Feast for Odin Starting Draws

I was procrastinating at work and reading Steph’s weekly blog about board games, when I came across her criticism of A Feast for Odin‘s starting occupation cards:

I wanted to start off by saying I really don’t think the starting cards are all that balanced, and I know that is mean of me to say but I could really feel it in this game. Ron was constantly getting material goods for free from the forests every time he visited a specific section on the board while I got a terrible 1 time bonus when I collected 4 sheep for milk and a couple wool tokens. I’m sorry but it really pissed me off. I don’t know what I am going to do about the starting cards for future plays, perhaps we will get 2 and keep 1 or just go through and remove the “lesser valued” ones.

I’ve been playing and loving A Feast for Odin quite a bit lately and I wondered if drawing two and keeping one would alleviate the problem. For instance, let’s assume that the cards can be distilled to an arbitrary power between 0 and 10. There’s a scenario where I draw a 5 and you draw a 7. Okay, that’s a slight power advantage for you. But if we do “pick two, keep one” and my second draw is a 2 and yours is a 10, then the difference in power goes from 2 (7-5) to 5 (10-5).

Being a game design teacher and all-around nerd, I decided to see if I was just cherry-picking an edge case. This upcoming analysis based on some assumptions that may not be true; specifically, that cards have an objective static value.

Anyway, I ran an Excel simulation at 1,000 repetitions based on three cases: each of two players draws one card with value 0-10, each player draws two cards with value from 0-10 and keeps the highest, and each player draws three cards with value 0-10 and keeps the highest. I then calculated an average power for each case and an average difference in power for each case. I then ran that simulation 1,000 times for one million total repetitions.

Remember that we are giving every card a score between 0 and 10 and assuming a flat distribution. Thus, we should expect that the average power in a “draw 1, keep 1” scenario to be pretty close to 5 after a million draws. This will be our sanity check to make sure we are doing this correctly. There shouldn’t be much variation after a million repetitions.

Here are the results:

Draw 1 Draw 2 Draw 3
Avg. Power 4.998 7.149 7.973
Avg. Difference 3.641 2.636 2.095

In the rules as written, you get an average power of 5, but the difference between players is, in my opinion, significant. Going to “Draw 2, Keep 1” cuts the difference between the two players by 27.6%.

However, I think the real benefit is not the reduction in difference but the increase in average power. Taking the higher card of the two means that players will both (1) feel better due to getting something more useful (which would not happen if you just went in and removed the lesser valued cards) and (2) feel a greater attachment to the occupation they choose to keep because they chose it. This is likely related to a number of cognitive biases such as effort justification.

Additionally, this is also likely affected by relativity effects. We are likely okay to have a gap in power between us as players as long as we feel like we have something to work with. This means the situation of a 1 vs. 4 feels worse than the situation of a 7 vs. 10.

Here is a histogram of one of the 1,000 run simulations of the number of times a player ended up with each power level:

screen-shot-2016-11-01-at-1-00-16-pm

In the Draw 2, Keep 1 system, you will see the junky numbers 1-4 just as often, but you are less likely to be stuck with a pair of them. In fact, the most likely scenario is that you end up with a card from the highest power decile.

I think I’ll try the Draw 2, Keep 1 next time we play.

Booooook

The biggest media event of December is here!

IMG_3047

I’ve been bombarding social media but forgetting about my poor old blog as I slave away in the education mines.

Players Making Decisions is out! You can buy it at Amazon, Barnes and Noble, right from the Publisher, or anywhere else fine game design books are sold. In January, I plan on poking various media outlets for coverage, but I figure that is a useless task this close to Christmas.

It is slowly trickling into real people’s hands, and if you own two of those lucky hands, I have a favor to ask. Would you please leave kind reviews at Goodreads and Amazon? Those two sites drive a lot of impressions.

Features:

  • Beautiful matte cover.
  • No The Force Awakens spoilers. However, the book does contain a game theoretic discussion of what Lando Calrisssian should have expected in The Empire Strikes Back.
  • Lots of images and diagrams to help distract from the author’s reliance on words.

But seriously, here’s a list of contents. If any of this sounds interesting, I’d be thrilled if you picked up a copy:

Part 1: Getting Started

1. What Is a Game Designer?

Responsibilities of a Game Designer
Attributes of a Game Designer
Make Things
Cultivate Your Gardens
On Ontology and Dogma
Formalism
Summary

2. Problem Statements

Defining the Problem
Low-Hanging Fruit
Functional Fixedness
Brainstorming
Summary

3. Development Structures

Production Methodologies
Waterfall
Iterative Processes
Climbing the Pyramid
Scope
Summary

4. Starting Practices

Analog Games
Theme and Mechanics
Next Steps
Designing for Others
Opening Questions
Summary

Part 2: Prototypes and Playtesting

5. Paper Prototyping Development Techniques

Software and Materials
Art
Cards
InDesign Data Merge
Summary

6. Playtesting

Playtesting Goals
Playtesting Benefits
Listening to Feedback
Fear of Critique
Confirmation Bias
Finding Playtesters
Iterating
Summary

7. Playtesting Methods

The Testing Environment
Keep Playtesters Talking
A/B Testing
Self-Playtesting
Summary

8. Prototypes and Intellectual Property

Part 3: Meaningful Decisions

9. Flow and the Fundamental Game Design Directive

Game Flow
Interest Curves
Learning Curves
Individual Differences
Summary

10. Decision-Making

Player Agency
Anatomy of a Choice
Less-Interesting Decision-Making
Blind Decisions
Obvious Decisions
Meaningless/Misleading Decisions
Handcuffing Decisions
More-Interesting Decision-Making
Trade-offs
Risk/Reward
Expected Value
Summary

11. Randomness

Completely Random Games
Completely Skill-Based Games
Fairness and Mitigating Randomness
Summary

12. Goals

How Players Determine Game Goals
Criteria for Goals
Solving Goal Problems
Summary

Part 4: Describing Game Elements

13. Mechanics, Dynamics, and Aesthetics (MDA)

What Are Games About?
MDA
Example: Realm of the Mad God
Example: Monopoly
Example: Habitat
More Dynamics
Turtling
Kingmaking
Button Mashing
Grinding
Press-Your-Luck
Summary

14. Milieu

What Is Milieu?
Polish
Player Types
Motivation
Milieu as Design Focus
Summary

15. Rules and Verbs

Rules
Qualities of Rules
Types of Rules
Verbs
Summary

16. Balance

Symmetry
Self-Balancing Mechanisms
Progression and Numeric Relationships
Balance Heuristics
Summary

17. Feedback Loops

Positive Feedback Loops
Negative Feedback Loops
Feedback Loops in Action
Fixing Problems
Summary

18. Puzzle Design

What Is a Puzzle?
Possibility Space
Breadcrumbs
Features of Ineffective Puzzles
Incomplete Critical Information/Missed Assumptions
Lack of Ability to Experiment
Brute Force
Triviality Surrounded by Complexity
Lack of Possibility Space
Arbitrariness
Types of Puzzles
Deduction Puzzles
Truth Puzzles
Deception Puzzles
Paradoxes
Other Puzzle Types
Critical Path Puzzles
Strategy Puzzles
Algebraic Puzzles
Physical Manipulation Puzzles
Summary

Part 5: Game Theory and Rational Decision-Making

19. Equilibria in Normal Form Games

The Prisoner’s Dilemma
Solving Games Using Strict Dominance
Using (and Abusing) Dominance
Zero-Sum Games
Stag Hunt and Coordination
Determining Nash Equilibria in a Larger Matrix
Mixed Strategies
Stag Hunt Redux
Summary

20. Sequential and Iterated Games

Game Trees
Promises and Commitment Problems
Iterated Games
Experimenting with Strategies
Successful Strategies
Summary

21. Problems with Game Theory

Rational Actors
The Dollar Auction
The “Guess Two-Thirds” Game
Second-Price Auctions
Summary

22. Marginal Decision Analysis

Marginal Nuggets
Balance on Margins
Summary

Part 6: Human Behavior in Games

23. Behaviorism and Schedules of Reinforcement

Operant Conditioning
Schedules of Reinforcement
Anticipation and Uncertainty
Ethical and Practical Concerns
Summary

24. Learning and Constructivism

Historic Approaches
Novices and Experts
Cognitive Load
Expertise Reversal Effect
Split-Attention Effect
Tutorials and Learning Design
Summary

25. Motivation

Two Types of Motivation
What’s the Problem with Rewards?
Self-Determination Theory and Challenges
Competition and Motivation
Personality
Other Motivation Effects
Summary

26. Human Decision-Making

Mental Shortcuts
Attribution Errors
Misunderstanding Randomness
Anchoring and Adjustment
Understanding Value in Uncertain Situations
Loss
Framing Decisions
Summary

27. Attention and Memory

Attention
Memory
Helping with Memory Limitations
Perception
Summary

Part 7: Game Design Tools

28. Documentation and Written Communication

The Game Design Document
The GDD Creation Process
Step One: Determine Purpose/Desired Scope/Connected Systems
Step Two: Research
Step Three: Idea Generation
Step Four: Murder Your Darlings
Step Five: Fully Detail the Best Answer
Step Six: Edit and Find Edge Cases
References
Documentation for Tabletop Games
States and Flowcharts
Summary

29. Probability

Probability Is Counting
Joint Probability
Conditional Probability
Adding Die Rolls
Example: The H/T Game
Being Careful
Problem #1: The Boy-Girl Problem
Problem #2: The Weirder Boy-Girl Problem
Problem #3: Isner-Mahut at Wimbledon
Summary

30. Spreadsheets for Simulation

Why Use Spreadsheets?
Basics
Formulas
Formula Operator
Basic Math
SUM, PRODUCT
MAX, MIN
AVERAGE, MEDIAN, MODE
RANK, PERCENTRANK, PERCENTILE
ROUND, TRUNC
RAND, RANDBETWEEN
CONCATENATE
VLOOKUP, HLOOKUP
IF
COUNTIF, SUMIF
OR, AND
Common Formula Errors
Anchors
Goal Seek and Solver in Excel
One-Way Data Tables
Summary

31. Monte Carlo Simulation

Answering Design Questions
Hot Hand
Monty Hall
Once Around the Board
Martingale Betting
Summary

32. Presenting Ideas

The Thesis
Text on Slides
Data-Ink
Do Not Waste Time
Documentation
Acquiring Images
Example: State of Mobile Games 2014
Risk
Risk Analysis
Pitch Questions
Summary

Part 8: The Game Design Business

33. Profit, Loss, and Metrics

Profit and Loss
Metrics
Virality
Cash Flow
Summary

34. Sustainable Lifestyles

Life in AAA Digital Game Development
Life as an Independent Developer of Digital Games
Life in Tabletop Game Development
Market Luck
Summary

Conclusion

News

I have news!

For the last two years in scraps of time here and there I’ve been putting together material to make my own game design textbook. Here is what I can tell you so far!

  • Pearson, the largest book publisher in the world, will be publishing it through its PeachPit imprint.
  • It should be out by the end of the year.
  • It doesn’t have a title yet! Titles are hard.
  • It is a platform agnostic game design textbook that looks at many commonalities between the design process and features of both digital and analog games.
  • One of the areas that I think this book covers better than almost anything else out of the market is player psychology. If games are about meaningful decisions, then how do we examine and design decisions? We can look at them through the lens of the rational player (game theory) or through the lens of the human player (behavioral economics/psychology).
  • I dedicated a LOT of time in the last few months finishing the draft. You may have seen a flow of all the other game design textbooks I could find clogging up my Goodreads this year as I tried to make sure I wasn’t making anything that already existed in some better form.
  • Currently, we are editing chapter by chapter and I’ve got a lot of tendrils out on the web trying to get permission to use all sorts of screenshots and photographs of various games. I thought the draft was hard work, but the editing phase is laborious.
  • As someone who is normally completely self-deprecating, I have to say I am really proud of this thing. It isn’t just another “this is what I think about Game Design” kind of book as is so prevalent. There is a little bit of that, but it is loaded with references so you don’t have to take my word for it.
  • You will be very tired of hearing me talk about this over the next five months.

Level Design: Hole 83 in Desert Golfing

Hole 83 in Desert Golfing.
Hole 83 in Desert Golfing.

Above is an annotated screengrab of Hole 83 in Desert GolfingDesert Golfing is a minimalist game with a surprising amount of subtlety. I’ve seen a lot of comments about it on Twitter, but little discussion of the level design, so I figured I’d give it a go after I grabbed this screenshot to show a friend a particularly devious hole.

First, a short explanation of Desert Golfing. Desert Golfing has essentially the same interaction as Angry Birds. You drag your finger to create a vector that defines the direction and speed at which you hit your ball. The object is to get the ball to stop in a hole, noted by a flag. If the ball leaves the screen, it is warped back to the original tee location. If you make it into the hole, the hole rises up to become flush with its surroundings, the screen pans to the right, and a new hole is revealed. Unlike most golf courses that offer 18 holes, Desert Golfing appears to be endless. Yet nonetheless, it keeps the player drawn to its simple presentation and physics interactions by varied and often maddening level design.

Hole 83. Hole 83 frustrated me so much that I deleted Desert Golfing. Then I redownloaded it and played the first 82 holes again just to get back to this level.

The first thing most players will try to do on this level is to shoot at about 45 degrees in order to hit the “green” area near the cup. However, in order to reach the green and not the slope before it, the player has to put so much force onto the ball that it will always end up overshooting the green and fall down the slope to the right, resulting in an out-of-bounds.

So what are the players options? I’ve annotated the surfaces above to show dangerous places to place the ball.

If the ball lands in the red-lined area I’ve marked as “Zone 1”, then abandon hope. Due to the vertical right wall of this chasm, there is no way to get this ball out of the chasm to the right. The only hope you have is to hit the ball out into the V-shaped chasm to the left of this area. This will likely cost you a few strokes or an out-of-bounds.

“Zone 2” above is placed under an overhang of the green. If the ball ends there, again there is no hope. The overhang prevents players from hitting any shot in the direction of the hole from that position. At this point you must hit the ball gently to the right to the yellow area. But don’t hit it with much force or the ball will land in “Zone 3” which is guaranteed to end in an out-of-bounds.Any shot with too much force is likely to hit Zone 3.

The yellow area of the green and the early part of the slope to the left of the green (between zones 1 and 2) is dangerous territory. Given the correct momentum and angle, the player can hit the slope and roll onto the green. However, most opportunities to do this will either be too slow and steep (leading to falling into the Zone 1 chasm) or too strong and flat, leading to falling off the green to the right and into Zone 3.

My strategy for this hole is to take one stroke to position myself in the chasm left of Zone 1, then hit a light arcing shot that lands on the flat part of the green. If this second shot is too light, it will fall into Zone 1. Chances are that most shots will roll off the green to the right, but a second-best scenario is that it ends in the small part of yellow-lined area off the ledge to the right of the green (right of Zone 2). From there, it is possible to hit a light chip-shot back onto the green, but God help you if you overshoot any of these parts.

The first time I played this hole, I rage-quitted after getting a +45 or so. After calming down and analyzing the hole, I was able to finish it with a +5. The hole made me think about it after dozens of straightforward holes where guessing-and-checking was sufficient strategy.

Worth noting is the amount of tactical decision making needed from very simple components. What are the pieces of Desert Golfing? There are holes, land, tee spots, and out-of-bounds triggers. That’s it. The ball is fired and controlled by implicit, consistent rules of physics. The land is variable in shape, but consistent in friction. The holes are consistent in shape, but variable in location.

There are thousands upon thousands of Desert Golfing holes, which leads me to believe that the holes were designed by algorithm. If this level’s design is due to chance alone, then bless the random number generator that created it as it provides a depth of play that is missing from most mobile games.