Monday, October 1, 2018

Solving the Raygun Problem with Evolutionary Games

by Cathelineau via
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.


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

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
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


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

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


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.

Wednesday, September 5, 2018

Build Your Own Blood Bowl Team Boxes

Last time out I was building a custom foam storage box for Infinity.  This time, I up my game from foam to magnets with my own spin... washers instead of steel sheets.

If you want to use my backgrounds... here is a PDF.

As always, thanks to Braddock Station Garrison for the music.  You can learn more about them at

Wednesday, August 1, 2018

CFR Organized Play 2018 Wrap-up

By my count 12 drivers had enough points to contend for the title of 2018 CFR Champion.  But only four of them were able to make the trek to the final tournament at the World Board Game Championships.

Doug Galullo entered the weekend with a solid points lead after having won the largest online tournament (P1) and the smaller in-person tournament held at PrezCon in addition to winning 3 individual races.

Don Tatum was 2nd in the standings -- trailing Doug by less than 40 points -- a sum he could make up if he won WBC.  Chris Long and Michael Polcen were also contenders.  Ranked 4th and 5th respectively before WBC they were separated by less than a point in the standings and trailed Doug by roughly 43 points.

Qualifying at WBC was dominated by three drivers.  Chris Long won all three heats he was in while Tim Mossman and Doug Galullo each won 2 heats.  No other driver won a qualifying heat.

Going into that final race of the season the top four drivers on the season all had some shot at the title with Doug sitting at 190.34 pts, Chris with 170.53, Don at 147.28, and Michael Polcen at 143.23.  If any of those four drivers won the race they would also claim the Organize Play title.  Doug probably could have finished 2nd to anyone but Chris and still won the title.

Tim Mossman was also in that final race and had climbed the rankings to 9th after his WBC qualifying run but still sat nearly 80 points behind Doug.  Not even the win at the WBC finals would have vaulted him to the OP title.

Organized Play 2018 Top 20
In the end Michael Polcen did win the WBC Finals, took home the plaque for that event, and edged out Doug Galullo for the 2018 Organized Play Title by 6 points.  Chris Long ended up 2nd in the race.

WBC was representative of Michael's whole season -- characterized by excellent timing.  Michael did not win a qualifying heat but a 2nd and 3rd got him into the finals.  In fact, Michael won only 3 races all season.  Three race wins is nothing to sneeze at but Doug and Chris both had 5 wins on the season and several other drivers picked up 4 wins this year.  But Michael picked excellent races to win.  The WBC Finals rated as the most competitive single race all season.  Michael also won the 5th most competitive race this season (race 2 in the top tier of Redscape).  Michael also won two tournaments including the 2nd (WBC) and 3rd (Redscape) most competitive events of the year.

Doug Gallulo was a worthy runner-up.  Doug won 5 races and 2 events and is one of two drivers to finish top 5 in OP both years.  Chris Long came up just short of the OP title this year and also won 5 races this year.   Despite the 5 race wins, he finished 2nd in two tournaments -- WBC and P1.  Michael, Doug, and Chris ended the season with a mere 12 points between them.

Rookie of the Year
I erased some of my older rankings data so the definition of a rookie has changed a little this year to mean having not participated before in an official Organized Play event.  By which count 70 drivers of this years 144 were rookies and 8 placed in the top 25 on the season.

But Gainluca Lari was clearly the best of that bunch.  He did not race once in the inaugural OP season of 2017 but won 4 of the 10 races he participated in this year and won the San Marino season to end up 5th in the rankings!  Honorable mention to Gary Sturgeon who won 2 races and won the Detroit season this year to finish 9th overall.

Most Improved Driver of the Year
Mike Aubuchon had a difficult 2017 -- scoring points in only 1 race of the 5 he participated in.  Mike came back strong this year -- finishing 2nd in a WBC qualifying heat and 3rd in the WBC finals to improve his rank from 85th last season to 29th this year.

Honorable mention to Claudio Orlandi for improving 41 spots this year from 79th to 38th.

Steward of the Year
Every year is a tough year to pick out a steward for special recognition.  This year saw many new seasons spring up including Detroit and San Marino and Washington DC.  The time and effort of every steward is the reason this community continues to grow.

But this year, I'll tap Chris Long as Steward of the Year.  Chris runs what is easily the largest in-person tournament on the calendar -- regularly involving two or three races running simultaneously.  Chris also went through a lot of effort this year to collect feedback and input to make sure that his event was as good as it can be.

Tuesday, July 24, 2018

DMV Race Report: Season 2, Race 1 Cleveland

I finally made it to a DC-Maryland-Virginia CFR race back at the end of June.  Chris B ran a bunch of races in the area starting last winter for their first season but I was never able to make one.

This race used standard rules on a custom track -- Cleveland.

The median car build for this track was a 60-60-160 with 60 start speed, 7 or 8 wear and 2 skill per lap but there were some outlier from this stock build.

I ran the only 100 start speed which I'll discuss more later.  Three cars ran 20 start speeds: Don, Brian, and Chris.

Chris also went with the only 80-80 car.  Will and Tim decided that they did not need as much deceleration and tried 60-40 cars.  Tim was also one of two drivers to start out with 140 top speed.  Mike P was the other 140 car.

Chris and I were the only cars with 6 wear per lap to start out the race.  The 7 and 8 wear cars were evenly split with Kevin, Dave, Brian, and Mike G taking 7 wear per lap; Will, Tim, Mike P, and Don taking 8.  Brian and Tim took 3 skill per lap with the bonus -3 skill chip.  Everyone else went with 2 skill per lap.

Pole bid was very interesting with 6 of 10 cars sitting on 60 start speeds and only I had a 100 start speed.  If I could start on row 2 anywhere I could test start speed and end up in the lead before corner 1.  So I targeted that, bid 2.5, and got lucky.

Kevin took pole with a 4.5 bid.  Will ended outside row 1 with 4.  Tim was inside row 2 with 3.5.  My 2.5 bid represented pretty great value as I knew I could overtake the cars in front of me having spent less then them and only 1/2 more than Mike P who ended up starting row 3 after bidding 2.  Dave, Don, and Brian bid 1.5 which worked out better for Dave who ended up outside row 3.  Chris and Mike bid 0 to start in the last 2 rows but having spent nothing.

Kevin's yellow car sitting on pole.  Will outside row 1, Tim inside row 2, me outside row 2.

Lap 1

I take the lead on turn 1.  Kevin behind me on the line.
Will placed himself outside when he could have been in the middle lane.

First turn went as hoped for me as I took the lead heading into turn 1.  On that same turn 1 Will placed himself in the wrong spot -- outside when he could have taken the middle lane -- probably lost a space unable to take the line (I think he was thinking about a slip from Kevin that would never happen with the corner in front of them).  Hint, that 1 space might become important later.

My plan was to spend my wear evenly through out the race.  I wanted to be up front because it made things easier but I did not want to spend wear silly in order to stay out front no matter what.  I was content to stay in touch of the leaders.

Tim, however decided to make a break through corner 3 -- taking a chance and taking the lead for the rest of the lap.

Tim passes me through corner 3 with a chance.
Will pulls even and would also pass me here.

Dave was part of the main pack through lap 1, but miss-ploted on the straight at the end of lap 1 which really hurt his race overall.

Tim ended lap 1 about a turn ahead of Will and I with Mike P just behind that.  The rest of the field was about 2 turns behind Tim with Mike G and Chris about 3 turns back at this point.

Tim out front after 1 lap.  Note Kevin keeps falling back all race.

Lap 2
Will decides that it is his turn to make a move in the middle of lap 2.  Through corners 3, 4, 5 and 6 he spends a good bit of wear and gains a turn on everyone else.

Halfway through lap 2, Will has passed and gaped Tim and everyone else.

Brian spends some wear early this lap to move up from the main pack.  But runs himself almost out of wear before taking a chance in corner 8 that results in a spin.  He drops from 3rd to 5th before ending up having to make 2 late brakes around corner 9 that result in brake failure and the race's first DNF.

Brian's car pulled off to the side of the track at the end of lap 2.
Will and Tim are out of frame in front of me in the blue and Mike P in the orange.

Lap 2 ends with Tim and Will a turn ahead of Me.  The field remains about 2 turns behind the lead.  Chris remains 3 turns back while Mike G has fallen to about 4 turns behind with a lap to go.

Lap 3
Don entered lap 3 with a race leading 12 wear -- more wear than anyone else on track and far more than many of the leaders -- but in the end it cost him too much to pass the pack leaving him not enough to challenge for a podium.

I was now in the position I had hoped to be in -- have more wear than the leaders and be in position to strike.  I passed Tim through corner 8 by using 2 wear.

Then I catch Will through the last 2 corners -- setting up a dice-off for the win.  Tim pulls in right behind me hoping for slips across the finish line.

I had the advantage over Will because I was going faster coming out of the final corner.  So testing my acceleration and top speed got me to a speed that Will could not match and I passed him at the line for the win.  Tim then made a couple tests and got 2 slips from me to also pass Will at the line for 2nd.

Last turn for the leaders.  Me in the all blue for the win.  Tim next to me for 2nd.
Will a space from the win in 3rd.

If Will could have found effectively 1 more space he would have won the race.  Instead he ends up 3rd.  While we mentioned that 1 space he probably lost through the first corner of lap 1, it is hard to project that one space there would mean 1 space 3 laps later but Will is still probably kicking himself about that unforced error.

The last corner of the race saw a couple chances as drivers made last minute plays to improve their positions.  Mike P ended up crashing out in the last corner for the race's 2nd DNF.  Chris spun and finished last.

Mike P crashed and Chris spun in the final corner.

Final results:
Doug Schulz
Tim Mossman
Will Kennard
Don Tatum
Kevin Keller
Mike Grason
Chris Brandt

DNFs: Brian DeWitt and Mike Polcen

Friday, July 13, 2018

Organized Play 2018 Enters The Home Stretch at WBC

The World Boardgaming Championships arrive in a couple weeks which means we are getting ready to crown another CFR Organized Play Champion.

Stats are updated so that only races from WBC are left to account for.  Doug Galullo remains in the lead but his lead continues to shrink for reasons I explained back in May.

You can see total points for the top 13 here or see the complete rankings for all 131 currently ranked drivers.

By my count there are 9 drivers who definitely have a shot at passing Doug G with a win at the finals table at WBC and at least 2 more who are close enough that deflation might get them there.

I am assuming that the finals will end up with an AFR+ around 2.00, each qualifying heat will have an AFR+ around 1.00, and the tournament at large will have a value of 1.83.  This assumes similar values to last year.

I am also assuming that the independent "demo" race being held at WBC does not have a huge impact on the event... although it could have some impact.

Calculating Potential Value for the Event
Based on assumptions above, a qualifying race win will be worth really close to 23 points.  A win at the finals will be worth 46 points for the race itself and 42 points for the tournament win.

But those are just raw points.  Remember that a driver's OP points is equal to their top 4 races and top 2 events by points.  For example, Don stands to gain 50 points at WBC.

If Don wins every race he enters at WBC. he would book 3 races worth 23 points each, 1 race worth 46 points, and 1 event worth 42 points.  That is only worth 50 points to Don because only the 46 point finals is more points than Don's current top 4 races and is only 23 points better.  The 42 point tournament is worth 27 points to Don as it is that much better than his current 2nd best tournament score.

But those 50 points are more than enough to potentially beat Doug who sits only 39 points ahead of Don. 

Who Needs to Do What to Have a Chance
First off, keep in mind that because all scores get re-adjusted after every race, scores can and will change a little even if a driver does not get a great result out of WBC... especially tournament related points.  So being close to closing the current gap to Doug G might be good enough and might not.

That said, the following drivers look like they can gain enough points just from qualifying for and winning the WBC finals. 

  • Don Tatum (would gain 50 points and is 39 behind)
  • Gianluca Lari (would gain 63 points and is 42 behind)
  • Chris Long (would gain 64 points and is 43 behind)
  • Michael Polcen (would gain 61 points and is 43 behind)
  • Chris Brandt (would gain 68 points and is 59 behind)
  • Dave Ling (would gain 76 points and is 68 behind)

Of the above, three might be able to pull off an OP title finishing 2nd in the WBC finals:
  • Gianluca Lari (would gain 44 points and is 42 behind)
  • Chris Long (would gain 45 points and is 43 behind)
  • Michael Polcen (would gain 42 points and is 43 behind)

The following four drivers might have to win a qualifying heat in addition to the finals in order to surpass Doug -- depending a bit on how scores get readjusted:
  • Gary Sturgeon (is 69 behind and would gain 71 points from just a Finals win and 76 if he also won a qualifier) 
  • Danilo Volpinari (is 72 behind and would gain 69 points from just a Finals win, 73 if he also won a qualifier, 76 if he also won two qualifiers)
  • Tim Baker (is 76 behind and would gain 79 points from just a Finals win and 90 if he also won a qualifier)

Mario and Jeff probably have to win two qualifiers on their way to a Finals win:

  • Mario Ales (is 73 behind and would gain 71 points from a Finals win and two qualifier wins)
  • Jeff Harrington (is 80 behind and would gain 80 points from a Finals win and a qualifier win and 82 if he also won a second qualifier)

What about Doug Galullo?
Obviously Doug has his destiny in his hands.  Winning the WBC finals guarantees him the OP title as well.

Second in the finals might also make it impossible for anyone to catch him -- adding 28 points to his total.  Third in the finals would net Doug 16 points which would probably knock many of the above drivers out of contention -- all except Gianluca Lari, Chris Long, and Michael Polcen. 

Fourth in the finals would only net Doug about 5 points -- enough to make the math harder in many of the close calls but not enough to keep one of the top competitors from winning WBC and snatching the title from him.  Same goes for a qualifying win without a top 4 finish at the finals which would net him about 2 points.

Everyone Else?
Everyone else, including 12th ranked Dave Ingraham, 14th ranked Tim Mossman, and everyone below that is probably out of contention for the OP title.   Even a newbie who shows up, wins 3 qualifying heats and the finals would "only" pick up 157 points.  Possibly good enough for second place in OP this year.

Remember that scores are fluid in this system.  The value of older races change every time a new race is booked and compared to every other race already run. 

The numbers above include some rounding because I'm lazy.

If more people show up to WBC it could increase the value of the event itself and give more people a better shot at overtaking Doug (30 different drivers participated in WBC last year but 37 participated the year before).  Same goes if higher ranked drivers make the finals (last season included a pretty highly ranked set of drivers making that race worth a good bit).

If fewer people show up to WBC it will make the event worth less in total and make it harder for people to over take Doug.  Same goes if the finals includes fewer highly ranked drivers.

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
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
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
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?


by Delapouite via
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.