A Relatively Modern Idea: Fairness in Dice Rolling

[Image courtesy of Larsdatter.com.]

This may come as a surprise to you, fellow puzzlers, but fairness was not always a priority when it came to rolling dice.

Nowadays, whether you’re going after that elusive Yahtzee, hoping for doubles to earn another roll in Monopoly, or trying to roll sevens in a game of craps, the basic concept behind throwing dice is that every outcome of a six-sided die has an equal chance to appear. Unless you’re dealing with loaded or gimmicked dice, your odds should be 1 in 6.

But a recent study by researchers from the American Museum of Natural History and the University of California, Davis, has revealed that fairness in dice rolling didn’t really become a concern for dice users until the Renaissance. Researchers gathered dice spanning 2000 years of human history to explore why this was the case.

[Image courtesy of Wikipedia.]

From an article on Science Alert:

Roman-era dice, the researchers found, were a mess when it came to shape. They were made from a variety of materials, such as metal, bone and clay, and no two were shaped entirely alike. Many were visibly lumpy and lopsided, with the 1 and 6 on opposite sides that were more likely to roll up.

In fact, it seems like variety was the name of the game in Roman times, since the number configurations, shape, and size were inconsistent across the board, although dice were fairly common in the time period.

[Image courtesy of Pinterest.]

The Dark Ages led to a downturn in dice frequency, as they become very rare between the years 400CE and 1100CE.

The use of dice rebounds after 1100, and are most commonly found in ancient Mesopotamia and Egypt in what is known as the primes configuration, meaning that opposite numbers add up to prime numbers. 1 pairs with 2, 3 pairs with 4, and 5 pairs with 6.

There was a reinvigorated focus on the mechanics of chance and calculating probability, thanks to names like Galileo and Pascal, as well as a spirit of greater scientific understanding overall. Those Renaissance influences led to both a standardized shape for dice and a change in the numbering system. At this point, most dice convert to the sevens configuration, where opposite sides add up to seven (1 pairs with 6, 2 pairs with 5, and 3 pairs with 4).

[Image courtesy of Smithsonian.com.]

And according to lead researcher Jelmer Eerkens, cheating may have been on the mind of manufacturers going forward. “Standardizing the attributes of a die, like symmetry and the arrangement of numbers, may have been one method to decrease the likelihood that an unscrupulous player had manipulated the dice to change the odds of a particular roll.”

That change from variable shapes, sizes, and designs reflects a sea change in thinking towards dice and chance. Before, the shape didn’t matter because the results were attributed to Fate or some greater outside force, but later on, an understanding of chance and probability pushed standardization of dice forward.

In the end, it’s amazing how much of our culture and worldview, both past and present, can be revealed by exploring how we solve puzzles and play games.

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PuzzleNation Blog Looks Back on 2017!

2017 is quickly coming to a close, and as I look back on an eventful year in the world of puzzles and games, I’m incredibly proud of the contributions both PuzzleNation Blog and PuzzleNation made to the puzzle community as a whole.

Over the last year, we explored board games and card games, strategy games and trivia games, dice games and tile games, do-it-yourself puzzlers and pen-and-paper classics. We met game designers, constructors, artists, and creative types of all kinds.

We unraveled math puzzles and tackled the Crossword from Hell. We accepted the challenge of diabolical brain teasers, optical illusions, Internet memes, and more, even pondering our place in the world of puzzles as electronic solvers like Dr. Fill and AlphaGo rise in capability.

We delved into puzzle history with posts about the legacy of female codebreakers in World War II, game dice from centuries ago, theories about Shakespeare’s secret codes, and the long history of cryptography and the NSA. We brought to light valuable examples of puzzles in art, popular culture, famous quotations, and even the natural world as we pondered whether bees are verifiable problem-solvers like crows and octopuses.

We spread the word about numerous worthwhile Kickstarters and Indiegogo campaigns, watching as the puzzle/game renaissance continued to amaze and surprise us with innovative new ways to play and solve. We shared worthy causes like Puzzles for Progress, as well as amazing projects like new escape rooms, dazzling corn mazes, and the ongoing Kubrick’s Game interactive experience.

We cheered the 75th anniversary of the New York Times Crossword, and chronicled the many celebrations that marked the occasion, from guest crossword constructors like Bill Clinton and Lisa Loeb to a puzzle-centric cruise across the Atlantic!

We also mourned as friends and fellow puzzlers passed on. We said goodbye to David Lindsey and Raymond Smullyan, two underappreciated giants of the field. The pun-fueled show @midnight this year, which inspired our monthly hashtag game, also closed up shop, sadly.

We celebrated International TableTop Day, made puzzly bouquets in honor of International Puzzle Day, marveled at the records broken at the Rubik’s Cube World Championship, attended the American Crossword Puzzle Tournament and New York Toy Fair, and dove deep into an ever-expanding litany of puzzle events like the Indie 500, BosWords, Lollapuzzoola 10, and Crosswords LA.

We found puzzly ways to celebrate everything from Pi Day, the Super Bowl, and Star Wars Day to Halloween, Thanksgiving, and Christmas, and we were happy to share so many remarkable puzzly landmark moments with you. We even discovered Puzzle Mountain!

It’s been both a pleasure and a privilege to explore the world of puzzles and games with you, my fellow puzzle lovers and PuzzleNationers. We marked five years of PuzzleNation Blog this year, I recently penned my 800th blog post, and I’m more excited to write for you now than I was when I started.

And honestly, that’s just the blog. PuzzleNation’s good fortune, hard work, and accomplishments in 2017 went well beyond that.

Every month, we delivered quality content for the Penny Dell Crosswords App. From monthly deluxe sets and bonus boxes to Dell Collection sets and holiday bundles, dozens upon dozens of topnotch puzzles wended their way to our loyal and enthusiastic solvers.

And just last month, we launched our newest puzzly endeavor — Daily POP Crosswords — bringing you fresh, up-to-date cluing and relatable themes in world-class puzzles created by some of the industry’s best constructors! (Many of whom you’ve gotten to know in our recent interview series, Meet the Daily POP Crosswords Constructors!)

But whether we’re talking about the Penny Dell Crosswords App or Daily POP Crosswords, I’m proud to say that every single puzzle represents our high standards of quality puzzle content crafted for solvers and PuzzleNationers.

And your response has been fantastic! Daily POP Crosswords is thriving, the blog has over 2200 followers, and with our audience on Facebook, Twitter, Instagram, and other platforms continuing to grow, the enthusiasm of the PuzzleNation readership is both humbling and very encouraging.

2017 was our most ambitious, most exciting, and most creatively fulfilling year to date, and the coming year promises to be even brighter.

Thank you for your support, your interest, and your feedback, PuzzleNationers. The new year looms large, and we look forward to seeing you in 2018!

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The Weird, Wonderful World of Dice

[Image courtesy of ThoughtCo.]

Dice have been an integral part of gaming for centuries. They’re the simplest way to introduce randomness to a game.

The six-sided die is, by leaps and bounds, the most familiar die. The d6, as role-players call it, is a staple of classic board games like Yahtzee and Clue, as well as the centerpiece of role-playing systems like GURPS.

But the d6 is hardly the only kind of die you see in gaming. Plenty of games and role-playing systems rely on dice of other shapes in order to run smoothly.

[Image courtesy of Wikimedia.]

If you play World of Darkness role-playing games like Werewolf or Vampire: The Masquerade, then the d10 is your friend. If you enjoy updated editions of Dungeons & Dragons (or even board games like Unspeakable Words or Scattergories), the d20 is a familiar sight, whether it has letters or numbers on it.

A standard dice set for beginners Dungeons & Dragons contains six different dice shapes: a pyramid-shaped d4, a d6, a d8, a d10, a d12, and a d20. (Many come with 2 d10s, one with single digits and one with double digits, allowing you to calculate percentages).

[Image courtesy of Instructables.]

Heck, if you think about it, flipping a coin to decide something is simply rolling a two-sided die.

But when you start delving into the history of games, it’s amazing to see just how far back some of these traditions and conventions go.

Did you know that The Metropolitan Museum of Art has a d20 in its collection?

Dating back to Roman times (somewhere between the 2nd century BC and the 4th century AD), the above die is inscribed with Greek letters. It’s not certain if this particular die was used for games or religious divination, but there’s no doubt it’s a beautiful example of craftsmanship.

And this is just scraping the surface. One of my favorite dice in my collection is an oversized 3D-printed d20 with Braille markings for every number. Such a cool piece.

Can you think of any strange dice in favorite games of yours, fellow puzzlers? We’d love to hear about them! (Unless they’re fuzzy dice hanging from your rearview mirror. Those don’t make reliable rolls in regular gameplay.)

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The Best of All Possible Puzzle/Game Worlds?


[A sampling of the wide variety of modern puzzles and games. Fluxx cards, Bananagrams tiles, a wooden puzzle box, Pairs cards, David Steinberg’s Juicy Crosswords from the Orange County Register, Timeline cards, last month’s edition of The Crosswords Club, Puzzometry pieces, Cards Against Humanity cards, multi-sided roleplaying dice.]

This is the most exciting time in history to be a puzzler or board game enthusiast.

Think about it. If you want to play a game or solve a puzzle, you don’t have to go any farther than your pocket, since a plethora of puzzly goodness awaits you on your smartphone.

Puzzle apps are our bread and butter here at PuzzleNation, so this might feel like a cheap plug, but honestly, it boggles my mind how much more accessible puzzles and games are now than they were even five years ago.

And the app revolution is only one part of the story.

I was reading a book the other day, as I am wont to do on the long train rides to and from PuzzleNation HQ. Titled The Revenge of Analog, it was all about the cultural response to digital media, highlighting the resurgence of vinyl records, film, and other tangible alternatives to electronic formats.

In the chapter “The Revenge of Board Games,” the author discussed the social aspect of tabletop gaming, and how sitting down with people and playing a game is a far different, more rewarding experience than online gaming and other social media-based interactions. (A fine point to consider, what with International TableTop Day a little more than a week away.)


While I do think that’s partially true, I also think that downplays the ingenuity of the puzzle/game community. I think we’re the best of both worlds.

I mentioned in my Tak review last week that puzzles are being created today that could not have been five or ten or twenty years ago. The advent of 3-D printing and laser cutters for homes and small businesses has brought design, construction, and promotion literally to the doorstep of entrepreneurial puzzlers.

Just last week I received a new edition of Puzzometry in the mail, a perk for supporting a team for a school robotics competition. This laser-cut plastic jigsaw will keep me guessing for hours (if its puzzly siblings are anything to go by), and it was designed and manufactured by a single individual.


Old and new styles are meshing as never before. Many puzzle constructors are partially or fully supporting themselves via email puzzle subscriptions and direct sales to the customer. Events like the Connecticut Festival of Indie Games are organized and advertised mostly online.

Crowdfunding has leveled the playing field for many companies and designers in both puzzles and games, allowing more products than ever before to enter the market. (According to Kickstarter, tabletop game projects raised $52 million dollars in 2013, and that number has surely gone up in the meantime.)

You’ve got a proper board game renaissance as classic games and styles of play are meshing with new technology, and games from across the world are shared on YouTube, at Friendly Local Game Shops, or even in puzzle cafes like Toronto’s Snakes and Lattes or New York City’s The Uncommons.

Whether you’re a pen-and-paper solver or a Penny Dell Crossword App devotee, a fan of classics like Chutes and Ladders or a proud tabletopper experimenting with the newest games, this is an amazing time to be a puzzler or board gamer.

So keep playing. Keep puzzling. And share that with others.

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The 2017 New York Toy Fair, Part 2!


On Tuesday, I gave you a general rundown of what it was like exploring the massive spread of puzzles and games on display at this year’s New York Toy Fair.

In today’s post, I’d like to highlight some of the puzzles and games that most impressed me. I think many of these will also appeal to many of my fellow puzzlers and PuzzleNationers as well.

So let’s dive right in!


One of the prime spots in the Launchpad area for first-time attendees was given to the team at Steamforged Games Ltd., who have brought the video game franchise Dark Souls into the board-game realm.


Between one and four players can test their mettle against various creatures, battling to capture their souls and use them to make your character stronger and more capable. The impressive array of miniatures, player cards, and tokens makes for an interactive experience that should satisfy both video game fans and board gamers alike.


For a more traditional family-friendly puzzle game, the crew at Befuddled Games has you covered with Kerfuddle and Tree Top Hop, both of which are suitable for solvers of any age group.

Kerfuddle combines a touch of Boggle with the ever-changing gameplay of Fluxx. Roll the dice and use them to form words, but be careful — the “Shake It Up” cards can make your word forming much more challenging.


Tree Top Hop is a great intro game for young players, as they move around the tree top, spelling words on their cards and racing to the treasure at the center of the board. By combining word-building and strategy, this is a terrific gateway game for new players.


Along the same lines as Kerfuddle is Twizmo! Words, except instead of dice, you have a Rubik’s Cube-style Twisty puzzle providing you with the letters you’ll use to build your word list. Designed by the same team who brought us Tak•tak, Twizmo! Words is a strong quick-play game for any Boggle fans in your household.


Snippets takes the list-building idea in another direction. Instead of random letters, you’re given a three-letter snippet of a word, and it’s up to you to come up with as many words containing that snippet as possible. So, if you’ve got TRA, you can write down EXTRA, TRAIN, STRAP, and so on.


And to close out this collection of word-forming games, we have Letter Tycoon, which adds a monetizing mechanic that really spices up the gameplay. Here, not only are you making money by forming words, but you can patent letters so that when other players use them, you cash in as well. It’s a really clever take on the word-building genre of games.


We now move on from combining letters to combining jigsaw pieces. The puzzles from Palmetto Puzzle Works all center around tessellations — shapes that repeat and interlock in many different ways.


Whether you’re trying to fit the pieces into a given space or you’re connecting them freestyle, these well-made wooden puzzles bring an M.C. Escher touch to the world of jigsaw-style solving.


Beasts of Balance, on the other hand, has players using game pieces in a different way, as solvers stack the animal shapes and try to keep their ever-growing tower of creatures and artifacts from toppling over. The game has a tablet interaction feature that enhances both the gameplay and the storytelling aspect of the game, making the most of new school and old school puzzling.


But if you’re looking to do some puzzly building in a different way, Maze by Seedling is a solid choice. Here, you can map out and design your own marble maze, and then tackle your own creation with a fully-functioning labyrinth board, complete with marbles, walls, and holes to avoid.


And while we’re on the subject of do-it-yourself puzzling, the crew behind Pinbox 3000 have designed a build-your-own pinball game system that allows for infinite customization. They give you everything you need to build a functioning game, and then leave the theme, bells, and whistles totally up to you.

I wrote about this one back when it was a Kickstarter project, and it was cool to see the brand continuing to thrive and grow.


Another gaming classic with a modern twist is Tatsu, which combines Asian-inspired mythology with backgammon-style gameplay. Designed by the same creative team as the tile-placement game Hive, Tatsu is a clever, elegant game all about strategy and guile. It’s easy to learn and tough to master, and I suspect it will do quite well.


If you’re looking to combine strategy with rapid-fire gameplay, Tenzi is for you. In Tenzi, you’re given ten dice, and you have to keep rolling them until all ten match. It’s like Speed Yahtzee! But with dozens of additional variant games at your disposal, from stacking to scoring to rule-shifting games, this dice game has legs and is easy to tote around to play anywhere.


If you’re looking to take your card games anywhere, the team at Narrows Hill have a great solution for you. The Card Caddy is not only a protective case for any deck of cards, but it opens up into a perfect card-dealing and sorting setup for ease of play.


We also got an early glimpse of a forthcoming addition to the Fluxx family of card games. Since Fluxx is celebrating 21 years on the market this year, the crew at Looney Labs is celebrating with Drinking Fluxx, a spirits-soaked version of their famous chaotic rule-shifting card game.

You can mix and match the various ingredients to try to create a winning formula (and perhaps a sideline as a bartender for your fellow players). Just make sure you call a cab after playing.


Whereas Tenzi and Fluxx are quite portable, Banana Bandits from CMON Games requires some space, since you have an entire 3-D building to set up as your game board. As you and your fellow players try to prove yourselves as worthy successors to the boss of the Banana Bandits, you’ll climb and explore the building, collect coins, and tangle with opponents, all on an impressively realized game space.

Will you be top banana, or is it time for you to split?


And the last game I’ll be discussing today is Doctor Who: Time of the Daleks, an elaborate galaxy-spanning game where you play as one of six Doctors traveling across time and space in order to complete missions, save the innocent, thwart your enemies, and generally wreak timey-wimey havoc.


Between the terrific miniatures and the expansive options available for players, this was one of the highlights of Toy Fair for me, and I can’t wait to see how they incorporate additional Doctors into the game later down the line.


Obviously this is just a small sample of all the fantastic, eye-catching puzzles and games that graced New York Toy Fair this year. But nonetheless, it’s an impressive group, covering so many different aspects of the puzzle and game world, and constantly blazing new trails in terms of creativity and innovation.

I have no doubt you’ll be seeing more about some of these projects as 2017 rolls onward.

[You can check out our full gallery of photos from New York Toy Fair on Facebook by clicking here!]

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It’s Follow-Up Friday: Hall of Fame edition!

Welcome to Follow-Up Friday!

Follow-Up Friday is a chance for us to revisit the subjects of previous posts and bring the PuzzleNation audience up to speed on all things puzzly.

And today, I’d like to return to the subject of Dungeons & Dragons!

I’ve written about Dungeons & Dragons and other roleplaying games in the past, because I think they are a wonderful, underappreciated part of the world of puzzles and games. Some of the best and most satisfying riddles and puzzles I’ve ever solved were an integral part of a game of D&D.

So I’m excited to announce that Dungeons & Dragons has been inducted into the National Toy Hall of Fame!

Housed at The Strong National Museum of Play, the National Toy Hall of Fame recognizes those products and improvised toys that have played a crucial role in the development of children and teens.

Whether they assist in hand-eye coordination, storytelling, deduction, athletics, or creativity, they are all classic examples of toys tied to fond memories of childhood. Previous inductees include the Rubik’s Cube (2014), Hot Wheels (2011), the Radio Flyer Wagon (1999), Jacks (2000), and Play-Doh (1998).

And I for one think Dungeons & Dragons is a very worthy addition to this club.

From the induction notice:

Dungeons & Dragons and its imitators actually changed the nature of play.

In Dungeons & Dragons players assume the roles of characters who inhabit a world moderated and narrated by a Dungeon Master, a player who explains the action to others and solicits their reactions to the unfolding story. The Dungeon Master’s storytelling skills and the players’ abilities to imagine add enjoyment to the game. Some aspects of the play are familiar, such as dice. But the special dice for Dungeons & Dragons hold up to 20 sides. Rolling them determines each character’s individual strengths, plots their complex interactions, and decides the outcome of their encounters.

More than any other game, Dungeons & Dragons paved the way for older children and adults to experience imaginative play. It was groundbreaking. And it opened the door for other kinds of table games that borrow many of its unique mechanics.

For over forty years, Dungeons & Dragons has been synonymous with roleplaying, collaborative storytelling, and good old-fashioned sword-swinging derring-do. And I think it’s fantastic that it’s getting some long-overdue recognition for the positive role it has played in so many people’s lives.

Congratulations to you, Dave Arneson and Gary Gygax. Thank you for hours and hours of brilliant, engaging fun.

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