‘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.

Just as the race started, Australia II was penalized for crossing the starting line early, which gave Liberty the lead. In an attempt to catch up, the Australian skipper decided to sail to the left side of the course, despite the fact that the wind was, at the time, more favorable on the right, in hopes that the wind would shift over time, and give him an advantage. The American skipper decided to keep his ship on the right side of the course, believing that this side would continue to offer the more favorable conditions.

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

Since each ship’s speed depends on getting good winds, the skippers both attempted to make an educated guess regarding which side of the course would have the more favorable conditions. However, while this was the smart course of action for the Australian skipper, who was the runner-up, the American skipper, who had the lead, should have simply “followed his follower”, meaning that he should have imitated the strategy of the competition that he was already beating.

Essentially, the Liberty already had the lead, if it had simply copied the strategy of the ship behind it, it would have sailed at the same rate throughout the rest of the race, thus keeping her initial advantage, and winning the race. Regardless of how sure Liberty‘s skipper was that his course was the better one, the smarter strategy in this case would have been to imitate his runner-up, which would have led to a certain victory.

 

Recognizing when the strategy is applicable

Follow the follower is a useful strategy, but one that can be applied effectively only in some cases. In the above scenario, there were only two ‘players’, and the only thing that mattered in the race that they were participating in was whether they won or lost. This meant that in this case, ‘follow the follower’ was a valid strategy, which could have helped Liberty win the race.

However, if the conditions were different, this strategy may have been ineffective. For example, because changing course cannot be performed immediately, if the race had more than two ships involved, then the leading ship couldn’t always adjust to match the runner-up without sacrificing her lead, meaning that the strategy wouldn’t necessarily be helpful in this scenario.

In addition, the scenario which was discussed here represents a somewhat simplified view of reality. This is because there could have been other considerations that affected the American skipper’s decision, such as:

  • Winning by a big lead could be considered more prestigious.
  • Imitating the loser’s strategy could be construed as a lack of confidence.
  • There could be risk involved in changing course during the race, which could have caused the ship to lose its advantage.

Keep in mind that we also don’t know how confident the American skipper was in his choice of course. Specifically, it’s possible that his calculations showed a very high probability that his original course was significantly better, which given the considerations shown above could have prompted him to maintain course rather than imitate his runner-up.

While these reasons don’t negate the fact that imitating the runner-up was the correct choice from a simple perspective of game theory, 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. At the same time, it’s also entirely possible that the choice of strategy was driven by ego or lack of strategic planning, rather than by careful consideration.

Overall, this illustrates how messy reality is, which is an important lesson to remember when considering the applications of game theory in real life. 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

  • ‘Follow the follower’ is a strategy when a leader in a competition imitates the strategy of their runner-up, in order to ensure that they maintain their original lead.
  • As long as the leader can perfectly imitate the closest runner-up, this strategy will lead to victory even if the runner-up selects a sub-optimal course of action.
  • For example, in a sailboat race with two competitors, the leading ship should always stay on the same side of the course as the ship behind it, in order to ensure that they win the race. The ship should do so even if it believes that a different course would have more favorable conditions, because by imitating their runner-ups, they ensure that they maintain their original lead until the end of the race.
  • This strategy is only applicable under certain conditions. It may not work, for example, in a race with more than two players, where there is a high cost to switching strategy in order to imitate the current runner-up, or in cases where it matters by how big of a lead the winner wins the game.
  • Even in situations where this strategy can be effective, ego and the desire to appear confident and win by a big margin could cause people to avoid using this strategy, despite the fact that it represents the best course of action.

 

The sailboat example and the rationale behind this 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.

 


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.
  • Increased overlap between the mental generation of output and the consequent production of text relating to that output. This means that you can write your thoughts down immediately as you are forming them, without suffering from a delay which hinders your thought process.
  • Improved performance in various academic tasks, and especially those that require a lot of handwriting, such as in-class essays or note-taking during lectures.

Below is a collection of tips and strategies, which can help you learn how to write faster by hand. 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 likely see a significant improvement in a small amount of time, and for only a minimal amount of effort.

 

Fix your handwriting technique

Good handwriting 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 handwriting 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 hand to tire out and cramp.

How to get your technique 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, using the guidelines for good technique which are listed above. Once you get used to these movements, try to implement them when you write on paper, while making sure to avoid the issues associated with bad handwriting technique.

 

Maintain a good posture

Don’t slouch over the paper as you write. Doing this puts unnecessary strain on your arm, which makes it more difficult to write.

To help improve your posture, you ideally want to be seated with your feet resting flat on the floor, and with your hips and lower back supported against the chair. At the same time, your knees should be flexed to approximately 90˚, and your elbows should be slightly flexed, with your forearms resting comfortably on the desk surface.

Make sure to set the height of the desk and the chair properly, as doing this encourages the use of a good posture. When the desk/chair combination is set with improper heights, you will find that it’s more difficult to maintain good posture, which hinders your writing.

 

Hold the pen whichever way is convenient for you

Surprisingly, your grasp (the way you hold the pen in your hand) doesn’t have much of an impact on your writing speed. Therefore, as long as you feel comfortable while writing, 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.

However, if the way that you naturally hold the pain is uncomfortable, and you decide you want to improve it, it’s generally advisable to go with the commonly used dynamic tripod grip, which is shown below.

 

grasping a pen using the dynamic tripod grip.
Source

 

Don’t grip the pen too hard

People tend to grip the pen too hard, especially when trying to write quickly. The problem is that doing this slows you down, and causes your hand to tire.

The best way to avoid this is to consciously check up on yourself while you write, and make sure that you’re not gripping the pen too hard; you want to hold it firmly, but without crushing it. If you consistently correct yourself, then over time, you should be able to maintain the appropriate grip strength naturally.

Note: if you find that you keep gripping the pen too hard, it’s possible that you need to get a new one, that better fits your hand. You’ll see more about this in the section below.

 

Use a good writing implement

Using a good-quality writing implement that fits your hand properly can make a huge difference in your writing, without requiring much effort on your part. There are three main things that you should pay attention to:

  • Pen thickness: pick a pen that isn’t so thin that you end up having to squeeze it tightly, or so thick that it ends up being uncomfortable to hold. If necessary, you can increase the thickness of a pen by putting a small rubber grip on it. The right size obviously depends on how big your hand is and on your personal preferences, so experiment and find out what works for you.
  • Tip size: pick a pen that has a tip size that you feel comfortable with (e.g. 0.5mm versus 0.9mm). Your preferences for this will be personal, so again, you should experiment and find out what works 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 handwriting style

You can increase your handwriting speed by making a few simple modifications to your handwriting style, and specifically by simplifying the way you write the letters. This means that you should try to get rid of excessive marks and styling, as long as omitting them has no impact on the legibility of your writing.

It’s also possible to modify the size of your letters, and in theory, if you decrease the size of your letters, you will 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 the individual letters. 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 writing systems use various symbols, which can replace letters, common letter combinations, sounds, or frequently-used words, in order to save time as you write. You can either learn an existing shorthand 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, such as ‘the’ and ‘to’.

 

Examples of frequently-used words written in Pitman shorthand

 

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

 

Summary and conclusions

  • Improving your handwriting speed can have significant benefits, such as increased automaticity, increased overlap between mental generation of output and the consequent production of text, and improved performance in academic tasks.
  • There are a lot of things you can do in order to improve your handwriting speed, and you can pick which aspects you want to work on, as each of them will lead to notable benefits by itself.
  • In terms of writing technique, make sure to use your fingers as guides, and move the pen using the forearm and shoulder muscles, while maintaining a good posture. Avoid drawing the letters with your fingers, moving your wrist constantly, repeatedly picking your hand up from the paper, gripping the pen too hard, or slouching over the paper.
  • Make sure to get a good writing implement that is convenient for you to write with, in terms of not being too thin or too thick, and in terms of having a comfortable tip size. Make sure that the pen is of high-quality, and that you don’t have to press too hard on the paper in order to write with it.
  • Finally, in order to increase your handwriting speed, you can also choose to simplify the way you write the letters, or use a shorthand writing system. The greatest benefits of using such systems comes from simplifying frequently used words (such as ‘the’), which saves you a lot of time while requiring relatively little effort.

 


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 to use color coding techniques, which can facilitate the vocabulary acquisition process.

In the following article, you will learn why color coding improves your memorization abilities, and see how you can implement it in your learning.

 

The benefits of color coding

In general, color-coded material is a more effective study aid than black-and-white material, because it helps you process new information as you’re learning it. 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 mechanisms which could explain this improvement, the overall consensus is that color coding new information increases the chances of that information being “encoded, stored, and retrieved successfully” by learners. This highlight the value of color-coding techniques, and suggests that learners can use them in order to enhance their vocabulary-learning process.

 

How to use color coding in your learning

When using color coding, there are three main factors that you need to consider:

  • How to categorize the words that you color-code. First, you need to decide according to which criteria you are going to 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.
  • Which coloring scheme to use. Once you choose based on which criteria to color-code the words, you need to decide how to color them. This can often be an arbitrary decision, 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. Another example is to use one set of similar colors for adverbs and verbs and a different set for adjectives and nouns (e.g. light/dark green and light/dark blue), in order to help you make the necessary associations.
  • How to color the words. There are various ways to do this, including writing the color-coded words in an appropriately colored font, highlighting the words in an appropriate color, and writing the words on colored sticky-notes or flashcards.

Note that you can also decide which words to color-code based on how familiar you are with them. For example, over time you might decide to only color new vocabulary words that you encounter in a text, while leaving old words that you already know in a default, neutral color (e.g. black). This could help draw attention to the new words, and might facilitate their acquisition.

 

Examples of color coding

Below are a few examples of color-coded words in various languages, which represent some of the 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-coded material is generally a more effective study aid than black-and-white material, because it improves your ability to encode, store, and retrieve the material that you’re trying to learn.
  • Language learners can use color coding in order to improve their ability to learn new vocabulary words in their target foreign language.
  • When color coding words, you first need to decide how to categorize the words; common options are grammatical gender (e.g. masculine/feminine) or part of speech (e.g. noun/verb). In some languages, you can also color other linguistic particles aside from words, as in the case of Mandarin Chinese, where you can color syllables according to their tone.
  • You also need to decide which coloring scheme to use. Try to use a scheme that involves colors that you intuitively associate with the categorization scheme that you chose. For example, if you chose to color-code words based on their grammatical gender, you might want to color masculine words in blue, and feminine words in pink.
  • The greatest advantage of color coding techniques lies in the fact that they are versatile, and can be easily implemented regardless of which vocabulary-learning strategy you decide to use overall. As such, you can integrate them into your learning in various ways, from using colored vocabulary flash cards, to highlighting, in specific colors, new words that you encounter as you read a foreign-language text.