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.)

Honey Bees Can Understand the Concept of Zero

The concept of zero—less than one, nothing, nada—is deceptively complex. The first placeholder zero dates back to around 300 BCE, and the notion didn’t make its way to Western Europe until the 12th century. It takes children until preschool to wrap their brains around the concept. But scientists in Australia recently discovered a new animal capable of understanding zero: the honey bee. According to Vox, a new study finds that the insects can be taught the concept of nothing.

A few other animals can understand zero, according to current research. Dolphins, parrots, and monkeys can all understand the difference between something and nothing, but honey bees are the first insects proven to be able to do it.

The new study, published in the journal Science, finds that honey bees can rank quantities based on “greater than” and “less than,” and can understand that nothing is less than one.

Left: A photo of a bee choosing between images with black dots on them. Right: an illustration of a bee choosing the image with fewer dots
© Scarlett Howard & Aurore Avarguès-Weber

The researchers trained bees to identify images in the lab that showed the fewest number of elements (in this case, dots). If they chose the image with the fewest circles from a set, they received sweetened water, whereas if they chose another image, they received bitter quinine.

Once the insects got that concept down, the researchers introduced another challenge: The bees had to choose between a blank image and one with dots on it. More than 60 percent of the time, the insects were successfully able to extrapolate that if they needed to choose the fewest dots between an image with a few dots and an image with no dots at all, no dots was the correct answer. They could grasp the concept that nothing can still be a numerical quantity.

It’s not entirely surprising that bees are capable of such feats of intelligence. We already know that they can count, teach each other skills, communicate via the “waggle dance,” and think abstractly. This is just more evidence that bees are strikingly intelligent creatures, despite the fact that their insect brains look nothing like our own.

Considering how far apart bees and primates are on the evolutionary tree, and how different their brains are from ours—they have fewer than 1 million neurons, while we have about 86 billion—this finding raises a lot of new questions about the neural basis of understanding numbers, and will no doubt lead to further research on how the brain processes concepts like zero.

[h/t Vox]

Can You Solve This Ice Cream Cone Riddle?

How much is an ice cream cone worth? In this visual riddle by Budapest-based artist Gergely Dudás (who posts comics on, the answer requires a little math.

The riddle asks you to determine how much an ice cream cone, a scoop of white-colored ice cream (let’s call it vanilla), and a scoop of pink-colored ice cream (let’s call it strawberry) are worth, according to the logic of the puzzle.

Stare at the equations for a while, then scroll down for the answer.

A math riddle that asks you to figure out what numbers each ice cream cone or scoop represents
Gergely Dudás


Are you sure?

OK, let's walk through this.

Three ice cream cones multiplied together are equal to the number 27. Since 3 multiplied by 3 multiplied by 3 equals 27, each cone must be equal to 3.

Moving on to the next row, two ice cream cones each topped with a scoop of vanilla ice cream added together equal 10. So since each cone equals 3, the vanilla scoops must each equal 2. (In other words, 3 plus 3 plus 2 plus 2 equals 10.)

Now, a double scoop of vanilla on a cone plus a single scoop of strawberry on a cone equals 11. So if a double-scoop of vanilla equals 4 (2 plus 2) and each cone is equal to 3, the strawberry scoop must equal 1. (Because 4 plus 6 equals 10, plus 1 for the strawberry scoop equals 11.)

And finally, one vanilla scoop on a cone, plus one empty cone, plus a double-scoop of strawberry and a single scoop of vanilla on a cone, all together equals 15. One scoop of vanilla on a cone is equal to 5 (2 plus 3), and an empty cone is equal to 3. Two strawberry scoops plus one vanilla scoop plus one cone can be calculated as 1 plus 1 plus 2 plus 3 (which comes out to 7). So together, one vanilla scoop (5) plus one cone (3) plus a triple scoop with two strawberries and one vanilla on a cone (7) equals 15.

And there you have it.

A cartoon-style legend that shows that one cone equals 3, one white scoop equals 2, and one pink scoop equals 1.
Gergely Dudás

If frozen dairy-themed challenges are your thing, he also has a hidden image puzzle that challenges you to find the lollipop in a field of ice cream cones. Check out more of his work on his website and Facebook.


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