignity who loses. And if this book is about anything, it is about the willing sacrifice of dignity on the altar of victory.

It is through a combination of such techniques, says Professor Kneebone, that some surgeons manage to keep going past an age when their hands start to shake. Any other insider tips? "It's a bad idea, most surgeons agree, to have a horrible hangover."RISKWHAT'S IT ALL ABOUT?

Had human history been different-had, say, Australian aborigines developed gunpowder-this is how things would have gone: biding their time, they would have waited for Genghis to rise and fall, and Charlemagne to do his thing, then they would have struck like a whirlwind, sweeping across the steppes and up through Siberia into the US. At least, that was what happened last time you played Risk. It is, admittedly, an outcome that presumes that aborigines also developed thermal underwear and snowmobiles.

HOW DO YOU PLAY?.

Fool your opponents into thinking you are weak, as they fight with laughable futility among themselves. Then, when the time is right, your strategic might will annihilate their pathetic armies.

Except, perhaps, for a single soldier left s.h.i.+vering fearfully in Kamchatka, so you have something to toy with.

HOW DOES IT END?.

With you alone, s.h.i.+vering in Kamchatka, wondering why you insist on playing games with such s.a.d.i.s.ts.

a.n.a.lYSIS.

"Victorious warriors win first and then go to war," said Sun Tzu, "while defeated warriors go to war first then seek to win." It turns out that brutal conflict in the first millennium BC has a surprising amount of overlap with a dice-based strategy game popular with computer scientists.

Risk works as a game because the probabilities-of success, or failure-are just slightly too complex for people to understand them intuitively. And so, instead we attack while uncertain of the outcome, letting the attrition of our men decide the result. A bit like Stalingrad, but with rather more hinging on getting a six, rather less hinging on getting Tractor Factory Number Six.

Just as in real war, you can never remove the element of chance-the rainstorm that left Napoleon's Waterloo guns stuck in the mud, the little s.c.r.o.t.e of a nephew who persistently rolls just the required number-but if you understand the chances, the game suddenly becomes as predictably unpredictable as snakes and ladders.

So, on the downside, it loses all excitement; on the upside, with a little bit of patience, you win. As Rommel said, "Sweat saves blood."

What, then, are the probabilities? Dice are at the core of Risk. When an attacker meets a defender,the attacker can roll three dice (a.s.suming he or she has three armies or more), the defender two (a.s.suming he or she has two or more). The defense advantage comes from winning if two dice are tied.

With each roll there are three outcomes. 1. Two of the attacker's dice are higher than the defender's; the defender loses two armies. 2. All of the attacker's dice are lower than, or equal to, the defender's; the attacker loses two armies. 3. Both lose one army. The question is, in any given battle, who is most likely to win?

It would be easy to answer if you were just throwing two dice each and seeing who has the highest, but this situation is a little more complicated. In fact, it is almost certainly a lot more complicated than the Risk creators ever intended, involving a branch of degree-level statistics that has been in existence for only a little more than a century.

Superficially, it seems relatively simple to work out who is most likely to win a given skirmish.

Most battles that decide a game will involve the clash of big armies-in which the attacker rolls three dice against the defender's two, and you keep on rolling until one side is destroyed.

The smallest battle with equally matched armies in which you can throw this dice combination is three versus three, and the defender wins 53 percent of the time. Since any bigger clash of armies is going to involve multiples of such smaller clashes, it appears clear that the defender has the edge.

What seems clear in probability theory is not necessarily so, however. In 2003, Jason Osborne, now a professor at North Carolina State University, applied a technique known as Markov chains to look at the statistics. What he found was that the idea that defense is the best policy is an illusion. For any evenly matched conflict of more than five armies a side, the attacker has a decisive, and growing, advantage.

For Professor Osborne, the conclusion is obvious. "The chances of winning a battle are considerably more favorable for the attacker than was originally suspected. The logical recommendation is then for the attacker to be more aggressive." Of course, this is only in the aggregate. In Risk, perhaps even more than in actual war, the best guide might not be Sun Tzu but Napoleon, who said, "I have plenty of clever generals but just give me a lucky one."

Which is something to console yourself with if you still find yourself forced to defend a small patch of Siberia while your nephew sweeps across Asia like a latter-day Khan.If both the attacker and defender are rolling the maximum number of dice, the chances of both losing an army is 33.6 percent. The chances of the attacker losing two is 29.3 percent. The chances of the defender losing two, however, is a whopping 37.1 percent. This is why, ultimately, the attacker has the advantage. The only reason why smaller battles tend to favor the defender is that they have a greater chance of ending up in a two versus two situation, the one occasion when there is a significant advantage for the defender.

Probability that the attacker will win There is a reason why Britain still holds on to Gibraltar, and it is not just so that we can get photographs of monkeys sitting on pillar boxes. It is the same reason why we fought a disastrous war over Suez and an even more disastrous war over Gallipoli.

These small strips of land control the access to even bigger ones-dividing Asia and Europe, Africa and Asia, the Mediterranean and the Atlantic. Just as in real life, controlling the choke points in Risk is crucial. Even more crucial is knowing where they are.

In the same way as the map of the London Underground simplified train travel to what is necessary for efficiently getting round London, so a paper by MIT student Garrett Robinson has simplified the Risk board to what is necessary for efficiently crus.h.i.+ng your opponents. In his study, t.i.tled "The Strategy of Risk," he produced a handy diagram-in which you can quickly see, say, that with just one entry and exit point, Australia is a continental fortress, while with five, trying to hold Russia could be your undoing. Just ask Hitler.POOH STICKSWHAT'S IT ALL ABOUT?

A whimsical attempt to evoke A. A. Milne childhoods that never were, this is a game generally instigated by parents trying to show children that wholesome walks in the great outdoors can be fun- and are viewed as proof of precisely the opposite by children.

HOW DO YOU PLAY?.

Drop two sticks off a bridge and see which pa.s.ses under first. Just make sure you start at the upstream end. And that it's not a road bridge. . . .

HOW DOES IT END?.

Anticlimactically.