Journey into the DAG: Puzzle Dependency Charts, Tentacles and YouJoshua Weinberg The Website is Down

Intro• Talk is about Puzzle Dependency Graphs

• I Applied this technique to analyze the game “Day of the Tentacle”

• I discovered non-obvious insights into the design of the game.

2

End Game

Shrunken Kids

Bowling Ball

Tentacle Boss

Back to the Present

Get Bowling Ball

Knock Out Ten Tentacles

Win The Game

Goal: Power Hoagie's Chron-o-John

Flag Gun

Exploding CigarLighter Gun

The Blanket

Red EdisonCan BuildBattery Gold Vinegar

Soap

Franklin inhis Room

Lab Coat

Super BatteryKite

Charged Super Battery

Hoagie'sChron-o-John

Powered

Vinegar inTime Capsule

Get into Dwayne's room

Get exploding cigar

Give plans to Red Edison

Make VinegarBuild a fire in the fireplace

Get the gold

Get the Super Battery

Get Soap

Start StormGet lab coat

Get Kite

Charge Battery

Power Hoagie's Chron-o-John

Get Vinegar

Goal: Get Diamond

Left handed statue

Access to VCR Fred

Opening Safe

Fred Tied Up

Rope

Red Ted Ted in Attic

Combo

Dr. Fred Contract

LucasArtsRoyalties

Diamond

Signed Contract

Get access to VCR

Record Safe Combo

Get rope

Paint Ted Red Get Ted in Attic

Rescue Dr. Fred

Get Contract

Get Signed Contract

Get Diamond

Sleepwalk Fred

Switch Statue Handedness

Mail Contract In Past

Intro

AccessGreen Tentacle's

Room

HelpWanted Sign

Access to Secret Lab

The Super Battery Plans

Red Paint

Wine

BucketWaterBrushHoagie

Hoagie

Oil

HoagiePatent Letter

Dr Freddrinking

his coffee

Hoagie

Access to Living Room

Chattering Teeth

Disappearing Ink

Stamp

Get Fake Barf

Begin Game

Find Dr. Fred's secret lab

Find Super Battery PlansGet Chattering Teeth Get Stamp

Goal: Power Laverne's Chron-o-JohnRed Paintto Hoagie

Laverne Laverne

Tentacle ChartCrank Scalpel to Bernard

Bookto Hoagie

Keys

Crowbar

Two Dimes

Crowbar

Vacuum Flier

Disguise

Name Tag

AccessLaverne's

Chron-o-JohnDentures

Access to History Room

Boxo' Laughs

Human ShowStartsDentures

Fork Spaghetti

Start Human ShowFake Barf

Hot Mummy No Harold

Club Tentacle pass

Cat

Mouse Toy Skunk on Roof

No Kennel Tentacle Guard Skunk

Extension Cord Laverne Access to Secret Lab

Access FutureIce Chest

Frozen Hamster

Access FutureLaundry Room

Sweater

Quarters

Defrosted Hamster Tiny Sweater

Vacuum

Access to Future Lab

ToastyWarm

Hamster

Hamster Generator Plugged in Chron-o-John

Laverne'sChron-o-John

powered

Get Laverne down from tree

Laverne Access Dr.'s OfficeLaverne Access Outside

Disguise LaverneGet Box o' Laughs

Get Dentures

Get Crowbar

Get Dime in Gum

Get Sweater

Get quarters

Make Vacuum

Get ticket to Human Show

Enter Human Show

Dentures To Laverne

Mummy Fashion Get Rid of Harold

Win Human Show

Turn off Kennel

Make Skunk

Get Skunk

Free Edisons

Plug in Laverne's Chron-o-John

Get Hamster to Laverne

Defrost Hamster

Get tiny sweater

Get Toasty Warm Hamster

Get Dusty Warm Hamster

Power Laverne's Chron-o-John

Journey Into The DAG:The Day of The Tentacle (LucasArts, 1993)

Puzzle Dependency Chart

Visualizations:

Tools:

yEdTulipGephiGraphviz

Puzzle Dependency Charts,

Tentacles and You

Hierarchical Dependency Chart,

ungrouped

Tasks that have no assigned resources

Begin GameFind Dr Fred's Secret LabGet Chattering TeethGet CrowbarGet StampFind Super Battery PlansGet Fake BarfGet Dime in GumGet quartersGet into Dwayne's RoomGive plans to Red EdisonPaint Ted RedGet DenturesGet SoapSleepwalk FredGet Lab CoatMake Vacuummake VinegarGet Laverne Down From TreeSwitch Statue HandednessGet SweaterGet Exploding CigarStart StormLaverne Access Doctor's OfficeLaverne Access OutsideGet Access to VCRBuild a Fire in the FireplaceGet KiteGet Box-o-LaughsDisguise LaverneDentures to LaverneRecord Safe ComboGet the GoldGet Hamster to LaverneMake SkunkGet Tiny SweaterGet Ticket to Human ShowGet VinegarGet ContractGet RopeDefrost HamsterGet SkunkEnter Human ShowGet Super BatteryGet Ted in AtticGet Toasty Warm HamsterMummy FashionGet Rid of HaroldCharge BatteryRescue Dr FredWin Human ShowPower Hoagie's Chron-o-JohnGet Signed ContractTurn off KennelMail Contract in PastFree EdisonsGet DiamondPlug in Laverne's Chron-o-JohnGet Dusty Warm HamsterPower Laverne's Chron-o-JohnBack to the PresentGet Bowling BallKnock out ten TentaclesWin the Game

0d 1d 2d 3d 4d 5d 6d 7d 8d 9d 10d 11d 12d 13d 14d 15d 16d 17d

13.0Effort (person-days per day)

Gantt Chart

Cambridge

Advanced

Modeller

To download these graphs and the Day of

The Tentacle Puzzle Dependency Graph

dataset visit:

http://thewebsiteisdown.com/devblog

5

1Hierarchical Dependency Chart,

swimlanes based on character 3 Dependency Structure

Matrix 4

A Puzzle dependency chart is a Directed Acyclic Graph (DAG).

Nodes represent puzzles. Edges indicate dependencies.

Hierarchical Layout grouped by downstream goal.

Nodes colored by game character. 63 puzzles in 5 groups.

Poster

In the Talk● I’ll make some bold sweeping statements:

● Like for example I will define what a puzzle is! ● I’ll make some dramatic claims along the way:

● Like: No two players have ever solved this game in the same way.

● And: Narrative development is incompatible with non-linear branching.

● Will introduce some practical tools which give layout and analysis advantages.

Who am I?● Writer / Director of comedy videos ● The Website is Down (websiteisdown.com) ● Creating an adventure game from the

Webseries ● Research for that game led to this

analysis

Puzzle Dependency Graphs What?● The idea is: Make a diagram with all the puzzles in your

game to show how they relate. ● Key insight here is that solving puzzles gives you things

you need to solve other puzzles. ● Thus a dependent relationship between puzzles.

Puzzle Dependency Graphs - Why• Visualize the puzzles in your game

• Give insight into size, complexity, difficulty and pace of the game.

• Visualizes non-linear Branching

• Not used during actual play, just design.

• Noah Falstein GDC 2013 talk. Credits Ron Gilbert for first use in game design.

PDG theory: graphs• A Puzzle Dependency Graph is a type of Dependency Graph. A dependency graph is a

type of graph.

• Graph is a general data structure. A collection of nodes and relationships between them.

• Graphs in general can be:

• Directed / Undirected

• Connected / Disconnected

• Cyclic / Acyclic

• In degree and out degree

PDG theory: Dependency Graph• Dependency Graph is a special application of a graph in

which edges represent dependent relationships between nodes.

• Dependency over time.

• DG have been around since the 60s : PERTT charts

• A common data structure

DG is a DAG• A Dependency Graph is

• Directed

• Acyclic

• Known as a DAG

• Can be connected or not

Puzzle Dependency Graph• PDG is the application of a dependency graph

to puzzles in a game.

• Nodes in a PDG represent puzzles.

• Edges represent dependent relationships or “the thing you get from solving the puzzle which you use to solve another puzzle”.

Puzzle / Dependency Definition• What is a puzzle?

• For the purposes of this discussion… A puzzle is anything you do in the game which satisfies the dependencies of other downstream puzzles.

• What is a dependency?

• Anything which you have to do to solve a puzzle!

• Recursive and self-referential definition which is totally lacking in mathematical formalism but still super useful.

Example• Need a sword to kill a dragon.

• Sword is in a locked chest.

• Need key to open the chest.

• “Kill the Dragon Puzzle” has a dependency on “Open the Chest puzzle”

• “Open the Chest Puzzle” has a dependency on “Get the Key Puzzle”

Let’s talk non-linear branching• Our example game is linear - each puzzle has a single

dependency and you must solve them each in order.

• Say the Opening the Chest puzzle had two dependencies - The hinge is rusty and you need an oil can to oil it before it will open - then you have a non-linear game segment.

• Player can solve Get the Key puzzle or Get the Oilcan puzzle in any order. Both must be solved to open the chest but the order is not important.

Day of the Tentacle• We’ve covered PDG in general.

• We talked about non-linear branching.

• Let’s talk about Day of the Tentacle.

• Classic LucasArts game released in 1993

• Written by Ron Gilbert and he used a PDG to do it.

The Day of the Tentacle• Play three characters in a time travel scenario.

• One primary goal - save the world

• Three sub-goals / sub-plots

• Power Hoagie’s Chron-o-John

• Power Laverne’s Chron-o-John

• Get a Diamond

• PDG is recreated here. Start with #1.

Day of the Tentacle PDG Features• Nodes are colored by the character.

• Dependencies show the “thing” you get.

• Graphs all have identical data, just different layouts.

What can we see here?• Single starting node

• Single leaf node

• What if multiple starting or ending conditions? This would mean multiple root or leaf nodes.

• Linear story game would have no branching and graph would be just a line.

Non-Linear Branching in DOTT• Non Linear Branching is when you have multiple puzzles “in flight” at the same time.

• With all their dependencies satisfied they are ready for the player to solve them.

• For example once you solve Get Laverne Outside you can solve

• Get Dentures to Laverne

• Get Box o’Laughs

• Disguise Laverne

• Visualized on the graph by Layers

What’s so great about non-linear branching?

• Pros: This has the benefit of giving plenty of things to do at any time and avoids holding up the game because the player is stuck on a single puzzle.

• Cons: (Dramatic claim #2) Non-Linear Branching makes narrative difficult.

Why does Non-Linear Branching make Narrative Difficult?

• Need to talk about Topological Orders

• A Topological Order is an order in which you can visit the nodes in the graph such that their dependencies have been resolved by the time you get there.

• In the case of a PDG it is an order in which you can solve the puzzles in the game.

• Topological Sort is an algorithm which can find a topological order. Generating a topological order is the most common use for a dependency graph.

How Many Topological Orders• There can be more than one valid order for a graph!

• How many?

• To get a lower bound on the answer we can just look at a single layer. Each layer can be fulfilled independently. So pick the third layer. There are 13 puzzles.

• To compute permutations you take factorial of the number of items in the set.

• 13! is > 6 billion ways in which you can arrange the elements of that set. So 6 billion orders those puzzles can be solved.

• Based on this number I stake my dramatic claim #1 (TM) that outside of using a walkthrough no two players have ever solved all the puzzles in this game in the same order.

Dynamic Storytelling• Professor Brian Moriarty’s talk about interactive storytelling: I sing the

Story Electric. Talk given at Practice 2015.

• A story is a particular causally related sequence of events

• Are these 6 billion paths through the graph all different stories?

• They are all particular sequences of events.

• But are these events causally related? We don’t know from looking at the graph. But from playing the game we know they are not.

No narrative thread• For example there is no narrative thread connecting

• Get the lab coat

• Get the Soap

• Make Vinegar

• Get the Dentures

• I got the lab coat, then I got the soap, then I made the vinegar, then I got the Dentures.

• These are puzzles with no connection to narrative.

Narrative Threads Go Vertically• There is a narrative thread moving down the graph.

• Get the Soap

• Start Storm

• Get kite

• Charge Battery

• Power-Hoagie’s Chron-o-John

• These events ARE causally related and thus are a story.

• “I got the soap which I used to wash the buggy which caused a rainstorm which caused Ben

Implications for Narrative• Non-linear branching makes narrative challenging. You can

have both easily but you can’t do them both at the same time easily.

• If you have a layer with two nodes then you could make a story for each path because there are only two paths. With three nodes there are 6 paths - still possible.

• The growth is factorial. If you have a layer with13 nodes… not possible.

How then?• So to create narrative and still have non-linear branching

you must isolate the sub-plots into their own dependency tree.

• Follow the dependencies backwards to ensure your plot points are all within the inverted dependency tree.

• This is probably why Noah Falstein and Ron Gilbert advise to start at the ending and work backwards.

Example• The graph on the right shows that in this game the

three major plots are almost completely isolated.

• Even within these sub-plots there is more isolation into sub-sub-plots.

• If you read the graph backwards you can make sense of the story. Reading it layer at a time, no.

Narrative Dependency Diagram• Untested theory - create a dependency diagram for narrative.

• Nodes would be anything which reveals a plot point

• Edges would be the plot points, narrative information

• The tree would represent multiple stories at once and could ensure that the narrative is consistent if the dependencies are satisfied.

• This might be able to be incorporated into the puzzle dependency graph also.

In short• Non-linear branching expands the graph horizontally.

• Narrative happens vertically.

• If you want puzzles to integrate with narrative you need to isolate the non-linear branching into manageable chunks

• This is exactly what DOTT does. See graph #3.

Tools• Why use tools?

• Graphs look better. Also they have automated layout algorithms and analysis possibilities.

• General graphing tools:

• Visio

• Omnigraffle

Tools 2• Graphviz - simple common file format

• Gephi - designed for larger graphs. Includes spreadsheet like functionality for extra node properties.

• Tulip - Sugiyama layout. Python scripting.

• Yed - The best for this purpose. Good hierarchical layouts with lots of options. Swimlanes. Very easy to use. Was used to create these graphs.

CAM• Cambridge Advanced Modeler

• Can generate DSM

• Can generate GANTT

• Can assign time range to each node and use statistical modeling to play with difficulty.

Summary• Make a puzzle dependency graph when designing your game

• Don’t fear non-linear branching

• Isolate narrative subplots

• Work backwards

• Use tools

• Thanks!