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.

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.


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.

Thursday, May 3, 2018

Two CFR Seasons End, Big Changes at the Top of the Rankings

Organized Play Top 5 after DMV
When I posted the last Organized Play update, I mentioned a couple big series that would end soon and have an impact on the rankings.  Well, one of them just ended and another smaller one did as well.

The DC-Maryland-Virginia season got off to a small, 4-race start this year with Chris Brandt organizing.  All races were held in my back-yard of Northern Virginia but my schedule never did permit me to attend one.  Next year I hope.

Chris ended up winning the final race last weekend and was able to take the season victory as well.  That gave him a little boost in the rankings up to 3rd from 6th.

Michael Polcen and Tim Mossman also benefited from doing well in DMV this year.  Polcen moved up from 15th to 7th and Mossman moved up from 11th to 8th.

OP Top 5 after San Marino
But then the San Marino 2017-2018 season concluded with Gianluca Lari winning the race and securing the season title as well.  The San Marino season was the longest in person season with 9 races and currently is the 2nd most valuable tournament in the rankings.

That gave Lari a huge points boost to propel him from 13th to 2nd!  Unseating Tatum who has been the #2 ranked driver for most of the last couple of years it seems.

Danilo Volpinari ended the San Marino season in 2nd and moved up the OP rankings from 17th to 6th.

Why Did Some Drivers' Point Totals Go Down?

Astute observers of the two charts above will notice that just entering a race and series result for San Marino cost everyone in the top 5 points except Lari.  Why did that happen?

Almost entirely the point loss was due to a change in the points each driver received from placing well in previous tournaments.

All points for the rankings in CFR Organized Play are adjusted based on the competition in a given race or tournament.  The points received from a race against average competition is multiplied by 1 (granting no bonus or penalty).  The points multiplier for an above average race is something greater than 1.  So, if the average race value changes, so does every races' multiplier.

At this point in the season, race multipliers are not moving much.  After 58 races, the 59th is not going to move the needle much.  However, San Marino was the 5th tournament in the rankings.  Which gives it a much bigger impact on the average tournament multiplier.  

Since the San Marino series ended with an above average value the average value increased.  That means that the P1 tournament Galullo won is now closer to the average and so the multiplier got smaller.  Effectively all multipliers for previous tournaments got smaller.

Oh, and expect this to happen again since Redscape and WBC have historically been graded as above average tournaments.

Tuesday, May 1, 2018

Indianapolis Build

Another track build from a request.  This time Indianapolis.  Although the oval was officially an F1 track from 1950 through 1960, scoring back then let you drop your worst couple results from your season total which let all the regular F1 drivers safely skip this race with no consequences.

It wasn't until Indianapolis built an infield section that the track held a real F1 grand-prix in 2000.   This new track configuration featured one of the famous banked corners and most the two straights on either end of it.  The rest of the track was a tight, twisting affair before dumping cars back on to the oval.

Not a ton of great video to watch from this track as YouTube is a glut of video about the infamous 2005 race when all but 3 teams withdrew because their tires were imploding under the stress of the banked corner.

I did find corner speeds online.  So, good data to work with there.  Notes (pdf) in hand, I came up with some initial corner ideas (PDF) and started a build.

This was a tough track as the main straight is super long but the track in total is pretty short.  So I had competing needs to put enough spaces in the twisty in-field to get me back to the main straight and make the main straight long enough to feel right and come in around 60 spaces.

Often when building a new track my first build is close and just needs tweaking and refining.  Not so this time.  I got a lap into a test of the first build above and decided it was terrible.  I was shooting for an infield that was close to 1-line but this attempt gave too few choices to drivers.  I also decided to exaggerate the short straight in the middle of the infield and compress the corner sections on either side of it.

A number of iterations later and I was happier with the final version (PDF).

As happened when I built Imola, shrinking up the number of spaces in the in-fields resulted in some creative corners.

Corner 1

This was the only real good passing opportunity for F1 cars when the track was used by them.  That said, the green line will usually be your best bet.  Although running wide so that you can delay braking before taking the 60s through the corner can work and landing right on the apex on the red line can also be an advantage for next turn sometimes.

Corner 7

This may be one of the oddest looking corners.  It was not meant to look this odd but the combination of my layout and how I had to twist the track to make it fit and allow cars to fit inside it...

Anyways, this corner is important because there is a short straight right after.  So speed exiting this corner can be important.

It also works closely with the corner immediately before it.  If you are clear of Corner 6, taking the 60s for a faster exit can be best.  But you can often spend the less wear to exit through the 40 space at the cost of a slower exit speed.

I've been building more corners like this based on an interesting insight I read a couple years ago from the driver who used to play the Stig on Top Gear.  It was a discussion of different racing lines through a corner.  While there is a theoretical ideal line through most corners.  Most drivers don't take that line.  They take some variation of it based on competing desires.

Some drivers want to brake later.  This has the advantage of allowing them to maintain speed longer before the corner.  However, they end up having to wait longer before accelerating out of the corner again.  My quick way to model this is to effectively take a speed limited space away from the beginning of the outside lane -- allowing the car to travel faster before having to slow down.

The other option is to brake sooner.  This gives them a slower entry into the corner but lets them get back on the acceleration sooner.  My quick way to model this is to take a speed limited space away from the end of the inside lane -- allowing a car to accelerate out of the corner sooner.

Corner 13

Of course the final, banked corner of the lap needs to be important for this track.

I played with some of the concepts I noted above and with different racing lines.  I ended up tweaking this corner more than any other.  Having 4 lanes for the first time in a CFR build was challenging.  Maybe because I'm not used to trying to develop that many meaningful options.  

The far inside lane plays off of the early brake / early accel concept.  The next 2 lanes are actually the most efficient.  The 3rd lane is more efficient if you get stuck in the corner but cars with lower top speeds may not be able to take full advantage of that.  The outside lane is sub-par.

Another oddity of this corner is that the two inside lanes have a 120 posted speed limit and are the same number of spaces in length.  The outside lanes both have 140 speeds and the same length.  This is a nod to the fact that it is a banked corner which should narrow the difference in distance traveled between lanes.  But the lines running through the two middle lanes create 4 different options.


Despite the super fast back end of the track, I think this will play out as a pretty tight track that favors running from the front.  However, I would not be surprised if it ends up being a yellow track at the end of the day.

Will its nearest comps end up being Sakhir (PDF) or Barcelona (PDF)?  We will begin to learn that as it gets played.  The track is scheduled to be run during Redscape's next season.

Thursday, April 26, 2018

WBC Tracks Announced for 2018

Since we decided as a group that we still want to know the track selections ahead of time, here is the much anticipated announcement of our track selections for this year's WBC.

The basic criteria we use is to cycle through the colors, one group a year.  So since this year it is Blue, Purple, Red, and Yellow that means that next year would be Purple, Red, Yellow, and Green.  That gives the greatest variety of tracks and keeps shifting what we play at any given time.  Within that selection, we simply pick tracks that either haven't been played at WBC before, or haven't been played in the longest amount of time.

So without further ado, here are the tracks:

Qualifying Heat 1, 2 blue tracks + 1 purple:
Valencia (PDF) last seen at WBC in 2015
Oyama (PDF) never seen at WBC [Edit: this track will run 5 laps because it is short]
Baku (PDF) never seen at WBC

Qualifying Heat 2, 3 purple tracks:
Sochi (PDF) first seen at WBC as last year's finals
Francorchamps 1983 (PDF) never seen at WBC
Castellet (PDF) never seen at WBC

Qualifying Heat 3, 3 red tracks:
Imola (PDF) never seen at WBC
Nürburg (PDF) never seen at WBC
Estoril (PDF) never seen at WBC

Finals, a yellow track:
Suzuka (PDF) last seen at WBC in 2013

Lots of the tracks above have never been used at WBC because they are very new.  Oyama, Baku, Castellet, Imola, Estoril have all been built in the last year or two.  Baku has only been on the F1 calendar for a couple years now.  Oyama, Castellet, Imola, and Estoril were all built as special requests of one variety or another and are older tracks from a variey of eras: 70s, 80s, and 90s.

Nurburg is a track that I built a good bit ago but yet has never made an appearance at WBC for no good reason.

Lots of tracks that should provide an edge to racing from the back this year until Q3 which is literally some of the tightest tracks ever.  Bidding in Q3 should be very interesting.

And then a great looking finals track in Suzuka.

Monday, April 23, 2018

CFR Rankings Shuffle

I spent some time last week updating the CFR rankings and noticed a couple things.  First, I was very far behind recording results from the Detroit series that just finished its 8th and final race.  Also, the Detroit series was the first tournament to have that many heats. 

Both of these events caused some shuffling in the rankings for different reasons.

In the past, tournaments were either online or at a convention and included 3, 4, or 5 heats.  Not much variation there.  But Detroit raced 8 times this year and San Marino will finish their 9th race soon.  That feels different to me and was not really taken into account in the way I was gauging series value before.  So, change.

I am now taking into account the number of heats that a series or tournament has when judging the value of said event.  This is in addition to the quality and quantity of competition that made up the majority of the original measure and determines the events Field Rating and AFR.  The last factor remains a bonus for events held live which is included in AFR+ as seen on this chart.

Otherwise, the addition of results from the last 6 Detroit races and the last San Marino race and most importantly the final rankings from the Detroit season rocketed some drivers up the poles.  Obviously, the reconfiguration of the series rankings had some affect on rankings as well.  With PrezCon results getting a bit of a bump.

Rankings Update

That said, Doug G still rules the roost.  Having won 3 races and 2 events already this season, has granted Doug a huge lead over current runner-up Don Tatum.

Gary Sturgeon was the big winner after this update and an early candidate for rookie of the year as he won 2 races in the Detroit series and won the season for a nice point total.

Mario Ales did well in the only tournament he ran in that has completed.  Dave Ingraham has some better race results than either Sturgeon or Ales but placed 3rd in the only event he has finished in the points for although is the early candidate for come-back racer of the year.


The next shoe to drop for these rankings will be the completion of the San Marino season in early May.  Probably followed closely by the end of the current Redscape season.

Current San Marino season leader Gianluca Lari is sitting 9th in the CFR standings.  A season win would likely vault him up to 3rd but he will have to fend off Danilo Volpinari and Palmiro Matteini who would both jump up into the top 10 with a season win.

Tim Baker seems like the odds on favorite to win Redscape this year which would likely jump him up from 12th into the top 5 in CFR.

Season Stats

So far 2018 has seen much more racing than 2017.  New or re-generated season in San Marino, Detroit, and Washington DC contributed to the 57 races included in the rankings so far.  47 were recorded for all of the 2017 season.  
The season is also on pace to include 7 tournaments and currently includes 126 different drivers.  Last season had 5 series and 100 drivers by the end.  

The downward trend in field size continues with races averaging 9.1 drivers.  Last season saw an average of 9.5 drivers.  This continues a trend I've seen even prior to organized play rankings.  Some of this is due to reductions in field size standards in both my PBeM as well as at WBC -- two of the larger CFR events.

I can not point out too often how much credit the community of CFR drivers and especially stewards deserve.  It continues to be a pleasure to be a part of.

Tuesday, April 3, 2018

PrezCon 2018 Results

Huge thanks to Chris Brandt for running the CFR event at PrezCon.  Its a great event.

Below is Chris' recap of the proceedings.



Prezcon 2018 was held February 19 - 25, 2018. The Championship Formula Racing (CFR, nee Speed Circuit) Tournament consisted of five races, each with some unique theme. We also changed the process for getting to the final. Although we count points for each heat (1 point for participating + 3 for a win + 1 for each driver you beat) it no longer determines the starting grid, so bidding for start position is still critical.

But, before we started racing, we held a brief ceremony in which Dave Ingraham was presented with a “FERRARI CFR SET”, consisting of a 1/87 Ferrari Enzo, numbered 18 for the year, a set of Ferrari speed cards and matching red dice. Let me tell you, 1/87 Ferraris are hard to find. This one was disassembled, stripped painted, and a driver positioned in the cockpit. An engraved plaque cited Dave as a driver and friend.

Heat 1 – Mystery Track! (Wednesday 2/21/18 – 1700)

The first track was built on the spot, a Prezcon tournament tradition. It was a lengthy track and we crammed 11 drivers onto it. Here’s a shot of the entire field, early in the first lap. 

As the race went on two things were clear Chris G, driving the Austin Healy and Mike L, driving the silver and orange 911 were going to rely on the dice. Chris used the cubes heavily to get out to an early advantage but, as they always do, they failed him eventually and he dropped out. Dave’s new Enzo, in the middle of the pack in this picture, waited for the right time to make a move. And, he had a lot of it, as the track was a bit too long for a tournament heat and people ended up burning through their wear. To the right is the full track, perhaps the drivers found the different pavement types distracting as many of the modular pieces were undergoing renovation.

So Dave’s Enzo ended up in a duel with defending Champion Don’s yellow DELL Porsche 911. As the went down the final straight, confusion ensued and Don, attempting to prevent a high speed draft opened the door for Dave’s Ferrari to slip inside and take the win when Don failed his top speed roll. The third picture of this race shows the final seconds as the cars flash across the finish line. Current number 1 ranked driver Doug Galullo finished third, but that trio left the others way behind.

Here are the final standings for the first race.
1. Dave I
2. Don T Failed TS roll to get edged by Dave.
3. Doug G - Failed ACC roll near the end.
4. Lane N - Came out of nowhere but was WAY behind the first 3.
5. Chris B - Broke brakes midway through, hurting the come from behind plan.
6. Mike L - Ran out of wear early... but didn't break anything!... except dice rolling records.
7. John S - Broke top speed pretty early but hung in to finish.
8. Stuart T - Had to leave.
9. Chris G - Left suddenly... must have made two dozen rolls successfully, of every sort...
chance, top, brake, accel... it was nuts.
10. Scott S- New to the game. Didn't expect it to last this long. Had to leave.
11. Bill Beckman - Crashed

Awarding points as described earlier gave Dave 14 points, followed by Don at 10, Doug at 9 and
so on.

Heat 2 – 90 Minutes du Prezcon. (Thursday 2/22/18 – 1300)

The 90 Minutes du Prezcon was an experiment in conducting a timed race. We raced for 90 minutes, finished that turn and then five more. This caused a LOT of confusion. Although we ended up racing just over three laps there was concern about how many laps of wear and skill we would get – the race rules stated, “Three laps of wear and skill”. There was concern about people “gaming” the system and delaying if they were doing well. (Editor’s note: Some people are painfully slow under all circumstances, not just in a timed race.) There was confusion over drafting in the long banked curve, even though it was repeated numerous times and posted on the track map and on the curve itself.

This race started the same as the prior one with a handful of drivers taking off at a sprint. Brian DeWitt, a twice-defending champion, missed the first race, but played skillfully in this one. The rest of the field went at a slightly more moderate pace, trying to conserve a little wear, and see what the leaders did to each other. Eventually the usual lack of wear slowed them all down, and the rest of us closed in. It once again came down to the last turn. Dave had passed Doug and Don and was behind Brian – and even got by him. But Brian came back with a little more speed and got inside of me in the last corner. There was drag raced to the finish, with Brian winning, by virtue of being on the inside, and Dave right beside him in second. The rest of the field was very close behind. For whatever complaints there were about the race, it was very hotly contested.

1. Brian
2. Dave
3. Doug
4. Stuart
5. Don
6. Lane
7. Chris B
8. Mike L

Sadly no pictures exist of this race, so perhaps time will eventually erase its memory. From a GM standpoint, I still think this is a good idea and it didn’t seem to faze most people. I’m not the GM next year, but would like to see some sort of timed race used again in the future. 

Heat 3 – Prezcon Mille (Friday 2/23/18 – 1300)

The innovation continued with Mille Prezcon - one long torturous track. This race drew a slightly smaller field, perhaps because people looked at the track and feared that we would be racing three laps, but we raced only one, although we allowed 3 laps of setup for wear and skill. At just about 200 spaces, this was a long track with 22 curves, many of which had varying radii, tight curves, long and short straights, and, of course, a bridge. Dave later noted, “It was a shining example of what is possible with a modular track design system. It was very cool.” 

Here’s one of the top ranked CFR drivers, Don Tatum, enjoying a aerial view of the track. This was all built using two different modular systems, a “parallel edge” system and a hex system, along with the conversion pieces to link them together. We were lucky that another game had left three tables together and covered for this nice setup. Surprisingly, Don kept smiling during the entire race.

The Mille turned out to be a unique race. There was no repetitive groove to be found because each upcoming turn was a new adventure. It was too big to pinulate, so Don had to drive by the seat of his pants, which was most unusual for him. 

Here’s a shot of the pack crossing our now famous bridge. Yes, it’s a little steep for race car suspensions, but we have not had a fatality… yet.

This race proved to be an interesting change of pace. The drivers appeared to enjoy it, it was very competitive, and we were able to pick up the track as we finished racing across pieces of it, speeding
cleanup, which is extremely important in a tightly scheduled convention with people ready to swoop down like vultures when a table comes open. 

Winner Dave Ingraham provided his own account of the race to another of the groups in which
he races. I could not improve on this!
The start went pretty well with the leaders, for once, not being able to pull away from the second pack, as least for a while, and a couple of us were able to still stay with them. Doug, Don, Stuart Tucker, myself and Mike Greason separated from the last three cars. We stayed in that pack for nearly the whole race, until wear started to get thin. By the way, I want to thank all of these four for providing a huge number of slipstreams to me. It saved considerable wear and kept me near the front. In the end, it came down to the last three corners. There was not much wear left in the front runners. I had the car with the most with three. Doug had one, Brian, who had caught up with the leaders had one, and the rest were without. I led, and after the next to last corner, had moved away enough to not be challenged, and finished in 1st by eight spaces by Doug, Brian and Don in very close order.
Thanks and congratulations to Dave!

Heat 4 - Short Track Mayhem (Saturday 2/24/18 – 0900)

No fancy poster for this race. This was five laps on a very short track with just four curves. However, each driver was given only THREE laps worth of wear. This meant that we did approximately the same number of curves and spaces as we did in the Mille, but this time we were repeating the laps and establishing an effective route was critical. With the confusion of the start and finish laps considered separately, this gave us three laps of consistent racing.

As you can see, the track is very simple, although it does incorporate our famous bridge. The bridge was also the only two lane portion of the track, meaning that passing was not too difficult. There were a wide variety of car designs for this race as different drivers approached the greater number of laps differently. 

The many different strategies meant that the field became very spread out. Don leapt out to his usual early lead, but the pack eventually reeled him in as his wear ran out.

With three curves to go, Dave was sitting on six wear and looked to be in  command. But a couple of very rare tactical errors at the end allowed Chris to sneak to the inside lane and take a win after three lackluster finishes… with Dave right beside him. This locked up Chris’s participation in the final, which had been in doubt (by Chris!) up until that point.
In the shot to the left, you can see how spread out the pack was about halfway through the race.  That’s Don’s yellow Porsche in the distance, but he was unable to maintain that lead.

This was another experimental race. We had not done this before and it seemed to be well received by the participants. I believe it’s worth considering for future events.

Finals – (Saturday 2/24/18 – 1600)

The finals were run on the Padborg Park track, one of several built from the modular system. Fortunately I have a bunch of books with track maps and there’s this thing called the internet to provide more data, including videos, of races at these tracks, so the modular system has proven to be very useful in creating just the right track for different types of races. 

Padborg Park is a difficult track for which to plan. There are some long straights, but there are also very tight curves. In addition, some of the curves are just close enough that it can be very expensive to spend wear in two of them at a time.

Nonetheless, current World Number One ranked Doug Galullo edged last year’s champ, Don Tatum for the win, with Dave Ingraham just behind in third. If you’re watching the rankings on the Speed Circuit and Racing Games Facebook group, you’ll note that these three drivers were #1, #2, and #4 ranked after Prezcon, which seems to bring a stronger field each year. 

Final Results:
1. Doug Galullo
2. Don Tatum
3. Dave Ingraham
4. Mike Lind
5. Chris Brandt
6. Stuart Tucker
7. Lane Newbury
8. Brian Dewitt

I present another of Dave Ingraham’s colorful writeups. Many thanks to Dave for these and some corrections he provided.
At the start Don Tatum stalled. Meanwhile, Brian DeWitt and Stuart Tucker jumped off to a quick, one turn lead. The rest of us hurried after them, with Doug Galullo leading this pack. Near the end of the first lap, Brian’s engine blew up, putting him out of the race. The rest of us continued to chase Stuart, with Doug pulling away from us, and closing on Stuart. By this time Don (in the yellow Porsche) had caught up with us, and was back in the chase.
The last two laps were a bit frustrating, as I couldn’t seem to get past a veerrryy wide BMW. When I finally did, it was too late. Doug won handily, followed by the comeback driver of the race, Don. I squeaked past Stuart for third, when he crashed in the last corner, with Mike Lind 4th and Chris Brandt 5th.
Here are some pictures from the finals. Enjoy the pictures and please come join us next year!
The Track – Not especially complex, but it was very competitive.

The Pack – Trying to catch Doug!

Doug’s Camaro stretches his lead on the way to victory.