Posts Tagged ‘math’

Dice are excellent for illustrating numerical patterns… or at least, the start of them.  Some patterns get out of hand really quickly.


Oh, and we have new prototypes for the Tinker Dice.  (Please join the campaign on Kickstarter!)

New Tinker Dice Prototypes

It’s still not quite right; the photo paper I printed these on via the local Kinko/FedEx store came out darker than designed, and you can see the tape that holds them together and the lines on the face edges… but these are much closer to what we’re looking to get from the factory.  I’ll shoot a video with them when I get a minute.

Speaking of numbers, though, we are a little behind on the “track” to getting the project funded.  I’m sending out another wave of emails to a variety of places, trying to get some press.  If you have a minute, and feel the project merits mention, will you please spread the word?  Facebook, Twitter, Reddit, Tumblr, MySpace, semaphore, smoke signals… whatever outlet you have, we’d greatly appreciate a mention!

Oh, and I’ll append this and the to the main post, but also speaking of numbers, I wanted to spotlight the “pound of dice” pledge tier, the “POUNDER” tier.  It’s the most cost-effective on a cost-per-die basis, but it is a fair chunk of change.  By default, I’ve described shipping those as a 5×8 cloth bag stuffed with 100 dice.  There’s another option that might make sense for some, especially when it comes to shipping to places outside of the U.S.  (Pesky shipping costs can be annoyingly expensive.)

You can use that tier as a group order, if you get together with some of your interested friends.  Instead of putting all 100 dice into one bag, I’ll put them into 16 sets of six (or 8 sets of 12, whichever you’d prefer; the smaller dice bags will hold 12 nicely) with the remaining 4 in an extra bag.  It’ll mean a little distribution on your end, but it’s a great way to save on shipping and even get a better price on the dice themselves.  I know, it’s a bit of legwork, but it might just prove to be worth it in some instances, so it seemed worth the mention.  Just let me know if you do wind up wanting to use this pledge tier this way, and how you want the bags.

Oh, and this is what the small bags look like… more or less.  This one spent a little time in the Mad Science lab.  If we wind up with 200 backers, all of the bags will spend some time in the lab, witnesses to (and maybe victims of) shenanigans in the lab.  Otherwise, the dice will come in clean, white cotton bags (mostly) like this.  (And you can always request clean bags, of course.)  If we get fewer than 200 backers but still fully fund, I’ll make Mad Science bags available via a small add-on cost.

Mad Science Bag



Thanks again everyone, and we hope you have a great weekend!

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Snowflakes are a seasonal craft around here.  Using my aforementioned Snowflake Seeds, my little family makes a variety of snowflakes to decorate our windows.  This year, I tried something a little different… a steampunk snowflake:

Steampunk Snowflake 1.0

I wasn’t sure that it would work… and I could do a lot more detail with a laser cutter… but for an experiment, I’m pretty happy with how it turned out.  I’m obviously cheating on the spans, and I’ll make one with better meshing teeth later.  It really should get the brass and grunge treatment, but the shape is what’s important for this initial test.  I’d really love to make one with working gears via Shapeways… maybe once I can carve out a bit more time.

Happy holidays!

Edited to add:  Now, with more sense!  This version of the Gearflake has one more gear at the center, and the shape is entirely gears, no support struts like the first one.  Way too much fun to make these, I tell you.  The great part is that they don’t need any weird laser cutting tools, you can do these just with paper and scissors.  All the cuts come in from the sides of the snowflake seed.  (I’ve got a picture around here somewhere of the folded/cut versions of these…)  Sure, the gears aren’t machine precise, and there are errors thanks to the paper folding thickness… but still, these are great to see take shape.

Gearflake 2.0

This is the pattern to make the Gearflake 2.0.  Once you have the snowflake seed wedge, you take this pattern (maybe fudging the teeth if you want it a little more precise) and cut out the dark parts.  Leave the blue-grey parts.

Thanks for stopping by, especially if you’re here from epbot.com.  Many thanks for the link!

Gearflake 2.0 Pattern

…aaand here’s version 3.0.  Each iteration comes with another layer of gears.  I’m running into cutting resolution issues and slight warping (though that can be cleaned up with iteration), so I’m not sure if I can go a layer deeper.  I guess we’ll find out.  The basics are simple enough, alternating sides for each successive gear arc when plotting them out on the ‘seed, as you might note on the 2.0 pattern.  I’m sure I could use Illustrator or even Photoshop to nail down some more precise gearwork… these have been just arcs I’m guesstimating by hand.

This is probably way more fun than it should be.  It’s just papercutting after all… but it’s also math, art and a little bit of whimsy.  I love playing in that space.  It’s a somewhat eclectic Venn intersection, but it’s satisfying to see things come together.  Left brain-right brain combinations and all that.

Gearflake 3.0

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My preteen niece seems to have a bit of game design in her blood.  She experimented with the design of Phase 10 and a standard deck of playing cards and wound up with her own game… almost a Rummy-light.  Since Phase 10 is part of the Rummy family, that’s not a huge surprise, but it’s interesting to see her chasing down those game design principles and applying them in new ways.  It’s instinctive, it seems, rather than the sort of analytical approach I might have used.  Color me impressed.

She also designed another game from the ground up, a curious little game that has little resemblance to anything I’m familiar with.  It’s pretty solid for a small game, and I’m still trying to suss out the strategies and balance.  She does all this game experimentation and design simply with a deck of cards, just noodling around with ideas.

That sort of game design experimentation is something I’ve tried to capture with a recently purchased set of dice.  It’s a standard role player’s collection, seven dice of varied shape.  There is one twenty sided die, one twelve sided die, two ten sided dice, one eight sided die, one six sided die (the ever-popular cube) and one four sided die.  These are usually abbreviated as D(whatever) dice, with the twenty sided die labeled a D20, and the six sided cube labeled a D6 and so on.  It’s a nice spread of dice, with a variety of potential applications.

I’ve tried to come up with math games using them to teach my children.  I’ve tried to use them to teach my niece a little about game design.  I’ve used them to play with variations on themes I see in games that already use dice, like Warhammer and Settlers of Catan (which plays differently with a D12 instead of 2 D6).  It’s nice to have these dice for when I want to experiment with a bit of randomization, but want to try something a bit less common than the standard D6 collection.

I’ll share a couple of rudimentary games, then, in the hopes of spurring some thoughts and conversation.  I’d like to see what else might be done with this set of seven dice.  I’m still experimenting, but I’d like to hear other ideas, if you’re willing to share.  I’ve been keeping things simple; no board, no cards, nothing much more than scorekeeping.  That’s not the only way to design, and certainly not a restriction for conversation, but it’s been nice to keep things simple while I’m getting a bead on exactly what I can do with these things.

Game One:  Pick n’ Roll (2-7 players)

Each player picks a die (youngest player first), then rolls their dice.  Highest number rolled wins.

Simple, maybe too simple, but gives young children the chance to see the differences between dice and hopefully, to relate shape to numbers.

Game Two:  Roll n’ Toll (2 players)

Remove one D10.  Player one picks a die, then player two picks two dice, then player one picks two dice, then player two picks one die.  Both players roll all three of their dice.  Highest number rolled wins.  (Alts:  Start with two sets; D20,D6,D4 vs. D12, D10, D8.  Players just choose a set.  Highest total wins.)

A bit different choice involved, and with the Alt rules, a more equal chance to win.  Even with equal total potentials (max of 30 if using either set), the “swingy” D20 will make for a sporadic win pattern.  Minor addition practice for kids, some probability considerations.

Game Three:  Mix n’ Match (2 or 3 players)

Roll one D10, rolled number is the target number.  Players choose a set and roll.  Closest roll to target number wins.  Use these sets if two players:  D20,D6,D4 vs. D12, D10, D8.  Use these sets with three players: D20, D4 vs. D12, D6 vs. D10, D8.  Any of their dice count for target roll.  (Alt: Use any simple math functions using your dice results to get close to target.  Ex:  Target = 6, rolls = 2,8,10.  8/2 = 4, 10-4 = 6.)

More math potential, estimation of probabilities to match target.

Any of these could, of course, be mixed and matched.  You could also add complexities and other players like this:

A third, neutral player (Judge) rolls the extra D10 and keeps the number secret behind their hand.  The other players roll one of their dice (they have either two or three, depending on how many players), and the Judge tells each player if their result is higher or lower than the target (if this first roll matches the target, declare an immediate winner and move to another round, ignore ties).  Each may choose to keep that roll (lock their choice) or roll another die.  Repeat for as many dice as you have (2 or 3), if the player chooses.  Previous rolls are ignored; only the latest roll may be the locked number.  When each player has a locked number, reveal the Target, and the closest roll wins.

These are pretty simple math games. You could introduce some sort of brinkmanship mechanic, or a bluffing mechanic. Maybe use the dice not for their numbers, but for their shapes. Maybe see who can stack the dice better and/or faster. See who can spin one like a top for the longest, and which dice spin better. There area lot of things you can do within the seven dice box before you ever try thinking outside the box.

So what would you do with this set of seven dice?  What can you do with just those dice?  Maybe add in a pad of paper?  A few coins?  A whole bag of varied dice? Miniatures of some sort? A game board?

I start with seven dice because that’s a nice, streamlined set of data.  It’s great for number games for kids, and might just help nail down some balance issues before layering a bunch of complexity into the system.

Whatever the limitations you choose for yourself, like my niece’s game design experimentation with a deck of standard playing cards, I believe it’s a good game design exercise to work with simple game units and see what sort of games you can come up with.  Once you have a feel for those simple elements, you can start introducing a few new factors and see how everything interacts.  What works with 7 dice may blow up with 15, and what works fantastically for two players might be painfully political with three.  Something perfectly balanced for three players might fall apart with four players.  Hidden information might make a game better or just frustrating.

Like learning any new language or skill, playing with basic elements is useful for comprehension.  Complexity and shiny blinginess can be added as occasion permits.  Nail down the core game design first, and become fluent with the tools, and then branch out.

Interestingly, after I’d written this but before I posted it, Raph Koster reposted an essay about The Fundamentals of Game Design, and how designing in small pieces can be a good approach.  His “prototype kit” is a bit more than seven dice, but it’s still pretty simple compared to some final games.  Really nailing down the basic elements of a game should, in my mind, take precedence over any of the window dressing, including art.  Even Wizards of the Coast famously does iterative design with what they call “playtest” cards long before they get the artists on board.  Game first, trappings later.  As an artist, I do believe that art and appeal are important, but without a solid game to hang them on, they just can’t do much.

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I’m an artist by trade, and I love creating things.  I grew up wanting to be a Disney animator, and my BFA degree is in computer animation.  I also happen to love math, and have spent a fair bit of time as a math tutor.  I grew up loving math and the intersection that it has with art in things like Origami, the Golden Ratio and Fibonacci numbers (there is a TON of math in art).  I love being able to take “right brain” and “left brain” notions and use them to reinforce each other.  It saddens me to see students that I tutor fear negative numbers or fractions.  Math and art are both deeply inquisitive ways to look at the world around us, and both have a great deal to offer to those trying to understand life and make their cognitive functions more effective, and to each other as disciplines.

Raph Koster brought “Lockhart’s Lament” to my attention, and it resonates with my experience.  I managed to find a deep fascination with math early on, and I persisted with it despite my deep disgust with memorization and busywork.  Of course, so-called “Investigations Math” is worse, as it doesn’t bother actually teaching anything, leaving students to figure things out on their own.  The truth is somewhere in between; students need to learn how math works, but more important, they need to learn why, and how to extrapolate the critical thinking required for mathematical analysis into other aspects of life.  Students need to learn how to think, not how to regurgitate.

Of course this has game design applications, since that’s what I talk about around here.  Game designers need to give players tools and show them how they work, then stand back and let players play.  Good math is playful, good art is playful.  It’s the experimentation and discovery that makes them both fun.  Games are very similar; the exploration of the game functions and artistic content is a significant part of the fun that can be derived.

To be fair, that’s not the only way to play (or design) games, or the only reason to do so, but it always bothers me when games quickly devolve into reflex checks or memorization hurdles.  Likewise, tightly straightjacketed games with little room to explore and experiment don’t hold my interest for long.  This is why level-gated games like WoW bother me; I’ve got to jump through the highly repetitive hurdles of leveling (with very repetitive combat) to see more content and get on with exploring and experimenting.

I think it’s no mystery why The Incredible Machine is one of my all time favorite games, and more recently, why Boom Blox and Crayon Physics are high on my list.

I wish people wouldn’t be afraid of math, or dismiss art as frivolous luxury.

I suppose there’s a tangent to be run exploring linguistics and how writing and wordsmithing is similarly creative and playful while being fascinatingly structured.  I do lean on alliteration and creative use of words around here, after all.  Perhaps that’s best saved for another article, though.

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Just a simple concept today:

Perpetual growth in a finite world is mathematically impossible.

Pretty easy, right? Limited resources cannot possibly meet the demand of an exponential growth curve.

The repercussions of that simple common sense notion are profound: (more…)

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