Showing posts with label Game Design. Show all posts
Showing posts with label Game Design. Show all posts

Monday, October 1, 2018

Solving the Raygun Problem with Evolutionary Games

by Cathelineau via game-icons.net
I like Evolution: the game, the theory, but in Chapter 13 of "Games of Strategy" I learned about something new -- Evolutionary Games.

An evolutionary game looks at a large population of players -- each using only a single strategy -- to find the balance of strategies that work best together given lots of repeat plays.

Borrowing concepts from natural selection, the mix of how many players use any particular strategy is changed until an equilibrium is found.  At that point, each player will do equally well after playing against every other player and their opponents' strategies.

For instance, 2 backstabbers in a group of 10 cooperators might be a good balance in a prisoner's dilemma game given the right payouts.  In many ways this looks a lot like mixed strategies -- having 2 backstabbers and 8 cooperators is similar to saying that I will backstab 20% of the time.  So having lots of players engaging in different strategies looks a lot like two players using mixed strategies.

An important difference is that each individual player is pursuing a single strategy.  Which is often more analogous to a single play of a board game.

Achieving Polymorphism

This equilibrium might only occur when all players are using the same, obviously dominant strategy (Monomorphism).  But you can end up with a mix of strategies (Polymorphism)... probably in the same situations where mixed strategies would be the best choice.

If Polymorphism is a goal of our game design, the idea of evolutionary games brought two paths to mind.

Rock-Paper-Scissors

The seemingly obvious answer is to make different strategies work best against each other in a daisy chain such that none of them are dominant against a full field of strategies.

I think I've seen this the most in complex TCGs like Magic: the Gathering.  In these games the meta often shift to favor a particular type of deck construction.  In theory as more and more players adopt that strategy, other decks that work well against it in particular will become more effective even if they are not as strong generally in the current meta.

This is easier to conceptualize if you think of a 4 item Rock-Paper-Scissors.  Lets call this game Rock-Paper-Scissors-Raygun.  In this game Rock, Paper, and Scissors interact with each other as you are used to but Raygun beats both Rock and Paper.  Only Scissors beats Raygun.  Raygun is easily the best strategy... except that when a majority of players carry rayguns, scissors is suddenly very effective... which eventually leads to more people playing rocks...

by Lorc via game-icons.net

Raygun Interference

A different way to deal with the raygun problem is to make rayguns interfere with each other.  Maybe each raygun brought to a game of Rock-Paper-Scissors-Raygun reduces the effectiveness of every other raygun.  Rayguns might start out with a relative value twice as high as everything else, but then everyone brings a raygun...

You see this in Railways of the World (Eatern US Map).  Concentrating in the northeast can be hugely efficient and effective in this game... if you are the only person doing it.  Otherwise it becomes cramped and dangerous.  Although, the second person to commit to that plan can be throwing their game away to try to stop a run-away leader.  (See Tragedies of the Game Commons).

In Championship Formula Racing, this can happen differently.  If a track looks to favor a particular over all strategy you can have a glut of cars commit to that strategy.  Since that commitment usually takes place during the simultaneous and private phase of car set-up there is no first mover advantage -- as you see in the Railways of the World example.

What About Monomorphism

Am I going out on a limb to suggest that game designers want Polymorphism?  Would a game ever strive for Monomorphism?  Maybe if something other than strategy contributes to success or failure like dexterity or trivia knowledge?

Something to think about.

Monday, September 24, 2018

Encouraging Cooperation in Board Game Design, Or Not

by Delapouite via game-icons.net
Not long after reading chapters 8 through 10 in "Games of Strategy" (discussion here: Ways to Create Space for Signaling in Games) I plowed on through chapters 11, 12, and 13 and then failed to write anything about them as the vacation part of my summer commenced.  School's back.  Vacation is over.  So know lets figure out what I learned.

Chapters 11 and 12 discussed variations of examples covered previously in the book and how those variations change outcomes and strategies.  Chapter 11 takes a look at what happens to the prisoner's dilemma if you play it over and over again.  Chapter 12 explores changes in strategies when you add more then the 2 or 3 players we've been normally considered.

Most of what I took away from these chapters is about encouraging or discouraging cooperation.  In this context, I am not talking about cooperative board games per se.  I am talking about how much a game encourages backstabbing or assisting others.  Below are three levers I think could be used to tweak the levels of that kind of cooperation in a game.


by Delapouite via game-icons.net

Payoffs

Remember that the core idea in the prisoner's dilemma is that I have a choice to share a reward or take all of the reward or possibly end up with nothing.  An example abstracted payout for this kind of interaction:


Some forms of basic game theory indicate that being mean is the best approach... you will never get 0 and you might get 3.  You also have to assume that the opposition will be mean as mean is the best response to either of your options.

Not shockingly, how you set penalties and rewards in a game like prisoner's dilemma tips the scales towards rewarding cooperation or backstabbing.  If A and B both got 4 when both were nice... that would change the equation a bit.

This is pretty obvious.  If I make the nicer play more valuable then the backstabby play the nicer play will get used more often.  As a designer, that is obviously a lever you can pull depending on what kind of game you want. 

Asymmetric Payoffs

If the payoffs and penalties for each result in a prisoner's dilemma game are different for each player you can create situations where some players might cooperate even if they know the other players will not because it is still worth it.


In the example above, B gets 2 more then usual when being nice.  B's best play is now to be nice regardless of what A is doing.  Interestingly A still wants to be mean in this game.


by Delapouite via game-icons.net

Repeat Play

However, if a prisoner's dilemma is played over and over again, the players are encouraged to be nice.  If we are both mean in the basic version of this game, we both get 1.  If we are both nice, we both get 2.  The more play repeats, the better.

Part of the secret to this that player's know that they can punish mean play in the future.  Maybe more importantly, players who might be mean know that they can be punished -- there are now future consequences to their actions that they have to consider.

Because of this concept nice play becomes less important near the end of the game -- backstabbing becomes more rewarding as the opportunity for negative consequences gets smaller.


by Cathelineau via game-icons.net

Externalities

An externality is a factor that impacts my payouts that I have no control over.  This sounds a lot like how decisions in a prisoner's dilemma impact each other.  The difference is that while your decision impacts me, my decision does not impact you.  Logically there are both positive and negative externalities.

From a game theory perspective, the action that rewards me the most is the action I am most likely to take regardless of whether it impacts someone else positively or negatively.  From a game design perspective, I can tweak those private rewards to encourage the actions I want taken.

Or, I envision a game where players can encourage actions that benefit them by adding rewards to those actions for others.  In fact, I'm sure that kind of interaction exits in gaming somewhere...



Summing Up


  • Tweak rewards to encourage the behavior you want in your game.
  • Remember that players can get different rewards from the same action.
  • Repeating interactions can encourage nicer play.
  • Be careful if my play impacts you but your play does not impact me.

Tuesday, July 3, 2018

Ways to Create Space for Signaling in Games

Hot on the heels (for me) of my previous post about "Games of Strategy" (June 1: Design Pattern: Repeat Play Within A Single Game) I just finished reading chapters 9 and 10.  OK, I mostly skim read.  Chapter 9 on uncertainty and information was interesting but I did not feel the connection to game design as strongly as some past chapters.  Chapter 10 on strategic moves had some really interesting core ideas and LOTS of examples... that I started skipping.

Look, if I'm going to finish this book any time soon I've got to make some compromises.

by Delapouite via game-icons.net
What is Signalling Again?
Signalling is something that the book discussed back in the first couple of chapters.  I talked about it a bit here.

Signaling is when you say or do something that implies your intent for the future.  It can be anything from an absolute guarantee that you will do X to a completely untrustworthy proclamation.

Chapter 10 talked a lot about signaling and strategic choices around signalling.  Parts of chapter 9 also delved deeper into signaling.

Why Do We Like Signaling?
I think signaling provides some really interesting strategic opportunities.  Social deduction games are an entire genre of around signaling.  Werewolf and The Resistance and their kin are built around trying to signal which team you are on -- either in truth or not.  Sometimes the signalling is all in the table talk but often there are mechanics that act as signals too.

Why does signaling have such value?  It gets to the core of what makes a game.  Remember that this book defines a strategic game in large part by having two or more participants who are aware of the impact their choices have on each other.  Signaling messes with that awareness and can add depth to the simplest of games.

Just think about Werewolf.  This is a game whose only required component is a small deck of cards -- from which you get 1 card each for the whole game.  Werewolf also has very, very few mechanics.  After set-up you basically have two things to do: talk and then decide who to hang.  That's it.  And yet this is a game that defines a genre and a game publisher.

Now lets look at three things that I think can be captured in game mechanics and generate space for signalling.

by Delapouite via game-icons.net
1) Partially Aligned Interests

In Chapter 9, the authors talk a lot about talk as a signal.  The big take-away is that talk's value as a signal is related to how aligned the interests of the participants are.  

If the players have perfectly aligned interests (and know it) their talk is a pretty reliable signal.  Think co-op games.  If the players' interests are completely competitive then talk is completely unreliable and best ignored as a signal.  But that leaves an interesting space in the middle -- a situation the authors term partially aligned interests.

Dead of Winter is a decent example of this.  In Dead of Winter, most players a shared public object and a unique secret objective.  So one goal is shared with the group and yet the other goal is not shared and sometimes those two goals are in conflict.  This creates an interesting dynamic where apparently sub-optimal plays can either be willful sabotage (there can be traitors), bad luck (they just don't have the cards to help), or prioritization of the player's second goal.


by Quoting via game-icons.net
2) Voluntarily Reducing Your Freedom of Action

The end of chapter 10 had a great section on ways to add credibility to your signals.

The first main category was reducing your freedom of action.  This harkens back to their old example of the game of chicken.  If the driver of one car throws her steering wheel out of the car, you know she isn't turning.  She is committed to going straight and you better turn.

I can't think of any games that really use this idea mechanically but I feel like this would be really interesting.  What if a game gave a significant advantage to the player who went first, but that player had significantly fewer options on their turn?

Hmmm...


by Delapouite via game-icons.net
3) Public Betting on Outcomes

The second big category in this section was entitled changing your payoffs.  This is something I do have some good examples for.  Nearly every horse racing game has you bet on different horses.  Sometimes publicly, sometimes not, sometimes semi-publicly.

Titan: The Arena is a good old-school example.  In Titan Arena you bet on various monsters that may or may not last the round.  Obviously that action changes your incentive to have that creature win and strongly signals that you will and can do things to keep the creature around.

Further Discussion
I'm behind in my listening to the podcasts by Messrs. Aaron, Austin, and Paul on these topics.  Here they talk about Chapter 9... here Chapter 10.  

I'm going to go do that now, in fact.

Friday, June 1, 2018

Design Pattern: Repeat Play Within A Single Game

I know, it has been a while since I last talked about "Games of Strategy" (October to be precise: Why Do Players Do It Wrong?).  But I did knock out chapters 6, 7, and 8 over the winter... and then got busy and stopped blogging.

So lets talk about repeat play.  I once heard Richard Garfield say that poker is close to being the perfect game.  One of the biggest reasons being that each iteration is very short and so the game lends itself very well to lots of repeat play.

I do not remember him going into all of the game theory behind why repeat play is so good (I suspect he knows and was just trying to spare his audience the math).  After reading this part of Games of Strategy I think Mr. Garfield was right to avoid the math.

Just kidding.  A little.  I did skip much of the math...


... But the idea of repeat play was my biggest take away from this part of the book.  So lets get into the weeds on why repeat play is good and then talk about my big idea of how to take advantage of repeat play when your game takes 2 hours instead of 5 minutes.

Mixed Strategies

In chapter 6, the book discussed mixed strategies.  The idea of mixed strategies will be familiar to anyone with a passing knowledge of strategies in sports from football to baseball to the book's favorite example of tennis.  A mixed strategy is when the ideal play is to randomize between a sub-set of choices.

For example, no football team will pass the ball every down -- even though it is almost always more effective.  Instead they run the ball some times... even on 3rd and long.  If teams did not mix their strategies, the defense would be able to predict the offense's strategy and pick the best defense every time.

The math I glossed over can show you the ideal mix of strategies -- maybe 60% pass and 40% run.

Repeat Play

But this all really works best if play is repeated.  If you are only playing one hand of poker, you play to win that 1 hand.  You are much more likely to simply use your best strategy. 

If you are playing an entire evening of poker, you are playing to win the night not each single hand.  Now it makes sense to vary your strategies.  Sticking with only one strategy through-out will just not be the most effective as the night progresses.

Games Within Games

Poker is a great example of repeat play creating a wider strategic space.  More options open up because you play the game over and over and various mixed strategies become the ideal options.

This is much more fun than a single game of poker.  But poker is a 5 minute game.  How do you do that if your game is an hour long?  How likely are people to play that hour long game more than once in a night?  Does repeat play have the same affect if the plays are months apart with different opponents?

What if a single long game can contain smaller mini-games that do repeat?  What does that look like?

The quick answer is that it looks a lot like a football game or a night of poker but I think there is a complication inherent in larger board games that you don't have in sport or poker.

I envision that the strategies I chose for the mini-game would not be constrained by the strategy I have for the whole game or by my current standing in that game.

I think this separation between the larger game and the mini-game is important.  If strategic options in the mini-game are affected by the larger game some of the mini-game's strategies can be made in-effective.  If that happens enough, than the mini-game loses its opportunity to have the 2-3 strategic options needed to allow for mixed strategies.

The Zero Sum Euro?

Euro games are largely non-zero sum games -- what you do hardly affects me at all.  This contributes to the lack of interactivity in most euros. 

It also means that strategic mixes are generally worthless.  The whole point of the strategic mix is to keep the opposition guessing.  But in most euros they are hardly paying any attention to you at all.

What if you put a zero sum mini-game inside a non zero-sum euro?

Now, I care what you are doing -- at least inside that mini-game.

Caveat

I do not hold out this idea as any sort of ideal of game design.  I enjoy a good 3-4 hour game that I will never repeat. 

But the idea of combining repeat play within a larger context is an idea I would love to explore.

---------------------------------

Hat Tip to Isaac Shalev at Kind Fortress who introduced me to the idea of game design patterns.  And to the excellent Lodology podcast where I first heard Mr. Shalev discuss design patterns.

Wednesday, October 4, 2017

Why Do Players Do It Wrong? Barriers to Nash Equilibrium in Game Design

I have finished reading chapter 5 of Games of Strategy by Dixit, Skeath, and Reiley.  You know the drill -- here are Messrs. Aaron, Austin, and Paul with their conversation.  If you listen to the end and notice that they mention me... here's my post they were talking about: "Is a Solo Game a Game and Other Thoughts on a Colloquium on Games of Strategy" and here is the podcast I appeared on to talk about it.

Nash Equilibrium
A lot of this chapter is the authors' defense of Nash Equilibrium.  They address a number of criticisms of the theory and provide their counter arguments.

Quick refresher... a Nash Equilibrium is when all players figure out that there is a single action each should take to maximize their return.  Effectively it is the combination of actions that is everyone's ideal play in a particular game.

Why is this important?

As a game designer, I think it is crucial to know if your game has ideal plays and how easy it is for players to recognize those ideal plays.  In some cases I want it to be hard for players to find a single ideal play.  I want multiple options to at least seem equally viable.  Otherwise people do not feel like they are making important choices.

In other cases I want players to realize what their best options are given another player's move.  If it is not obvious how to counter one player's move, that can lead to a bad experience for all.  This is especially important in asymmetric games.

If we assume that players can logically or intuitively find Nash Equilibrium, obstacles are important to know about.  In no particular order, here are some of the obstacles they discussed.  All of which can lead people to playing non-ideal strategies whether you want them to or not.

Loss Aversion
Loss aversion is the well studied psychological effect where people are much more concerned about what they might lose than what they might gain in any particular situation.  The loss of $100 is felt more than a gain of $100.

Consequently, while the math may definitively point to an ideal play, loss aversion might steer people away from it.

Belief of Others' Choices
One of the cornerstones of Nash Equilibrium (and most of game theory it appears) is that each player has perfect knowledge of the other players' choices and the associated values of those choices to those players.

But if one player is wrong about their assumptions or misinformed or simply makes a mistake, they can think they have an ideal strategy when they do not. [ 1 ]

Complicated Systems
This is not a specific concern that the authors' raise but there is a part of this chapter that is very math heavy: "...each player's payoff is a quadratic function of his own strategy..."  I guarantee you that very few players are doing quadratic functions in their heads at the table.  Some might get close.  Some might intuit an approximate answer.  Some might do the equations in their spare time at home.  But most will not.

Which means that a few people may know or be very close to knowing ideal plays while others will not.

Experience
As hinted at above, people often do not figure out a Nash Equilibrium immediately.  Sometimes it takes trial and error before players figure out the ideal plays. [ 2 ]

But unless the same group of people have the same amount of experience, you can end up with people who have different understandings of the ideal play.  In some cases this might be ok.  Some games are designed to be very competitive.  But this is also why cooperative games can turn into solo games.

Example Time
Pole Bidding in Championship Formula Racing is a great example of all of these barriers to finding ideal plays.

Starting a race of CFR in the front row is better than starting in the back.  The game tries to balance this by making people bid for position on the starting grid.

But several players have noted to me that people generally do not bid enough to balance out the various grid positions.  Statistical analysis suggests that they are correct.

Why?

I assume that there is a Nash Equilibrium that exists for every position on the grid and what the ideal bid is for all players that would result in an even valuation of those spots.  However, I can see that there are a lot of reasons we don't end up there.

I think the biggest issue is complication.  There are a ton of variables involved in this calculation including the number of players (from 2 to 12) and different tracks.  I honestly have no idea what the value of these bids should be.  Since I'm not sure anyone can accurately value these bids, no player will have perfect information about everyone's choices.  Loss aversion could also be a factor.  You lose what you bid... so that could certainly tamp down the amount people are willing to bid.  Given the wide number of tracks available and the fact that many players I know play against a wide range of competition, experience is hard to apply from one race to another.

Solutions?

One adjustment I made to encourage larger bids was to break the bidding into two parts.  The idea was to create more of an auction feel.  People are generally known to over-bid in auctions because the desire to win an auction can skew one's valuation of the thing to be won... turns out my players are smarter than that.

I'm trying to solve the complication barrier by doing more and more statistical analysis.  It might help eventually, but I'm not there yet.

Experience has always been my hope for the fix.  That would require a bit of a closed ecosystem of players and tracks that I tend to avoid but others could certainly enforce within their own groups.

Conclusions
I hope I illustrated above how these criticisms of Nash Equilibrium can be very helpful in trying to solve game design challenges.  I definitely think that the logic can be useful even if it has not solved my bidding problem yet.

In Case You Missed It
Last chapter I discussed how I thought that the tools they discuss can be tools for finding broken bits of a game design -- Nash Equilibrium included.  This chapter they offered up another variant in that vein: plays that are "never the best response."

Footnotes and Sidebars
[ 1 ] Interestingly, this idea that the correct application of game theory hinges on perfect information about your opponents' choices and how they value them reminds me that there are games that can be broken by random play.  I had a good friend who would play poker without looking at his cards.  Which made people's attempts to determine his strategy hopeless.

[ 2 ] Playtesting note: the authors note that people learn somewhat faster by observing others play than by playing themselves.  

Wednesday, September 6, 2017

Finding A Game's Broken Bits

I have finished reading chapter 4 of Games of Strategy by Dixit, Skeath, and Reiley.  Before I provide my thoughts, again here are Messrs. Aaron, Austin, and Paul with their conversation.

Reading this book as a game designer is both fascinating and a little odd.  Chapters 3 and 4 have both taken the same basic approach: analyzing the best way to "solve" a specific type of game.

My knee jerk reaction to this approach is concern.  If you tell a game designer that you solved their game I suspect you are breaking their heart.  It would certainly break mine.  To me, solved games are broken games.

But I think designers can take this a step further.  We can't stick our heads in the sand and pretend our games aren't broken.  Instead we should use the tools Dixit, Skeath, and Reiley discuss to discover the specific bits that are broken so they can be fixed.

So what are we looking for? In chapters 3 and 4 the authors have focused on finding three different things that would make your game broken: Dominating Strategies -- the strategy that always wins, Dominated Strategies -- the strategies that never win, and Nash Equilibria.

In the hobby game environment a Nash Equilibrium feel to me like those odd ruts you get into where Player A feels obliged to do X and Player B feels obliged to do Z in response and they never really have a good reason to do anything different.  In fact, every other action they could take seems less optimal.  I suppose this is just a redefinition of a Nash Equilibrium -- a combination of strategies or choices where each player gets the best value given the variety of each others' responses.

And how do we find them?  In chapter 3 the authors discussed decision trees. In this chapter they introduce the decision matrix.  Where trees helped analyze sequential move games (I take a turn, you take a turn, ...) matrix help analyze simultaneous move games.


Above is a matrix for Rock-Paper-Scissors.  The results are expressed from the perspective of the Right Hand.  RPS is a 0-sum game so we only need one set of results.  In non-zero-sum games you would list a number for each player showing their reward in each situation.

One thing you can say about RPS is that it does not have a dominant or dominated strategy.  Below we change the rules of the game to say that rock always wins but still ties against another rock.  And the matrix clearly shows that rock is the dominant strategy.


Now this would have been obvious without a matrix, but most games are more complicated.  Below is a decision matrix for a very specific situation that can come up in Championship Formula Racing.

Image two cars in a racing game sprinting for the checkered flag. The trailing car could end up gaining spaces from slipping the lead car in certain situations.  Without going into all the rules and reasons why, here are the cars' choices and results from the perspective of the lead car.  Also note that a result of 0 will likely mean that the lead car wins.


Dominated Strategies: For the trailing car, going 160 is dominated... it never results in the trailing car winning.

Dominating Strategies: There are no strategies for either car that always wins.  200 is closest for both cars, but if they both play 200, the trail car will win.

Nash Equilibrium: There is no Nash Equilibrium either.  No matter what speed one car picks, they might have a better play depending on what speed the other car picks... basically this scenario turns into a guessing game.

Below is a matrix for the same situation but with different choices.



Dominated Strategies: If the trailing car goes either 140 or 160, they can't win (remember 0s mean they will lose).

Dominated Strategies: Meanwhile the lead car can not lose if they go 160.

So this situation is clearly solved.  If this where the whole game, this would be a problem I would need to fix.


Tuesday, July 18, 2017

The Tragedy of the Game Commons

I finally got around to reading chapter 3 in Games of Strategy by Dixit, Skeath, and Reiley.  I've fallen way behind Messrs. Aaron, Austin, and Paul.  They recorded their discussion of the chapter and Paul followed up with some written notes as well.

Decision Trees
The decision tree is a method put forward by the authors for how to create a strategy for a sequential move game -- a game where each player takes a turn in sequence as opposed to simultaneously.

These trees or flow charts start with a list of the choices the first player has -- each option being a different branch of the tree.  The second player's options branch off of each possible play by the first player, etc.  So If my choices are A or B and the second player's choices are Y or Z then the tree would look like this:


The four boxes on the right side are the 4 possible end results of this two-turn game.  From here, you can analyze the value of each of those 4 results, then predict the 2nd player's best actions after either A or B, then decide what the first player's best choice is.

Multiple sequential turns can be added on and further branch from here to model the entire game.

Tragedy of the Game Commons
One specific example in the book immediately reminded me of a classic awkward gaming moment.  In the example a handful of neighbors decide, in turn, if they will pitch in to fund the upkeep of a common area.  Although they all want the area maintained, only a certain number of them have to pitch in to make it happen.  After building the decision tree, the game theory "correct" play for the first person is to never fund the upkeep because the other people will.

In economics there is a similar concept called the tragedy of the commons.  Which describes how in real life no one ends up paying to maintain the common area described in the books example.

I think we've all seen this behavior in board games.  One player is winning and something must be done to stop that person.  But stopping the leader does not help the person doing the stopping -- it only hurts the leader.  So no one wants to.

Eventually, everyone teams up to stop the leader or one player is forced to do so and this never feels fun.  In fact, sometimes it feels so un-fun that no one ends up prevents the leader from winning.

Obviously, Tragedies of the Game Commons are something games should strive to avoid.  Can decision trees help us designers see them coming?

Tuesday, May 2, 2017

Street Racing: a hand management, push your luck game for 2 players


This game was inspired by two complaints about racing games I heard from different people in the industry.  Jim Dietz of Jolly Roger games once told me that there were not enough two player racing games.  Not long after that Tom Vasel wondered why racing games were never quick playing.  I don't recall which review it was in.  Both comments stuck with me and at the risk of pigeon holing myself, I started working on a quick-playing, two-player racing game.

Ironically, BGG is currently running a 2-player game contest that I entered the game in.  So if this already intrigues you, go print out the game and give it a play.  While you are there, find other 2-player games you might like.

Development

The initial version was an attempt to model real life production sports cars.  Each deck of cards had different values for acceleration, braking, and handling.  Each turn you would play any number of cards one value or another.  When you hit a corner, you would draw tokens from a bag equal to your speed minus your handling hoping not to draw too many of the bad ones.

The initial problem was that card draw luck was too dominant.  Each card could only do one thing.  If you did not draw enough of what you needed, when you needed you would lose through no fault of your play.

So I gave each card two abilities at different levels.  This helped, but the whole system was still too much based on card draw luck.  Each player had an identical deck of 12 cards.  Which 4 or 5 you drew to start and as the game progressed defined your play.  There really were not enough good choices in the game.


As I continued to refine and play test I realized that I needed to simplify and focus on the two elements I had chosen for the game: hand management and push your luck.

Push Your Luck
In early versions of the game, you would draw a certain number of tokens from a bag based on your speed.  In this version, each time a token is drawn the player can chose to stop and slow down or continue drawing tokens and possibly incurring a penalty.  This ratcheted up the decisions.  Instead of making 1 push-your-luck decision per turn, a player could end up making several different ones as their turn progresses.

Hand Management
I decided to thin the deck down to 5 cards and give all 5 to each driver to start the game.  This focused the game on your choices of when to play each card and removed the luck of the draw.  I also tried to create different decisions based on your opponent's play and your current hand size.

Each card is numbered 0 - 4.  The value of the cards indicates how much to increase your speed this turn.  Faster is pretty much always better.  Some cards also give you a bonus to handling.

The Push (4) card is generally the best card you have with the highest value and the best handling bonus.  But the only way to put cards you have played back into your hand is to play other cards with special abilities.  So you will have to play other cards.

The Pass (3) and Block (2) cards can do different things base don your opponent.  The Pass card is actually better than the Push if your are behind in the race.  While the Block card counters the advantages of the Pass card.

The last two cards will have to be used to replenish your hand.  The Cruise (1) allows you to put one of your previously played cards back in your hand while the Coast (0) allows you to put all of your cards in your hand.  When to play each of these cards is crucial to a fast race.

Play Test
As I noted above, the game components and complete rules are available on BGG.  Please note your thoughts on that page and try out other games in the contest too.

Friday, March 31, 2017

Is a Solo Game a Game and Other Thoughts on a Colloquium on Games of Strategy

The esteemed Aaron and Austin of Dr. Wictz fame started a Colloquium with Paul Owens as they read through college text book "Games of Strategy" by Dixit (no relation to the board game), Skeath, and Reiley.  I have always found Aaron and Austin to be smart engaging people and I love the word Colloquium but I didn't want to listen to their take before reading along.

On the internet I picked up a copy of the 3rd edition, because the current version is priced as if the only people who would consider buying it are the rich parents of Ivy League students.  I'm through chapters 1 and 2 now so I went back and listened to the Colloquium part 1 which covers the same ground.  Then read Mr. Owen's Notes on Games of Strategy -- an addendum to a colloquium?

So now I'll talk about my thoughts relating to solo games, signals, screening, and my nomination for the most meta textbook section title ever.  Some time in the future I'll read chapter 3 and talk about that.

Is a Solo Game a Game?
Early in their discussion Aaron, Austin, and Paul discuss the book's particular definition of a strategic game.  First, that for a game to be strategic, it can not be purely skill based (a 40-yard-dash) or completely luck based (Russian roulette).  They also suggest that a strategic game requires two or more contestants that are mutually aware that their choices impact each other.

Aaron, Austin, and Paul suggest that the particular style of Euro games described as multi-player solitaire may not qualify as games under this definition.  Paul in his blog post suggests Black-Jack as a non-game under this definition as well.  All because each player's actions are made without regard for their opponents actions.

Maybe because I've spent some time recently thinking and working with solo rules for Championship Formula Racing, I immediately wondered if a solo game of CFR is not a game.  Is any board game I play solo a game?

If we take the book's definition literally, the answer is no.  In fact, many co-operative games may not be games either.  But if we treat the AI at the core of the game as if it were a person, does that change the answer?

Does the AI use other player decisions as inputs for its decisions?
For CFR the AI's decisions are made independent of what decisions other drivers have or may make.  So it may not be a game at that point... it might be a puzzle.  I feel like that might be true of many solo (and co-operative) games.

However, I could see how games could have AIs that take player actions into account.  I would not be shocked if it has not already been done.  More importantly, how could I add that to the AI in CFR or other games I might design?

If it feels like the AI is taking my decisions into account, does it matter if it isn't?
If I think the AI is using my decisions to inform its decisions I think I am playing a game.  That feeling is not actually dependent on the reality of how the AI works.

This may not happen a lot in board games, but it does with video games.  Many video are solo experiences where you feel like you are playing a game as Dixit, Skeath, and Reiley define it.  We know there is no human on the other side, but we certainly suspect that our actions and signals change the game's behavior.

I have often found myself playing a solo game of Plants vs. Zombies Heroes and completely forgetting I was playing the computer and not another person.  I will find myself thinking that they are likely to kill this Zombie because it can be trouble later and that's what other players often do.  Then I remember that I'm not playing a person.  I am playing an AI that may or may not be taking my play into account for its decisions.

Signalling and Screening
This is another really interesting concept that was touched on in chapter 2 of the book and discussed at length in the colloquium and also Paul's blog post.  It can also be a hard concept to grasp.

These concepts were raised in the book in the context of games with imperfect information.  A signal is defined as a decision that credibly reveals information you have and your opponent does not.  Screening, on the other hand, is a decision that is made in an attempt to force your opponent to make a signal.

Signals seem a relatively easy concept although you can hear Aaron, Austin, and Paul struggle a little with credibility and bluffing and how they relate to signals.  Screening sounds straight forward until you try to give examples.

Examples
Scotland Yard was brought up in the colloquium as a great example of a game with imperfect information.  In that game, a signal as Mr. X might be to play a metro token.  It clearly signals that I am on one of a limited number of spaces.  Taken together with previous signals, it signal gets even clearer.  On the other hand, moving an investigator towards one of those metro spaces might be screening -- an attempt to force Mr. X into further signalling such as the use of a x2 token to escape near capture.

In Championship Formula Racing certain car builds signal certain strategies.  A 100 start speed probably means that I am trying to race from the front.  It may not, but it probably does.

In most collectible card games, certain cards signal certain deck types.  In Plants vs. Zombies Heroes, playing a Headstone Carver signals that I am playing a lot of other gravestone zombies.

Do signals have to be true?
I think there is a difference between true and credible and wonder if there is a continuum that signals exist on where bluffing may be on one end.  Is there a point on this continuum where the action stops being a signal?  How awesome that continuum and colloquium are both words in this sentence?

I suspect these concepts will be investigated more later.  We'll not the one about continuum and colloquium.

What's up with screening?
Coming up with good examples of screening that are not parts of hidden movements games seems really hard.

Sure, hidden movement may be one of the more common and more extreme imperfect information game types right now.  But many, many games have at least some imperfect information.  Lots of games have hidden personal objectives or hands of at least relatively unknown cards.

This feels like open design space.

Most Meta Textbook Section Title Ever
Section 3 of chapter 1 is titled "Our Strategy for Studying Games of Strategy"

Textbook mic drop.

Tuesday, March 7, 2017

Asymmetry in Plants vs. Zombies Heroes

I've been playing a lot of Plants vs. Zombies Heroes lately and have really come to appreciate the asymmetry Electronic Arts designed into their free-to-play CCG -- elements that could certainly be borrowed for physical game design.

In case you've never played... PvZ Heroes has some pretty standard CCG elements to it: 40 card decks, cards arranged into classes, power for playing cards increases by 1 every turn, 20 life, race to kill your opponent.

While deck construction provides all CCGs with some built in asymmetry, PvZ Heroes adds layers to that by making your opponent play with completely different cards in a completely different way.

Turn Structure
True to the game's name each match pits a zombie deck against a plant deck.  This means that your opponent's deck has zero chance of sharing a card with yours.  But the 4 phases of a turn really extend the asymmetry:

  1. Zombie Plays -- but only creatures not tricks (think spells)
  2. Plant Plays -- anything the want
  3. Zombie Plays -- but only tricks not creatures
  4. Fight -- each lane does the usual damage exchange
So the zombie player has to commit their troops first -- generally a disadvantage.  Also, they are limited to only creatures in this first phase, no tricks.  So they have to think through their card interactions.  They can't play a trick and then a creature.  They have to remember to save some brains (zombie power) for the tricks phase if they think they need it.

Plants get to play any of their cards in any order during their phase.  They get to see and react to where the zombie forces are.  But they have to wary of that zombie trick phase.  How many brains has the zombie saved for their tricks phase.  Does that telegraph a play or did they just run out of stuff to do.

Card Differences
This asymmetric turn structure is reinforced by the kinds of cards each faction has.  Zombie creatures tend not to affect other creatures or the opponent when they are first played.  Most zombie cards that affect other creatures or players are tricks.

When a zombie player puts a creature on the board, they often have to sweat out the plant phase before they can buff it.  That buff they hoped to play in the tricks phase may not have a target by then.  Or the plant they were hoping to remove from play in the tricks phase may get buffed out of range of the zombie removal.

On the other hand, if a zombie player is out of brains the plant player can play a creature they can't buff until next turn.  Knowing that the zombie player has few options in the first phase for creature removal.

On the other hand, when a zombie player has brains left for tricks, nothing done in the plants phase is safe.  While the zombie player knows that they will have the last chance to change the board state before combat every turn.

Gravestone and Trick Zombies
Of course, there are exceptions and the exceptions can be very interesting.  There are Zombie tricks that summon creatures (but not a lot).  And then there are gravestone Zombies.  

The Hail-a-Copter trick can summon a particularly large zombie (admittedly the trick is expensive to play).  By being able to play it in the tricks phase, the zombie player may be able to be more tactical about its placement knowing the plant player can not respond until next turn.

A gravestone zombie is hidden in a "gravestone" when it is played.  The plant player does not know what it is and can only affect it with a small number of cards.  Also, the amount of brains spent on that creature is hidden.  So the plant player is left guessing as to what the zombie player did.

When the tricks phase starts, all gravestones are revealed in order (left to right).  A good number of gravestone zombies have affects that trigger when they are revealed.

For me, these exceptions play into the whole structure of the game.  These cards interact with the asymmetry in different ways than a traditional CCG.

First Player Advantage
Another thing I like about PvZ's asymmetric turns is the unique way its deals with the first player advantage.  Magic was forced to tack on rules to try to deal with first player advantage.  Hearthstone built in the coin idea but both are simply add-ons.

I don't even think about first player advantage in PvZ Heroes.  Zombies always go first.  But in the context of the turn structure, I'm not sure how much that matters.

Final Thoughts
This is a level of asymmetry that you usually see in a complex dungeon crawl or hidden movement game.  Among CCGs, this reminds me more of NetRunner than anything else.  I can't help but wonder how creative asymmetry can be used in board game design.  It feels like an area of fruitful exploration.

While not intended as a review, I will close by saying that I do recommend Plants vs. Zombies Heroes.  In addition to my thoughts on the core game design, it works well and does not fall into the pay-to-win trap that hurts many free-to-play games.  I have not spent any money yet and am still enjoying the game.

Wednesday, June 15, 2016

I'm on a podcast

Furthering my sister's theory that I am now famous... I'm on a podcast talking about Championship Formula Racing.  Go take a listen and many thanks for the great people at Random Access Podcast.  They were great, had good questions, and were very patient with me until I figured out that my computer mic was turned off.

http://www.rapodcast.net/

Thursday, June 9, 2016

Creating Automated Opponents (AOs) for a Board Game

When Jim Dietz and I discussed the final form that Championship Formula Racing (CFR) would take, one item in particular stood out on Jim’s wish list - a way to race against the best drivers in history.  The vision was to create a Historical Driver system where different drivers had different personalities, tendencies, and difficulty levels.  It was important that the top historical drivers in the world would be hard to beat, not just rolling obstacles.

I wasn’t sure how this would work when I started but this ended up as one of my favorite parts of CFR.  The challenge forced me to consider some core concepts for creating Automated Opponents.  Below I’ll share what I learned for any other game designers or tinkerers who might also want to go down this road.

Identify Strategies
My first step in creating an Automated Opponent (AO) was to figure out what broad strategies I wanted each to pursue.  Most hobby games have multiple paths to victory.  Write down those paths and variations and note which are more popular than others.   Don’t worry if some strategies are not as good as others.  If people pursue a strategy, include it on your list.

Having multiple strategies that an AO can follow allows you to have multiple AOs that end up doing different things.  Some games are just better with a lot of players so the ability to have multiple diverse AOs can fill in that gap.  If only a few AOs would ever be used at the same time, a variety of AOs will keep each use fresh.

I like an automated system that makes me feel like I am playing against actual opponents.  Real players have tendencies and goals.  Making popular strategies better represented or more frequent in your AO design will keep the meta game consistent with or without AOs.

Championship Formula Racing Example

In CFR broad strategies focus on how quickly to spend your resources.  Spend them early for the early lead and try to hold on, save them for late in the race when everyone else running on bald tires, or spend them evenly throughout the race.  I created variations on those three broad strategies for the AOs in CFR.  However, the popularity of different strategies varies based on the track being used so I tweaked each AO to pick a different strategy based on the track.

For example, James Hunt will use one of three different strategies: U (more of a mid to late game strategy), Mathy (more of a mid to early game strategy), or Front A (an early game strategy) -- typically in that order.  But if the track is particularly suited to an early game strategy he reverses his order of preference.  Most of the Historical Drivers in CFR do something similar.

Decision Trees and Set-Up
Now that we’ve identified the broad strategies that our AOs will pursue, we need to build a decision tree for each. 

For each strategy, figure out what their ideal play would be and rank all of their other options based on how that will help their strategy.  As a general example, if an AO is pursuing a military strategy in a game, their first choice for an action on a turn could be to buy the largest sword, second choice might be to buy more armor, third choice… etc. 

You’ll probably figure out pretty quickly that there are variations on how an AO could pursue the same basic strategy.  Maybe one flavor of military AO buys swords first, while another makes sure to balance swords with armor.

Don’t forget set-up.  Are there set-up options that might favor one strategy over another that individual players can choose?

CFR Example

CFR’s basic strategies lend themselves pretty cleanly to different choices on a given turn.  But the reality is that these strategies exist on a continuum so I ended up creating 10 different strategies along that continuum:

Front X: uses a ton of resources early and then keeps spending resources until it is in the lead
Front A: pretty much uses resources as much as it can until it runs out
Front B: uses some resources early and then really uses a lot of resources in the middle of the race
Stalking: uses some resources early to stay ahead of most cars, then tries to use resources evenly from then on.
Mathy: will use resources for best effect as soon as possible
Even: attempts to use resources completely the same and evenly throughout the race
U: uses some resources early, saves resources in the middle of the race, then spends the rest at the end
Random: starts out saving its resources, but can switch to spending everything at any time
Back S: spend little at the beginning and then spends more for the rest of the race
Back X: spends little for most of the race before spending everything at the very end

Set-up is also a big part of CFR.  Certain car builds and pole bids lend themselves to different strategies.  If you want to spend your resources early for an early lead, you might as well design a car with a high start speed and spend more on the pole bid to start at the front of the grid.  Obviously there is a continuum to set-up options as well.

Tactics Change as the Game Progresses
A diversion into my theory on the three phases of game play, as illustrated by Ascension.  This structure does not apply to all games but it does apply to a lot of medium to heavy weight modern board games.

Many games can be split into three parts: Build the Engine, Run the Engine, Grab Points. 

Early in a game, you want to acquire the tools that you need to pursue your strategy.  When I play Ascension, I spend the early game acquiring cards that let me best acquire more cards or kill off the junk cards I started with.  Initially, I don’t care how many points cards are worth, and I don’t care how cool its special power is unless it gets me more cards or kills more junk.

Once you have your tools, its time to augment that engine and run it.  Twenty points into a sixty point game of Ascension, I switch over to buying cards that have synergy with what I’ve already acquired.  I’ll pay a little more attention to point values now, but mostly I’m running my engine.  I’m probably not continuing to acquire more ways to thin my deck.

Near the end of the game, there are no long term consequences for your actions - it’s all about the short-term play that helps you win.  In the last twenty points of a sixty point Ascension game, I no longer care if the card works with what else is in my deck, and I stop thinning out junk unless it’s harmless to do so.  It’s all about  acquiring maximum points.

Now think about the game for which you are designing your AOs.  Are there recognizable phases?  How do you measure which phase you are in.  Is it based on the progress of the game, or a player based metric?  Should your AOs’ decision trees change based on the phase of the game?

CFR Example

CFR strategies are all about how your tactics change over the course of the race.  I developed two tools to trigger those phase changes.  I split each lap into three sectors.  No matter how many laps are being run, we can figure out if we are in the first, second, or last third of a race.  Next to each corner I noted how many corners were left in the race.  Corners are where resources are spent, so knowing how many corners is left compared to how much wear an AO has left is an alternate way to figure out what part of the race that strategy should be in.

For most of the race my Even strategy will spend resources depending on if the car has more resources then the number of corners remaining.  That way, the car spends resources pretty evenly through out the race.  On the other hand, the Back S strategy will spend very few resources before the 2nd third of a race.

Obfuscate
If I know what the AO is going to do before the AO does it, that AO will be a lot less effective.  This will be more or less true depending on the level of player interaction.  If there is little player interaction, you might be able to skip this step.  If there is a lot of player interaction, this step is crucial to creating a competitive AO.

Randomness is your friend here.  Each AO should have at least 2 things it might do on a given turn, or two ways it might do those things.  This way, human opponents are not completely sure what it will do.  Be careful not to resolve that randomness until you absolutely have to -- right before the AO needs to take an action or figure out if they will take an action.

But don’t take the randomness too far unless that is the actual strategy.  You want the choices an AO takes to make sense for its strategy.  The choices may just be slight variations of each other.  They probably should not be completely opposite.

CFR Example

I made sure that each AO in CFR had a choice between at least two different decision trees during each phase of its strategy.  Often this was just a reordering of choices or a slight variation.  After every corner you roll dice to re-pick a decision tree for the next corner.

On the right you can see a sample phase from CFR's Front A strategy.  Each line is essentially a decision tree giving the car 2 to 4 different choices for how many resources to spend in the next corner.  In turn this will determine the car's speed.

The choices at the top direct the car to spend more then the ones further down until the stars indicate that those resources will only get spent if the use is particular efficient use.

Simplify then Cheat
After all of this, your AOs are likely bad at the game and your decision trees are so complicated that it takes twice as long to take an AO turn as a real turn.

Go back over your decision trees and simplify them.  Then do it again.  Pay particular attention to anything you had previously done to obfuscated or randomize AO actions.  Does the obfuscation or randomization make it more time consuming to play an AO turn then a human turn?

Now find ways to have your AO "cheat".  Cheats can do three things: speed up AO play, make AOs harder opponents, and give AOs more character.

For instance, consider some mechanics that might take a while to resolve.  Having an AO always succeed at performing one or more types of actions will speed up play, make them better at the game, and reinforce their personalities and strategies.  Having an AO "cheat" more or less will also make some AOs better than others.

CFR Example

Originally, I obfuscated too much.  The symbols I used in decision trees had little relationship to the choices they represented.  I eventually switching to symbols that better represented the action desired, were easily remembered, and required less translation.

Basic AOs in CFR are passable, but to create challenging AOs I added a number of "cheats."

Many get bonuses during set-up.  This is my main method for creating some AOs that are harder than others.  A normal set-up in CFR uses 2 points to build a car.  Stirling Moss' car, shown on the right, uses 4 points including some options (9 wear per lap) that are beyond what is normally available.

All of the AOs in CFR can auto-pass certain die rolls during the game.  This is mostly a time-saver, but also clearly gives them some advantages.  Normally skill is used as a die roll modifier that helps drivers temporarily improve their car's performance.  Historical Drivers use skill to automatically pass those same die rolls.

Finally, many have special abilities or bonuses that reinforce their character and strategy but also give them advantages.  Stirling Moss can effectively use 3 wear in a corner, which is illegal for anyone else.

Diversify Your AOs
Look at your AOs.  Are there parts of each that can be swapped into another similar AO to create something new?  That’s a great way to generate a lot more AOs then you thought you had.

For instance, maybe you built 3 AOs that are variations on a military strategy.  Each has a slightly different set-up and slightly different decision trees.  If you separate the set-ups from the decision trees and randomly recombine them before each game you now have 9 different AOs, where you used to have 3.

Or maybe you find that you can split each AO’s decision tree into 3 parts.  Now you have 3 early game decision trees, 3 mid game decision trees, and 3 late game decision trees for each military AO creating even more variety and obfuscation.

CFR Example

In CFR I created 10 different decision trees (strategies) and 24 different set-ups (drivers) that come with in-game "cheats."  Each set-up uses one of three different decision trees.

This went through many changes during testing.  Originally, I had 12 generic strategies that were married to particular set-ups.  Then I separated set-ups from strategies and was able to reduce both the number of strategies and set-ups but still retained a lot of variety.

Conclusion
The most important part of designing AOs is the same as all game design:  testing.  Very few games come with Automated Opponents.  So there is a lot of space to practice using the games already on your shelf.


I’ve started designing AOs for one of my son’s and my old favorites, Valley of the Mammoths.  I’ll share the results of that project when I’m done.  Below is what I ended up with for CFR (development, not final version).