‘Follow the Follower’: a Lesson in Strategy from Sailboat Racing

Picture of a boat sailing.

 

Sailboat racing offers the chance to observe an interesting reversal of a “follow the leader” strategy… The leader imitates the follower even when the follower is clearly pursuing a poor strategy. Why? Because in sailboat racing (unlike ballroom dancing) close doesn’t count; only winning matters. If you have the lead, the surest way to stay ahead is to play monkey see, monkey do.

The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life

 

America’s Cup is a prestigious sailboat race, and one of the world’s oldest international sports competitions. In 1983, the American boat Liberty was leading 3-1 against the Australian Australia II, in a best-of-seven competition. Since they needed only one more victory in order to win the cup, it appeared that Liberty was ready to extend the US’s 131 years long winning streak.

Right at the start of the race, Liberty took the lead when Australia II was penalized for crossing the starting line early. The Australian skipper then attempted to catch up by sailing to the left side of the course, in hopes of catching good winds. The American skipper decided to keep his ship on the right side of the course, believing that it would have more favorable winds.

Soon after this, the wind shifted in favor of the left side of the course, leading Australia II to win the race. Following this victory, Australia II went on to win two more consecutive wins, thus winning the cup and breaking the long-standing American winning streak.

 

What should have happened

In this situation, the speed of each ship depended on the wind, and each ship’s skipper can only make an educated guess regarding which course is the best to take.

Since the Liberty was already in the lead, if it had simply imitated the strategy of the runner-up, Australia II, it would have sailed at the same rate as her, thus maintaining the initial advantage, and winning the race. Regardless of how sureLiberty‘s skipper was that his course was the better one, the smarter strategy in this case would have been to imitate his runner-up.

 

Recognizing when the strategy is applicable

“Follow the follower” is by no means a strategy that always works. In the above scenario, there are only two ‘players’, and the only thing that matters in the race is whether you win or lose. However, if these conditions were different, the strategy may have been ineffective. For example, if the race had more than two ships, and changing course was not an immediate action, so that the leading ship couldn’t always adjust to match the runner-up, then the strategy wouldn’t necessarily work. This is because each follower can take a difference course, while the leader can only commit to one of those courses.

In addition, the original scenario discussed here is a relatively clean and simple view of reality. There could have been other considerations that affected the American skipper’s decision:

  • Maybe it’s considered more prestigious to win the race by a bigger gap, and imitating the loser’s strategy can be construed as a lack of confidence.
  • Perhaps there is a high cost or risk in changing course, which could have caused the ship to lose its advantage.
  • We also don’t know how confident the American skipper was in his choice of course; it’s possible that his calculation showed a very high probability that his original course was significantly better.

While these reasons don’t negate the fact that imitating the runner up was the correct choice from a purely strategic perspective, they offer some possible explanations as to why the American skipper made the choice to maintain his course. If, for example, the benefits (in terms of prestige) that come from winning the race by a large gap were significant enough to be worth a small chance of losing, then his choice may have been smart after all. Of course, it’s also entirely possible that the choice of strategy was driven by ego, and not from careful calculation.

This illustrates an important lesson regarding the applications of game theory in real life: reality is messy. There is a reason why simplified models are preferred in game theory; the more factors you add in, the more complicated the game becomes.

 

Summary and conclusions

  • In certain cases, the best strategy for the leader is to imitate his runner-up.
  • By doing the exact same thing as his follower, the leader can win a ‘race’ by maintaining his original lead. This is true even in cases where the follower select a non-optimal course.
  • Be selective in using this strategy, as it’s only applicable in certain cases. For example, it may not be relevant when there are more than two ‘players’.
  • Once you are familiar with the strategy, the important thing is learning to recognize situations where you can implement it.
  • Ego may lead people to avoid using this strategy. Make sure to overcome this issue in yourself, and to take advantage of other people’s failure to do the same.

 

The sailboat example and the rationale behind the strategy come from “The Art of Strategy: A Game Theorist’s Guide to Success in Business and Life”. It’s a good read for someone looking to understand basic game theory and how it applies to real-life situations.

I recommend it over the earlier version of the book (“Thinking Strategically”), because that’s what the authors themselves recommend. However, the difference between the two versions isn’t too crucial.


How to Easily Improve Your Handwriting Speed

Picture of a pen resting on a notebook.

 

Handwriting is one of those skills that you generally learn as a kid, and then never try to actively improve it as you grow up. However, being able to write faster has some significant benefits, which are especially important for people who often need to write things by hand, such as university students. These benefits include:

  • Increased automaticity, which lessens the burden on working memory. This means that you don’t have to actively concentrate on the act of writing itself, and you can instead focus on thinking about what to write.
  • Improved performance on various academic tasks, and especially those that relate to composition and literacy.
  • Increased overlap between mental generation of output and text production. This means that you can write immediately as you form your thoughts, without suffering from a delay which might hinder your thought process.

Below is a collection of tips and strategies, which can help you improve your writing speed. Some of these can be implemented immediately with no effort, while others require a bit of practice. You don’t have to do everything that’s listed here. It’s fine to pick out even a single aspect that you want to focus on; you’ll still see a significant improvement in a small amount of time, and for only a minimal amount of effort.

 

Fix your technique

Good technique: Use your fingers as guides, and move the pen using the forearm and shoulder muscles. This allows you to write quickly without tiring out or getting cramps.

Bad technique: “Drawing” the letters using your fingers. Moving your wrist constantly. Repeatedly picking up your hand from the paper in order to move it across as you write. These issues slow down your writing, and cause your hands to cramp and tire out.

How to get it right: In order to get a sense of which muscles you should use, try holding your arm in front of you, while writing large letters in the air. Remember these movements, and try to implement them when you write on paper.

 

Don’t grip too tightly

People tend to this this subconsciously, especially when they try to write fast. However, this slows you down and tires your hand. Make sure to consciously remind yourself not do this, until it becomes natural.

 

Hold it whichever way is convenient

Surprisingly, your grasp (the way you hold the pen in your hand) doesn’t have much of an effect on your writing speed. Therefore, as long as you’re comfortable, you can just stick with whatever works for you. Also note that when writing for extended periods of time, it’s natural to sometimes vary the way you hold the pen, so this is not necessarily indicative of a problem. If you decide that you still want to focus on this, it’s generally advisable to go with the commonly-used dynamic tripod grip.

 

Maintain a Good Posture

Don’t slouch over the paper as you write. It puts unnecessary strain on your arm, and it’s bad for you anyway.

 

Use The Right Pen / Pencil

This one is easy to do without making any effort to change your writing technique. Things to pay attention to:

  • Pen thickness: pick a pen that isn’t so small that you end up having to squeeze it tightly. If necessary, put a small rubber grip on it. The right size obviously depends on how big your hand is, so experiment and find out what works for you.
  • Line thickness: there are advantages and disadvantages to different thicknesses (e.g. 0.5mm versus 0.9mm). Again, this is personal, so experiment and find what’s right for you.
  • Use a good-quality pen that doesn’t require you to press hard on the paper. This alone can make a huge difference, and a good pen doesn’t cost more than a few dollars, so there’s no reason why you shouldn’t just buy one.

 

Improve Your Writing Style

The best thing to do is to simplify the way you write the letters. This means that you should try to get rid of excessive marks and styling, as long as you can maintain legibility.

Regarding letter size: In theory, if you decrease the size of your letters, you need to move your arm less when you write, which should enable you to write faster. However, this is not necessarily true in practice, and reducing the letter size might end up slowing you down by making it more difficult for you to write. Since this is also something that varies from person to person, try to experiment and see what works for you.

 

Use a Shorthand Writing System

 

A sample text written in Gregg shorthand

 

Shorthand systems use simplified symbols and rules which take less time to write than regular orthography. The symbols can replace letters, common letter combinations, sounds, or frequently-used words. You can either learn an existing system, or develop your own. Commonly-used shorthand variants include Gregg, Pitman, and Teeline.

One of the ways to benefit from the use of shorthand without having to put a lot of effort into learning it, is to focus only on a small number of words which appear frequently in the language.

 

Examples of frequently-used words written in Pitman shorthand

 

Keep in mind that the more you rely on shorthand, the more difficult it is for others to decipher your notes. This can be either an advantage or a disadvantage, depending on your perspective.

 

Summary and Conclusions

  • Improving your handwriting speed can have significant benefits.
  • There are a lot of things you can do in order to write faster, such as loosening your grip, writing with your arm, and maintaining a good posture.
  • It’s not necessary to put a lot of effort into this. Even focusing on a single, minor adjustment can make a big difference.

 


Use Color Coding Techniques to Learn Vocabulary More Effectively

Color-coded words in various languages.

 

Expanding your vocabulary is an important but difficult aspect of learning a new language. One way to make it easier is through the use of color coding. This article gives you a brief explanation of why color coding is effective, and shows you how to implement it in your learning.

 

Why use color coding

In general, color-coded material is a more effective study aid than black-and-white material, because it helps learners process new information. Specifically, in the case of learning a foreign language, studies found that color coding new vocabulary words helps people learn those words better. While there are several possible theories which can be used to explain the cognitive mechanisms behind this improvement, the overall agreement is that color coding aids memorization, a fact which language learners can take advantage of.

 

How to use color coding techniques effectively

One of the main reasons why color coding techniques are so useful is that they are easy to implement in a similar way regardless of which vocabulary-learning strategy you use. There are two main things you need to consider:

  1. How to categorize the words. Essentially, according to which criteria you color the different words. Common options are grammatical gender (e.g. masculine/feminine) or part of speech (e.g. noun/verb). In languages with tonality (such as Mandarin Chinese), you can also color syllables according to their tone.
  2. Which coloring scheme to use. This is subjective, so use whichever coloring scheme makes sense for you. If possible, use colors that you would intuitively associate with the categories in some way. For example, if you color code words based on their grammatical gender, you might want to color feminine words in pink, and masculine words in blue.

 

Examples for color coding

Keep in mind that this is just a small sample of the various ways in which you can implement color coding.

 

Color coded words in French, based on grammatical gender (blue for masculine, pink for feminine).

L’enseignant fâché cuisinait dans la vieille camionnette.

The angry teacher cooked in the old van.

 

Color coded words in Spanish, based on part of speech (green for nouns, orange for adjectives, blue for verbs, and light blue for adverbs.

La madre rubia finalmente consiguió sus naves.

The blonde mother finally got her ships.

 

Color coded characters in Mandarin Chinese, based on tonality.

媽     1st tone = red

麻     2nd tone = orange

馬     3rd tone = green

罵     4th tone = blue

吗     neutral tone = black

 

Summary and Conclusions

  • Color-coding new vocabulary words makes it easier to learn them, by aiding the memorization process.
  • You can color words according to categories such as grammatical gender (e.g. masculine/feminine) or part of speech (e.g. noun/verb).
  • In some languages, you can also color other linguistic particles. For example, in Mandarin you could color syllables according to their tone.
  • Use intuitive color schemes where possible, meaning that you associate the colors with the categories that they signify.