Friday, February 19, 2016

A little advantage is better than none

kw: book reviews, nonfiction, decision theory, advice

It's time to decide who's paying for lunch. Flip a coin? The "I flip-you call" method is probably about as fair as possible. "I flip-I call" is a setup for a two-headed coin. But what about Roshambo (also Rochambeau), or Rock-Paper-Scissors? Here we go, 1-2-3, what do you throw?

[For those who don't know, Roshambo is done in pairs. Each person waves a closed fist two times and then on the third time does one of three things. Rock is keeping a closed fist, Paper is opening the hand fully, and Scissors is opening only the index and middle finger in a narrow "V". Rock breaks Scissors, Scissors cut Paper, and Paper covers Rock. If both person throws the same, you repeat. Each "throw" can beat one of the others, and loses to the other, so there is no guaranteed winner for any throw.]

According to research (yes there is, lots of it!) cited by William Poundstone, if you're male, you'll probably throw Rock first, and if you're female, probably Scissors. Psychologically, the Rock is more macho, while Scissors is more the female's weapon in preference to rocks and other bludgeons. Knowing this, if you are "playing" against a man, choose Paper, otherwise, choose Rock.

But of course it is not so totally simple. Lots of folks prefer a "2 throws out of 3" game. You also repeat the process when there is a tie. The psychology of successive throws is a lot like the psychology of successive pitches by a baseball pitcher. A lot depends on how well the other folks know you. Suppose you throw the same thing the first two times. If you don't win in the first two throws (and aren't already "out"), is it better to throw the same, or a different choice? The best advice is, do whatever you aren't known for doing. With someone who doesn't know you, go ahead with the same choice a third time in a row. It is least expected!

Little things like this, that gain little advantages on average, inform the second chapter of Rock Breaks Scissors: A Practical Guide to Outguessing & Outwitting Almost Everybody, by William Poundstone. Part One of the book shows a dozen ways to take advantage of the fact that humans are very bad at doing anything randomly, and equally bad at distinguishing genuinely random sequences from "random looking" sequences that are actually patterned. Part Two takes on Hot Hand Theory, the notion that a series of "wins" is more likely to continue when skill is involved, such as successive baskets at the free throw line. Its converse, the Gambler's Fallacy, is the notion that a series of wins or losses is more likely to be "balanced" by the opposite happening next, whenever human agency is not involved, such as in spins of a fair Roulette wheel.

It is interesting. When we want to be random, we can't. When we want to prolong a chain of successes, we have no guarantee that we can! Here is a string of light and dark blocks. Is it random?


It really isn't. Compared to a truly random sequence, it alternates too often and the length of the "runs" is too short. What about this one?


This has fewer alternations, and longer runs. It is from a random sequence of numbers, with darker chosen for numbers in the smaller half of the range, and lighter for the rest.

People given a series of five of these colored blocks, and asked to choose a sixth "at random", usually choose a lot less randomly than they'd like. If the string of five is ░█░█░, for example, some folks will say it "doesn't look random enough", but that if they must, they'll follow with a light box; others just glance over and also add a light box. Hardly anyone chooses dark as the more "random", and it isn't. Both dark and light are equally "random"! It doesn't matter what is in the first five boxes. If people are shown string of five that are all light, most will choose a black box, even though, again, the chance of light or dark is 50%.

Flip a coin six times. Write down the sequence, perhaps HTHHTT. How likely is it that you will flip six heads in a row? Once in how many sets of six throws? Did you say 100? or 1,000? The true odds are that you'll toss six heads in a row once in 64 sets, on average. But there is no saying that, the first or second time you make six tosses, you won't get six in a row. Just that if you do sets of six throws hundreds of times (it takes patience!), about 1/64th of them will be six heads. This chart illustrates the number of times each possible set of six throws occurred in 6,400 sets of six, calculated using the RAND function in Excel. Two total groups of 6,400 sets are shown:

If all 64 outcomes were equally likely, we would expect 100 of each. These are all near 100 occurrences each, but note how they nearly all cluster in a range from about 80 to about 120. If I'd used 64,000 rather than 6,400, the spread would be less, about one-third the proportional range, with about 1,000 occurrences of each outcome, nearly all contained in a range from 930 to 1,070.

Chapter after chapter of Part One shows how to take advantage of others' inability to guess randomly. Making play-by-play bets (or challenges with no money changing hands) in Football, for example, the author recommends, "…expect the opposite type of play (running or passing) next time, especially when the current play fizzled or was repeated twice in a row." (p. 86). Yet, since the coach on the opposing team is probably making the same estimation, the more winning strategy for the team is to make the SAME play about half the time, even if it just fizzled or would be a third-in-a-row play.

In the chapter "How to Outguess Passwords", after a discussion of how hard it is to pick and remember a truly random password, the author suggests, more slyly, for us to do the unexpected. We know that password-cracking hardware is able to try tens of billions of combinations per second, when calculating every possible encrypted password in a stolen .pwd file. Thus, a long password is better because lots of characters means the "cracker" will have to try many more combinations. How many? If you're allowed to use a very long password, but one you can easily type, you might get away with text only. For example, the string "strangerinparadise" has 18 letters. There are 26-to-the-18th power possible strings of 18 lower-case letters, or 30 trillion trillion. But most banks and online shops will require you to use "at least 8 characters, with at least one upper and one lower case letter, and at least one number". Now, if you meet this minimum requirement, the total number of combinations is at worst 26-to-the-sixth times 52 times 62, or almost exactly one trillion. A hardware cracking machine that can try 100 billion per second would figure that out in 10 seconds. Add a ninth character, and mix-n-match your string better, and the number of combinations is at least 62-to-the-8th, or more than 200 trillion. Few hackers are willing to wait the the half hour it would take to crack this one. The author's suggestions are useful, and I'll leave the rest for your own reading.

I turn instead to "Hot Hand". There are several folkloric explanations for "streaks". None can explain the fact that, when a series of, for example, free throws are analyzed for randomness as compared to some kind of "streakiness", they always are seen to be random. Random series include many short streaks, fewer streaks of medium length, and smaller numbers of longer streaks, both "good" and "bad". A professional basketball player who hits only half of his or her free throws is considered rather mediocre. Particularly when some players seem to score 90% of theirs. But statistical analysis shows that a streak of any particular length is half as likely as a streak of one "hit" shorter, for a shooter who scores 50% of the time. A shooter whose long-term average is 70% at the free throw line will frequently score five or six times in a row, and there is nothing "hot" about it. It is just, if the last four throws scored, there is still a 70% chance that the next throw will also score.

All this means that people are bad at recognizing randomness, and you can take advantage of that. There is even a long discussion in the last chapter about getting an edge on the stock market. The stock market is considered random, and it is in the sense that trade-to-trade or even day-to-day motions of a stock's price are not correlated at all. For example, if you record a stock's price at every day's close for a year or two, then determine the percent change from day to day, you can plot them with an offset of one day to see if there is any pattern. There is not. The result is a dot cloud that very symmetrically surrounds the (0,0) point. But in the long term, the profitability of a company, or better yet, the aggregate profitability of companies in, for example, the S&P 500 Index, shows long term trends. The author shows how to use a particular 10-year trend statistic that provides a Buy or Sell signal for a 500 Index fund, and it mainly allows you to avoid catastrophic bear markets. Beating the Index by just a couple of percentage points can be very beneficial to your 401-K bottom line.

This was certainly a fun book to read. Even more, it helps to gain more insight into the way most people think. The more the behavior of others can be anticipated, the more likely we are to gain an advantage. One might think from the title that "outguessing and outwitting" others could be a malicious pursuit. Con artists do use similar tricks, to our detriment. But the behavioral learnings in this book are quite benign. While some of them (consistently winning an office betting pool is an example) might cause you to lose a friend or two, they are generally a way to stay on top of things, rather than a way to put others down.

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