CLOSE

Games and Their Overvalued Points

Carl Bialik of the Wall Street Journal brings us a smart article on overvalued points in games. In short, the issue is that rule changes in games like Scrabble (allowing new words like "qi" and "za") allow players a new way to exploit the system, throwing it out of balance. Some high-level players argue that when a rule change allows in new high-value type of play (like "za"), the overall scoring system needs to change to account for it, rebalancing the game. Others disagree, seeing the rule change as a simple evolution of the game's already-complex rules. From Bialik's piece:

For some -- especially opponents -- "za" is too cheap and easy. The New Yorker recently published a letter from Matthew Butterick, a Los Angeles lawyer and Scrabble player, bemoaning the preservation of the original tile values as long as the new words are being added. He acknowledges changing the rules might hurt his won-loss record: "I realized that fewer people wanted to play me because I like to use words like 'xi' and 'xu,' which most casual players consider to be a form of black magic."

Larry Sherman, who has been ranked as high as 35th by the National Scrabble Association, also would like to see score changes. "X, Q, Z and J were originally assigned high values because of their rarity in our language," Mr. Sherman says. "Dictionary additions that make it much easier to use these letters contradict the game's internal logic."

But his brother Joel, a former champion, responds, "Good players adapt their play to the changes in the dictionary; changing the values only accommodates weak players."

The argument of those wanting to rebalance the tile scores seems to hinge on an assumption that the original game (in this case, Scrabble) was perfectly balanced -- meaning that the letter scores and the allowed word list were somehow in perfect harmony. As a nonprofessional (and indeed, sort of bad) Scrabble player myself, this seems unlikely -- the official Scrabble word list (see SOWPODS) is huge, and its relationship with the tile scores is unimaginably complex. Letting in new words undoubtedly changes the balance in some way, but it seems that only the highest-level professional players will ever notice...and haven't they already benefited from such imbalances throughout the game's history? Bialik points out that this problem is not isolated to Scrabble:

For amateurs, these are hard points to come by. But as professional kickers have specialized and improved their technique, field goals have become more common. National Football League teams last season made nearly 85% of field goals, compared with barely 60% in 1974, according to Brian Burke of Advanced NFL Stats. There were two successful field goals for every three touchdowns last season, compared with barely two for every five touchdowns in 1974.

Read the article for a nice overview of the issue, including an image showing Alfred Butts's original letter frequency tabulation.

(Photo courtesy of Flickr user garlandcannon, used under Creative Commons license.)

nextArticle.image_alt|e
iStock
arrow
fun
No One Can Figure Out This Second Grade Math Problem
iStock
iStock

Angie Werner got a lot more than she bargained for on January 24, when she sat down to help her 8-year-old daughter, Ayla, with her math homework. As Pop Sugar reports, the confusion began when they got to the following word problem:

“There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?”

Many people misread the problem and thought it was a trick question: if there are 36 more small dogs and the question is how many small dogs are competing, then maybe the answer is 36?

Wrong!

Frustrated by the confusing problem, Angie took to a private Facebook group to ask fellow moms to weigh in on the question, which led to even more confusion, including whether medium-sized dogs should somehow be accounted for. (No, they shouldn’t.) Another mom chimed in with an answer that she thought settled the debate:

"Y'all. A mom above figured it out. We were all wrong. If there is a total of 49 dogs and 36 of them are small dogs then there are 13 large dogs. That means 36 small dogs subtracted by 13 large dogs then there are 23 more small dogs than large dogs. 36-13=23. BOOM!!! WOW! Anyone saying there's half and medium dogs tho just no!"

It was a nice try, but incorrect. A few others came up with 42.5 dogs as the answer, with one woman explaining her method as follows: "49-36=13. 13/2=6.5. 36+6.5=42.5. That's how I did it in my head. Is that the right way to do it? Lol I haven't done math like this since I was in school!"

Though commenters understandably took issue with the .5 part of the answer—an 8-year-old is expected to calculate for a half-dog? What kind of dog show is this?—when Ayla’s teacher heard about the growing debate, she chimed in to confirm that 42.5 is indeed the answer, but that the blame in the confusion rested with the school. "The district worded it wrong,” said Angie. “The answer would be 42.5, though, if done at an age appropriate grade."

Want to try another internet-baffling riddle?


Here's the answer.

[h/t: Pop Sugar]

nextArticle.image_alt|e
iStock
arrow
fun
If You Can Solve This Math Puzzle, You Might Be a Genius
iStock
iStock

by Reader's Digest Editors

Do you think of yourself as a secret mathematician? This math brainteaser has even the biggest number nerds scratching their heads.

People’s Daily, China tweeted out this math puzzle in which each picture represents a number.

These algebra problems might seem easy at first glance, but hold on. People’s Daily was nice enough to give away the answer before you began. If you didn’t get 16, you did something wrong. Take a closer look at the pictures—you probably missed a few key details.

Still stumped? We’ll walk you through it. For the sake of the explanation, we’ll call the shoes S, the cat C, and the whistle W.

The first equation sets up the whole math puzzle. Three pairs of shoes added together equal thirty. S + S + S = 30, so divide 30 by three. Each pair of sneakers represents the number 10. Easy enough.

 
See Also...

The Town Located at the Center of North America Has the Absolute Perfect Name
*
Take a Sneak Peek Inside Largest Starbucks Store in the World
*
Why Airlines Don't Tell You How Long Flights Really Are
 

Now the second equation is clearer. Sub the shoes out for a 10, and you’ll find out 10 + C + C = 20. Subtract 10 from each side, so C + C = 10. Each cat must represent the number 5.

Look closely at the next equation before you jump into it. In the third equation, there are two whistles in each line, but the final one only has one whistle. So 5 + 2W + 2W = 13. If 4W = 8, then each whistle represents the number 2.

OK, so that clears up a bit of the next equation—until you plug the numbers in. Sub S + C x W for 10 + 5 x 2. Remember your order of operations? Multiply first, then add. So 10 + 10 = 20. What went wrong?

The key is in the cat’s clothes. In the second and third equations, the cat has a whistle around its neck—but not in the last one.

No need to go back and redo all your hard work. Just change the last equation to S + (C – W) x W. Now plug the numbers in: 10 + (5 – 2) x 2. Work your way through it. The equation goes to 10 + (3) x 2, then 10 + 6. Finally, you get 16—problem solved!

SECTIONS

arrow
LIVE SMARTER
More from mental floss studios