models of some reality

Talking to Strangers

2017-07-08T10:48:00+02:00

Context

I've been reading role playing poems again recently – they are very short role playing games (or storytelling games, or improvisation exercises, in case you have a very narrow definition of RPG), 15 minutes or less, and because they ar so short, they can and have to explore a single, very narrow theme. Often they play with ideas that have no place in bigger games – like emotions hitting close to home, boredom, identity, body. Somehow, the following one sprang to my mind. I'm sure it needs refinement.

Talking to Strangers

A game poem for three or more friends walking through town.

One player plays the Stranger. They should play to be a person with similar interests, but possibly a different personality to themselves. The other players play a group of Friends, walking through town minding their own business. The Friends must have names different from the players. By chance, the Stranger is walking in a very similar direction as the Friends, at a very similar pace, unable to not listen to their conversations.

The game proceeds for about 8–12 minutes, until the departure point where the paths of the Stranger and the Friends would split. (They can there make the decision to hesitate shortly, or even join to go to one destination.)

If the Stranger reaches the departure point without talking to the Friends, the Stranger wins.
If a Friend asks the Stranger for some contact details, the Stranger wins.
If the Stranger talks to the Friends, the Friends win.

Notes

This is not a zero-sum game: One side winning does not mean the other loses.
The win conditions want to achieve the following: The first condition wants to motivate the Stranger to be shy and mind their own business. The third condition wants to motivate the Friends to have a conversation that is so relevant to the Stranger that they cannot but join. The second condition wants to motivate the Stranger to open up, make a good impression and make Friends, but also be a small incentive to the Friends to not be too open with the Stranger who just joined them out of no-where (because they have already won, see? Denying the Stranger the victory will be the next-best thing.)
I'm not sure about the title.

Games, games and games

2017-07-07T22:00:00+02:00

My List of interesting Games

Actually, this is a list of lists, as BESW notes. And maybe it should actually be something else – a two-dimensional graph, with axes “I have played it this much” and “I want to play it this much”. Also, this is of course a snapshot. It contains those games that I, at this point in time, found on one of various places where I kept lists like these in the past. And it is likely to change in the future, because I learn of new games, I change or refine my tastes, I try things that turn out not as good as anticipated, and so on. With that in mind, here are some games I know of, which I may or may not want to try.

List 1: Games I want to play more of

There are a few games that I have tried, and they have withstood the test and now I would like to play more of them. Some I have played only for one session or two, some I have played campaigns in.

For Campaigns

Fate Fate is very much a setting-agnostic story-building engine: The game is powered by the ebb and flow of Fate points, an out-of-game currency that makes narrative descriptors of characters and the world (“Aspects”) matter. The way this works means that meta-gaming is encouraged, which may be off-putting to some people, but in most cases I prefer the narrative effects of “players conspiring against their characters” to those that come from “playing games with secrets and revelations”. I have played some one shots and a marvellous “Mythos against Logos” campaign set in mythological/ancient Greece. I have liked the game where I saw it, and I think I could do even better – I have mostly GMed Fate, with some play experience from the initial sessions of a Star Wars campaign.
Dungeon World / Apocalypse World It may not be fair lumping these two games together entirely, but DW is a deep hack of AW, that is, a setting translation, which in the case of games Powered by the Apocalypse essentially means re-writing the system from first principles, because setting and system are fundamentally intertwined. PbtA games very much run on tropes: The moves, obvious choices of what a player can have their character do, explicitly express genre conventions about – for example – the Ranger being easily able to “follow a trail of clues left behind by passing creatures”. Because they are small, distinct chunks of setting-encapsulating rules, the systems are easy to learn, but lack an overall unified mechanic – although there are many moves that say “Roll 2d6+X. On 6–, interesting misadventure; on 7–9 success at cost; on 10+ success”, this is by far not the only way a move can work, and the specifics of “success” vary. I have GMed and rarely played these games in games of various lengths, and because they are uncommon, but easy to pick up, they are my go-to games to GM at conventions.
Mouse Guard Mouse Guard is a game about trying to be a hero in a dangerous world, where many things are out to eat you (literally, because you are a mouse with a cloak and a glorified toothpick, and there are wolves, weasels, hawks and so on out there), but you are not alone. You are one of the guard, and that's why you have your spear and your cloak and the determination that it doesn't matter what you fight, but what you fight for! The core interesting mechanic is the ebb and flow between the pressures from missions and the limited time the Guardmice can spend in civilization, following up longer-term goals and resting and recovering. The mechanics may be slightly jarring to people who don't like metagaming: The more you play to the disadvantages of your character during the patrol (or GM) turn, the more spotlight you get during the players' turn to pursue whatever you find worth pursuing. Big conflicts (fight, chase, argument, whatever) are played out using a hidden-action-selection method with an abstract disposition measuring how far the sides are to achieving their goals. This system took some getting used to, but now it's running very smoothly. I have GMed campaigns and convention games of Mouse Guard, and I keep coming back. It would be lovely to play it for once, but the campaign I am GMing at the moment (i.e. summer 2017) is also very rewarding.

For a session or an adventure

Montsegur 1244 is not a light-hearted beer and pretzle game. Very much the opposite. This is a game about delving deeply into the mindset of strongly religious people and trying to understand how that works. The scenes are played out in freeform, but the framing of scenes follows a strict predetermined narrative, and we know that in the end at least one main character will voluntarily choose being burned at the stake instead of rejecting their belief. I have played it three times. While it's quite straining, completing the game is quite a cathartic (no pun intended) experience with the right kind of people, and I am willing (“happy” is not the right term, you see) to play it again from time to time.
Lady Blackbird is on the run from an arranged marriage in a smuggler skyship that has recently been captured by an imperial cruiser, in this tiny standalone game where the rules fit on the bottom half of the character sheet. The rules are amazing. They condense genre expectations (adventure, escalation, personal moments, character focus) and give very strong, but not pushy incentives to play the character to the hilt. Characters and the starting situation are predefined and the setting is very sketchy, with – together with the rules set – makes this excellent for one shots and convention play. And yet, even though I have played and GMed this a small number of times, it's never the same and has a great replay value.
Torchbearer is a gritty dungeon delver game based on Mouse Guard, so a lot of my comments about MG above also applies to this. The pressure in Torchbearer is the dungeon, with its darkness (did you bring enough torches?), dead ends (did you bring enough rations?) and promises (you are worn out, but the next room might contain many treasures! It might also contain something that might eat you, though, so yo you want to risk it?). Torchbearer is more rules-intricate than MG, though, and requires quite a chunk of prep from the GM, which is why I haven't played it more than twice – with the same adventure, an avalanche-buried Dwarven wayhouse each. Basically, your dungeon should be about twice as large as you imagine the party will manage in a one-shot, following some notes on rpg.se that's a set of about 10 rooms which you need to know the ecology of.
Fiasco prides itself to be “a game of powerful ambition and poor impulse control”. It's a GM-less freeform game inspired by the movies where some ordinary people have big plans and even bigger desires, but not enough competence, so everything goes wrong for nearly everybody in the end. (It also works nicely with Icelandic Sagas. There's a helpful sheet for facilitating Fiasco and I've had some good games and spread this game further.
Microscope is yet another GM-less game, this one is about building a linear history in a non-linear fashion by zooming in on interesting periods, events and scenes. Microscope is probably the least an “RPG” of all the games in these lists. You don't play the same character throughout the game and actually outside of scenes, individual characters don't really matter at all. Unless you really concentrate and have good reason to stay on the serious side, the histories coming out of Microscope tend to be a bit whacky, but that hasn't kept me from facilitating it several times to different groups, with good games coming out of it most of the time.
A Parsely is a game in the spirit of text adventures or interactive fiction games, except that a human with a sheet of paper replaces the parser. Parselys work nicely in a quiet corner of a group staying somewhere, or as forum games. (In that context, I should probably list Atop a lonely tower and Doomed Pilgrim, from the Sundered Lands, as well.)

List 2: Games I want to try, but haven't yet

Because I haven't organized it yet

More role playing game poems – Often really strange shortform (the target is 15 minutes) games exploring one theme or method. There's a big list in a Google spreadsheet, and it generally links to the source.
Roll for Shoes – A minimal game written for light-hearted improvisation games. At some point I thought about running a large drop-in-drop-out table of it starting as “Dungeon Ball” as an RPG introduction, but I have never even got round to playing it straight at a normal game table yet.
The Extraordinary Adventures of Baron Munchhausen – A very stylish game about telling extraordinary adventure stories. You play a group of noble drinking buddies engaged in a story-telling competition with much one-upmanship.

Because I don't feel able to GM or facilitate it (yet)

Shock: Social Science Fiction (Science Fiction as in “What do replicators do to society?” and not as in “Yea! Replicators! Nice macguffin, why should society change from that?”)
Ars Magica (All medieval myths are true, and you are a wizard)
Dogs in the Vinyard (you are a 14 year old, given a gun and a book and the authority to be the justice in the wild west)
Great Ork Gods – A beer&pretzle game about the short lives of orcs, gouverned by their, gods who hate them: The Gods (who set the difficulties of tasks) are played by the other players, so this game is nearly/easily GM-less and targeting fast, ridiculous action.
More games powered by the Apocalypse – There are some gems among those games and I am a big fan of the system. However, most of them I haven't even seen, not to mention read or internalized.

Because it needs very specific people

Breaking the Ice (Two players, playing two people dating)
Everway (An ancient RPG using arcana cards)

List 3: Games I might play again

If someone nice runs a campain and I have nothing better to do

Diaspora
InSpectres
Legend of the five Rings
Star Wars: Edge of the Empire/Age of Rebellion/Force and Destiny – There are some cool Star Wars-y mechanics in there.
Cortex Plus, eg. Firefly – I played a campaing of Firefly in 2016 until early 2017, but the system didn't sing for us. It was good, but it had its issues. In particular, it feels very Fate-like, but it lacks Compels (it effectively only has self-Compels) and the collaboration focus at the table is less prominent.

If someone asks

I will not actively look for sessions of these games, because they are not my priority now, but these are games I liked enough to be happy to play them again. If you are interested in playing them, tell me!

FreeMarket (Transhumanist Science Fiction RPG: What do you do on a space station, if you are practically immortal and all basic needs are taken care of?)
Wilderness of Mirrors (You are a group of spies. Has some very interesting mechanics, among them a two-way split: First the planning/legwork, where you come up with complications and solutions, and then the implementation, where stuff actually happens.)
Sundered Lands (any)
Sagas of the Icelanders
Cheat your own adventure
The Quiet Year
Dog eat dog (How does colonization affect the locals? How can they retain their cultural identity and get rid of the foreign power?)

List 4: Games I might try

If someone else organizes a one-shot

These games sounded nice enough when I heard about them first that I picked up a copy of the rules. However, when I actually read the rules in more detail, my immediate urge to play them was reduced. That is not to say I won't be willing to play them! I just won't put any energy into organizing play myself. Whoever wants to run one of these can borrow my copy of the rules, but I'm not pushing for it.

Hillfolk is the reference implementation of Robin D. Laws' “Drama System”. It is written for high-stakes interpersonal conflict, where emotional strife between the characters matters more than the characters versus the outside world. It never clicked with me.
Bubblegumshoe is a Gumshoe game about kid sleuths. I've not been convinced by the Esoterrorists, another Gumshoe game about horror investigators. I don't much appreciate horror, but in this case it's more that I didn't come to gripes with the system. However, I have heard good things about Bubblegumshoe, in particular about its relationships mechanic, so I would give it a try.
Eclipse Phase (If the existential dread is turned down)
Aγων (Competitive)
Blood Red Sands – Competitive rules-intricate dark fantasy. Actually, by the rules you have to play a tournament of several sessions, but that's asking a lot.
Prime Time Adventures

List 5: Other games not on my play list

Games I tried and they didn't stick

D&D 5 – It's okay, far better than the other editions I've played of it, but it still doesn't address what I want in RPGs as much as the other games.
D&D 3.5, Pathfinder
D&D 4
Hârnmaster I used to enjoy the very pseudo-medieval deep realism. My preferences have changed.
Midgard This was the first system I tried. For quite some time, I liked it quite a lot, these days I still appreciate the world and would borrow heavily from it for any generic fantasy I play, but I get the impression Midgard doesn't know what it's about, and that's a severe disadvantage in my book.
Shadowrun I loved the Magicpunk setting. I'd still play in the setting or something similar, less retro and with some different focus on other social issues, I guess.
Scion The game was fun while it lasted, but it's god-awful (pun intended) at doing mythology.
Worlds of Darkness These games are not what they want to be about, and I like to steer my character's character, not have dice decide their morality. (Also, if done properly, they would be horror. I don't like horror.)
Death Watch Not my setting (dark crazy space magic), not my character types (guns-blazing space marines), not my system (strong classes, trap options, strong levels)

Games I own that I don't think I'll play

Burning Wheel, Burning Empires I prefer its smaller siblings Torchbearer and Mouse Guard, BW is quite a chunk of game and apparently requires some system mastery to be proper fun, which I'm not willing to acquire.
The Riddle of Steel It started from some presumably good ideas about medieval sword fighting and making “what you fight for” important. I think I encountered a fan project looking for a 2nd edition at some point, I might have a look again if something comes out of that.
GURPS (Lite) I like specific games, and low-rules ones.

Gebärden schreiben

2016-12-11T14:50:00+01:00

Wie man Gebärdensprachen schreibt

Vor ein paar Wochen habe ich in einem Seminar für Deutsch-Studenten hier an der Uni einen Gastvortrag über Gebärdensprachschriften und -notationssysteme gehalten. Falls jemand das interessant findet, kann er den Vortrag (mit verlinkten, also fehlenden Videos) hier finden.

RPG Preferences

2016-10-03T14:50:00+02:00

What I Like

RPGs are a favourite pastime of mine, and over the time I have gained experience with various ways of running them or participating, and I have acquired some quite precise ideas of what I like in a game and what I don't like, in general – though I will at times be happy to go out of my comfort zone and try something new, I prefer to sign up for that explicitly.

There are some different models of describing what I like in games. Giving you these various descriptions and some links to their sources might help you sort out better games for yourself, so even if you never intend to play role playing games with me, have a look!

BrainHex

BrainHex is a player satisfaction model, focussing on video game play, categorizing gameplay behaviour in terms of 7 (non-exclusive) classes. The model uses self-report questionnaires to extract factors of your reward system, building on earlier purely phenomenological classifications and neurobiological research. The research paper is behind a pay wall, but you can take the questionnaire yourself under http://survey.ihobo.com/BrainHex/

My personal outcome is Seeker-Socializer with very low scores for Achiever, Conqueror and Survivor.

Seeker: 19 Socialiser: 18 Mastermind: 11 Daredevil: 4 Survivor: 1 Conqueror: -2 Achiever: -4

This gives me the following description, which I am quite comfortable with.

You like finding strange and wonderful things or finding familiar things as well as hanging around with people you trust and helping people.

No Fear: You do not enjoy feeling afraid, preferring to feel safe or in control.

No Punishment: You dislike struggling to overcome seemingly impossible challenges, and repeating the same task over and over again.

No Commitment: You dislike being asked to complete everything, preferring to pick and choose which tasks you will attempt, or simply messing around with a game.

While Survivor managed to be the top one of those three, Horror/Thriller is a genre I don't like to be immersed in, whereas competition (Conqueror and Achiever) is just a thing I don't appreciate in role playing games, but which I don't mind in board games.

Metagame Rewards

I stumbled upon metagame rewards for the first time on a Philipine gamer's blog.

To put it simply, metagame rewards are a form of reward that encourages the players to keep coming back. These aren’t things “in-game” that boost character stats, or represent new gear, these are the rewards that make the player himself lean back with a grin, look the GM in the eye and say, “Great Game!”

Partly, the terms go apparently back to French Sociologist Roger Caillois and his book «Les jeux et les hommes» (1958), but the list got mostly compiled by Amagi games and people still find things missing, so my personal list has had Neugier (from discussions with other, German, gamers, who are apparently also somewhat Seekers) and Asabiyah (from the comment thread under the blog post) added to that list, and now sports a glorious 18 different metagame rewards, with names from Greek, Latin, German, Arabic and English, with short definitions. In the following, I have listed them very roughly in my order of preference: Items above the double dividers I consider necessary for enjoying games, and those after the single divider may actually harm how much I like a role playing game. (The order is vastly different when we're talking about board games, for some reason!)

EXPRESSION: The simple desire to be creative at the table
SOCIABILITY: The fun of being able to spend time with other people and enjoy their company
NEUGIER: The joy of learning new things and exploring new places

KENOSIS: The feeling of being deeply engaged in a character or in the fiction at a whole
KAIROSIS: The feeling of fulfilment that comes from change and development
KINESIS: Tactile fun, fiddling with maps, handouts, dice, etc.
ASABIYAH: The group feeling from getting their kicks from teamwork, usually with the rest of the group
CATHARSIS: A feeling of release that follows an intense or overwhelming experience
NACHES: The enjoyment of seeing someone that you have taught, or are responsible for, go on to do well with that knowledge
PAIDA: Free-wheeling player fun, where rules are a convenience
HUMOR: Gaming for laughs
CLOSURE: The feeling that there’s nothing more that needs to be done, and the thing is finished
SCHADENFREUDE: Delight in the suffering of another (the thrill of seeing the villain get what they deserve is a pretty common expression)
ALEA: The gambler’s thrill, the fun of taking a big risk, the tension that comes with it, win or lose
FIERO: The feeling of triumph, or winning, of defeating a challenge, or overcoming adversity
AGON: The thrill of winning against another person at the table

LUDUS: Fun from working the system and optimizing performance within the rules
VENTING: The desire to work out player frustrations or other emotions, using the game as means

Games I Like

I have encountered and played a variety of games of various size, page (in the same-page-tool sense above), setting, and goal. But while listing the games I like and the games I don't like may help explain my preferences in games, it is worth a separate post, which shall be forthcoming.

Man Nehme Stattdessen 1: Paprikakuchen

2016-01-26T11:00:00+01:00

Ausschreibung

Im Winter-exPuls 2015 haben wir folgenden Wettbewerb ausgeschrieben.

Wir haben dazu zwei Einsendungen bekommen, die wir euch im Folgenden vorstellen.

Sieger: Tarte Tatin aux Poivrons

Medea Menzel schickte uns folgendes Rezept für eine Tarte Tatin.

Tarte Tatin aux Poivrons

Mürbeteig: 250g Vollkornmehl 100g Butter 75g brauner Zucker 1 Ei 1 große Prise Salz Zu einem glatten Teig verkneten und im Kühlschrank ruhen lassen. Belag: 150g Zucker 3 EL Wasser 1 Prise Salz 50g Butter 400-500g rote und gelbe Paprika

Zucker, Salz und Wasser in einer Pfanne karamellisieren lassen. Leicht abkühlen lassen und die Butter hinzufügen. Paprika waschen, Stiele entfernen und in Streifen schneiden. In einer Tarte-Form das Karamell verteilen und die Paprika darauf anordnen (Außenseite nach unten). Den Teig ausrollen und die Paprika damit bedecken. Vor allem am Rand gut andrücken. Teig mehrmals mit einer Gabel einstechen. Tarte im vorgeheizten Ofen bei 180 Grad Umluft ca. 35 Minuten backen. Danach eine Platte auf die noch warme Tarte legen und diese stürzen, ggf noch in der Form haftenden Belag auf den Teig legen. Warm servieren. Guten Appetit!

Paprika-Nuss-Kuchen

Von Charlotte Eisvogel bekamen wir außerdem folgendes Rezept für einen Paprika-Nuss-Kuchen.

Für eine Springform mit 26 cm Durchmesser.

Mürbeteig:

200g weiche Butter 175g Zucker 1 Päckchen Vanillinzucker 1 Prise Salz 400g Mehl 1 TL Backpulver

Belag:

6 Eier 2 rote Paprika 300g gemahlene Haselnüsse 1 Bourbon-Vanille-Aroma 50g Zucker

Zubereitung:

Butter, Zucker, Ei, Vanillinzucker und Salz verrühren. Mehl mit Backpulver vermischen und in kleinen Teilen unter den Teig rühren. Den Teig in die Springform füllen, glattdrücken und dabei einen Rand hochziehen.

Für den Belag Eier trennen und das Eigelb mit den gemahlenen Haselnüssen, der Paprika und dem Bourbon-Vanille-Aroma zu Schaummasse rühren. Dann das Eiweiß steif schlagen und den Zucker hinzufügen, anschließend erst den Eigelb-Belag auf dem Teigboden verstreichen und den Eischnee als Haube oben draufsetzen.

Den Kuchen bei 160°C Umluft ca. 55min backen.

Vor Verzehr sollte der Kuchen einen Tag ruhen, damit sich das Paprika-Aroma entfalten kann.

Correlated Characters

2015-11-10T10:00:00+01:00

When constructing models that we want to use in the inference of human cultural traits, we often encounter a problem of (possible) dependency: The individual features that evolve are not necessarily independent of each other. This can be due to obvious implications – a culture living inland will hardly have any traits related to sea fishing. But there are less evident connections, such as many linguistic universals. When describing the transitions of these traits through a continuous-time Markov chain (and there are other models, like Felsenstein's threshold model), there are a few shapes of transition matrices we could consider. Each of these CTMC structures has different advantages and disadvantages, so let's have a closer look at each of them, before comparing them.

Independent Evolution

In the simplest case, we ignore the dependency between the characters. This may be a reasonable model when the actual dependency is weak, but otherwise this is precisely the model we want to get away from, because it is too restrictive for our assumptions.

Fully-Dependent Evolution

The other extreme is to assume that all possible transitions between any combination of traits can occur. This is the least restrictive model, unfortunately it means that the number of parameters of the model explodes.

Cardinal-Directions Evolution

Another model assumes that only one character can change in infinitesimal time, but the transition rates depend on the current combination of traits. This shape has gained wide use in the literature. Dunn et al. use it to investigate word order universals.

Cardinal-Directions with Clamped Rates

Pagel and Meade have suggested a set of reversible jump operators that interpolate between the independent model and the CDM. They allow different transition rates to be clamped to the same value. The case where two characters are independent is then the special case of the CDM where rates are clamped in a way to not depend on the other states.

Continuous-Time Bayesian Networks

Continuous-Time Bayesian Networks were developed by the probabilistic graphical model community. The CDM above is a special case of CTBNs. A CTBN specifies for which traits the transition rates depend on which other traits. In the case that for all traits, the transition rates depend on all other traits, we recover the cardinal-directions model. If, on the other hand, the transition rates for each trait depend on no other trait, we recover the independent transition matrix.

Kronecker-Coupled CTMCs

In the computer science literature on model-checking continuous-time Markov chains (eg. Buchholz et al.), a different way to generalize away from the independent model can be found. This class of transition matrices is used to model parallel systems with locking states. The fundamental addition to independent Markov chains is therefore the introduction of synchronisation events. Such a Markov chain with synchronized transitions can be easily decomposed into Kronecker products of simple matrices, which makes sparse storing and matrix exponentiation very simple. On the other hand, this ansatz shares a severe disadvantage with the independent evolution model. Kronecker-coupled CTMCs can never express that a single combination of states is impossible. All other dependent models described above allow me to set some rates to 0, such that a single state cannot be reached. But this is not possible in a Kronecker-coupled CTMC: If one state is made unreachable by setting a rate to 0, at least one other state will also become unreachable.

Comparison

[A table showing 2×2 transitions, number of parameters, probability of independent model, other notes]

All structures listed here have some advantages and some disadvantages when being used as transition models for the evolution of correlated characters. I am sure I have missed some other way of restricting CTMC transition rates, so I would welcome any comment about those. In addition, there are other classes of models that we should maybe look at. And yet, there are only two (point five) of these that I have seen used in phylogeny of anthropological features – it might be worth changing that.

models of some reality

Talking to Strangers

Context

Talking to Strangers

Notes

Games, games and games

My List of interesting Games

List 1: Games I want to play more of

For Campaigns

For a session or an adventure

List 2: Games I want to try, but haven't yet

Because I haven't organized it yet

Because I don't feel able to GM or facilitate it (yet)

Because it needs very specific people

List 3: Games I might play again

If someone nice runs a campain and I have nothing better to do

If someone asks

List 4: Games I might try

If someone else organizes a one-shot

List 5: Other games not on my play list

Games I tried and they didn't stick

Games I own that I don't think I'll play

Gebärden schreiben

Wie man Gebärdensprachen schreibt

RPG Preferences

What I Like

BrainHex

Metagame Rewards

Social Contract

Games I Like

Man Nehme Stattdessen 1: Paprikakuchen

Ausschreibung

Sieger: Tarte Tatin aux Poivrons

Tarte Tatin aux Poivrons

Paprika-Nuss-Kuchen

Correlated Characters

Independent Evolution

Fully-Dependent Evolution

Cardinal-Directions Evolution

Cardinal-Directions with Clamped Rates

Continuous-Time Bayesian Networks

Kronecker-Coupled CTMCs

Comparison