Wednesday, October 18, 2017

Infinity Battle Report -- Chimera

Michael and I got a good battle in recently.  We decided to pair down our lists to 200 points and try to use as vanilla a set of guys as we could field.  So our lists include very few odd or complicated skills.  We are obviously also not using any advanced rules and are still very much learning how to do this.

Michael's PanO army is largely based around the Jotum.  Jotum is the lieutenant for an extra order and can also push some buttons with the crabbot.  The Dronbot is there to provide some AROs.  Trauma-Doc and Palbot are mostly there for button pushing.  Two Akal Commandos give this list some element of surprise.  Michael really likes AD: Combat Jump.  The Fusilier is there to round out the team with an extra order that can push a button if she has to.


My Nomad army is based around using the Sin-Eater and Grenzer to lock down some lanes with great ARO capability.  Let the Gecko and Mobile Brigada make room for the Alguacil paramedics to go push buttons.  If I have to the Gecko Pilot can jump out and push buttons as well.


The mission is one I came up with myself, I describe it a little at the beginning of the video but here is a PDF mission description as well.



Thursday, October 12, 2017

Solo Race #9: Nurburg

I tried something a little new for this race.  I took photos but also recorded short videos periodically through the race... here is the result all stitched together into 18 minutes of video!


If you want to step through each turn in the race at your pace including the video commentary, see the Google Album.

Links to the rest of the series can be found on the series page.

Monday, October 9, 2017

Congress of Gamers Fall 2017 Post Race Report

Turn 1 sees 5 cars lining up for Eau Rouge.
Michael and Tim in front.
Eight cars pulled up to the start grid in Rockville Saturday at Congress of Gamers Fall.  I typically build a track revision for this race and this year we ran an old version (1983 vintage) of Francorchamps.  See my previous post for details on that track.

On the right you can see the results of turn 1 in the race.  Michael Schulz is in the lead after starting outside row 1 and out-gunning Don Tatum from there.  Tim Mossman moved up from row 2 after pushing his start speed to pull even with Michael.  Don, Will Kennard, and Kevin Keller filled out that large 1st group.  I'm in the white car in the middle distance while Dave Nace and Joe Powell bring up the rear.  The 3 of us started in the last 3 rows.

The 5 cars in front pushed through Eau Rouge and down into Les Combes as a pack.  But I had gained contact with the pack by then and Dave and Joe were not far behind. 

Below you can see the result of the field thinning out as we enter the mid-field section.  Michael spent some wear to take the lead again.  Don pulled up even with Tim while the rest of us held position.

Michael, Tim, Don Will, Kevin, me... into the mid-field.


Almost the end of lap 1 and Kevin joins Don
and Michael at the pointy end after Tim's spin.
Nothing too exciting happens the rest of lap 1 until the leaders make their way through the old Bus Stop Chicane.  Tim took the corner for 2 wear and a chance roll for what he is convinced would have given him the eventual win.  He spun despite spending 2 skill.

Kevin and Don ended up catching up to Michael as they exit the Bus Stop -- 3-wide heading into La Source.  Pretty much everyone ends up passing Tim as a result of his spin.  You can see Tim in 7th here.

As we began the 2nd and last lap of the race a couple turns later, I jumped out of my car and rookie Anna Pisto jumped in to finish the race -- waving off many of my suggestions as she went.

Through Eau Rouge again and down to Les Combes for the last time, Anna has pulled the white Tyrell into the lead pack just behind Kevin.  Don and Michael are still right behind Kevin as well but Kevin has more wear than anyone right behind him and already seems to have the race in hand.

I forgot to take pictures after this... Michael made a chance roll here.

By the time the cars have rounded Pouhon.  Kevin and Don are back out in front of the field.  Michael has damaged his car and makes a chance in Pouhon but pulls off instead of crashing in Fagnes.  Anna has some wear left but will come up short of 2nd after a couple missed die rolls.

Will pulls back into 4th and Tim falls back to 8th.  Kevin wins and Don gets 2nd.

Final Track Thoughts
Because this was a new track effectively, I wanted to talk about it.  I love it.  I've always liked Francorchamps -- maybe more than some -- but I like this version the best.

Starting at the beginning of the long back straight was a lot of fun.  Getting 5 cars through Eau Rouge is super interesting with all of the lines and slips and choices.  And we had a bunch going into that corner on lap 2 as well because the old La Source profile is wider and has a higher line that makes it a lot less of a bottle-neck than the modern version of that corner.

6 cars getting through La Source at the end of lap 1!
I will say that I like the modern Bus Stop better than the old one.  I love the modern bus stop.  But the old bus stop is not bad, it just is not as interesting.

All in all, the track became a lot less of a race from the front leaner.  It became very hard to pull away and I definitely think I will see people run this successfully from the back.  I can't wait to get this out into the wild more.

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.