Journey into the DAG:
Puzzle Dependency
Charts, Tentacles and You
Joshua 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.
Poster
Begin Game
Find Dr. Fred's secret lab
Puzzle Dependency Charts,
Tentacles and You
Access to Living Room
Find Super Battery Plans
Hierarchical Layout grouped by downstream goal.
Nodes colored by game character. 63 puzzles in 5 groups.
Disappearing Ink
Get Fake Barf
Get Stamp
Goal: Power Hoagie's Chron-o-John
Hoagie
Patent Letter
A Puzzle dependency chart is a Directed Acyclic Graph (DAG).
Access
Green Tentacle's
Room
Access to Secret Lab
Get Chattering Teeth
Get exploding cigar
Chattering Teeth
Get Soap
Exploding Cigar
Lighter Gun
Wine
Build a fire in the fireplace
Dentures
Make Vinegar
Laverne
Laverne Access Outside
Access
Laverne's
Chron-o-John
Crank
Get Box o' Laughs
Switch Statue Handedness
Crowbar
Laverne Access Dr.'s Office
Scalpel to Bernard
Dentures To Laverne
Hoagie
Get Crowbar
Laverne
Get Dentures
Goal: Get Diamond
Keys
Get Laverne down from tree
Book
to Hoagie
Flag Gun
Hoagie
Goal: Power Laverne's Chron-o-John
Red Paint
to Hoagie
Get into Dwayne's room
Nodes represent puzzles. Edges indicate dependencies.
The Day of The Tentacle (LucasArts, 1993)
Puzzle Dependency Chart
5
Intro
Journey Into The DAG:
Crowbar
Get quarters
Get Dime in Gum
Tentacle Chart
Two Dimes
Disguise Laverne
Dr Fred
drinking
his coffee
Left handed statue
Get access to VCR
Sleepwalk Fred
Fred
Opening Safe
Access to VCR
Get Sweater
Record Safe Combo
Quarters
Help
Wanted Sign
Tools:
Access to
History Room
Bucket
Water
Brush Soap
Hoagie
Get lab coat
The Super Battery Plans
Get the gold
Franklin in
his Room
Gold
Get Kite
Gephi
Tulip
yEd
Visualizations:
1
Give plans to Red Edison
Lab Coat
Graphviz
Hierarchical Dependency Chart,
ungrouped
Vinegar in
Time Capsule
The Blanket
Start Storm
Oil
Red Edison
Can Build
Battery
Name Tag
Fork Spaghetti
Kite
Super Battery
Dentures
Charge Battery
Box
o' Laughs
Human Show
Starts
Mummy Fashion
Charged Super Battery
Enter Human Show
Fake Barf
Mouse Toy
Get Skunk
Start Human Show
Sweater
Get Hamster to Laverne
Hierarchical Dependency Chart,
swimlanes based on character
3
Dependency Structure
Matrix
No Harold
Dr. Fred
Win Human Show
Gantt Chart
Toasty
Warm
Hamster
Skunk
Vacuum Flier
Make Vacuum
Access to Future Lab
1d
2d
3d
4d
5d
6d
7d
8d
9d
10d
11d
12d
13d
14d
15d
16d
Extension Cord
17d
Begin Game
Laverne Access to Secret Lab
Vacuum
Find Dr Fred's Secret Lab
Get Chattering Teeth
Plug in Laverne's Chron-o-John
Get Stamp
Get Dusty Warm Hamster
Find Super Battery Plans
Get Fake Barf
Get Dime in Gum
Get quarters
Plugged in Chron-o-John
Get into Dwayne's Room
Give plans to Red Edison
Hamster Generator
Paint Ted Red
Get Dentures
Power Laverne's Chron-o-John
Get Soap
Sleepwalk Fred
Get Lab Coat
Make Vacuum
make Vinegar
Get Laverne Down From Tree
Switch Statue Handedness
Get Sweater
Get Exploding Cigar
Start Storm
Laverne Access Doctor's Office
Laverne Access Outside
End Game
Get Access to VCR
Build a Fire in the Fireplace
Get Kite
Get Box-o-Laughs
Disguise Laverne
Dentures to Laverne
Record Safe Combo
Get the Gold
Get Hamster to Laverne
Make Skunk
To download these graphs and the Day of
The Tentacle Puzzle Dependency Graph
dataset visit:
Get Tiny Sweater
Get Ticket to Human Show
Get Vinegar
Get Contract
Get Rope
Defrost Hamster
Get Skunk
Enter Human Show
Get Super Battery
Get Ted in Attic
Get Toasty Warm Hamster
Mummy Fashion
Get Rid of Harold
Charge Battery
Rescue Dr Fred
Win Human Show
Hoagie's
Chron-o-John
Powered
Laverne's
Chron-o-John
powered
Back to the Present
Shrunken Kids
Get Bowling Ball
Bowling Ball
Power Hoagie's Chron-o-John
Get Signed Contract
Turn off Kennel
Mail Contract in Past
Free Edisons
Get Diamond
Plug in Laverne's Chron-o-John
Get Dusty Warm Hamster
Power Laverne's Chron-o-John
Back to the Present
Get Bowling Ball
Knock out ten Tentacles
Win the Game
Effort (person-days per day)
13.0
http://thewebsiteisdown.com/devblog
Stamp
Mail Contract In Past
No Kennel Tentacle Guard
Get Crowbar
Contract
Get Signed Contract
Signed Contract
Free Edisons
Tasks that have no assigned resources
0d
Ted in Attic
Rescue Dr. Fred
Turn off Kennel
4
Get Ted in Attic
Red Ted
Club Tentacle pass
2
Get Contract
Rope
Paint Ted Red
Tiny Sweater
Get Toasty Warm Hamster
Combo
Get rope
Red Paint
Defrost Hamster
Defrosted Hamster
Fred Tied Up
Get tiny sweater
Frozen Hamster
Get Rid of Harold
Hot Mummy
Power Hoagie's Chron-o-John
Make Skunk
Skunk on Roof
Access Future
Laundry Room
Access Future
Ice Chest
Cat
Get ticket to Human Show
Vinegar
Get the Super Battery
Cambridge
Advanced
Modeller
Disguise
Get Vinegar
Knock Out Ten Tentacles
Tentacle Boss
Win The Game
Diamond
LucasArts
Royalties
Get Diamond
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!