Greg's Design Blog

A collection of posts by game designer Gregory Carslaw, including mirrors of all of his blogs maintained for particular projects. A complete index of posts can be found here: https://boardgamegeek.com/blogpost/58777/index

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Three design lessons from a heap of trouble

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I don't want to dwell on this, but I think a 2 month gap in posting needs some explanation: My health problems were somewhat worse than anticipated. I've spent most of the last 5 months in bed. I am very bored of bed. The next 5 months are supposed to be better, but there are no guarantees. I am probably not going to die before you do. I am going to try to attend MCM and UKGE and give SatW the attention that it deserves. Few people read this blog for news about me, it's about game design tips and seeing the inside of the game design world. To that end, let's talk about three lessons that I've learned through card design in SatW:

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Some rules exist in a game because you want them to be there. Other rules exist because you need them to be there.

I wanted the game to have a bidding element in which players were trying to anticipate and exceed their opponents bids. So I wanted the rule "The highest bid wins". In an ideal world I'd leave it at that, but sometimes players would rudely bid the same amount and since it's a think that *can* happen, the game needs a rule for when it *does* happen.

Some games will dodge this sort of problem by other means. For instance by setting up resources such that one player will always get a +0.5 bonus and having all other values be whole numbers, so that a tie is impossible. You'll also see games that use a required rule to solve another problem, such as by breaking ties in favour of the losing player and creating a catch-up mechanic. It is an art to elevate a solution beyond "solving this issue" and to "improving some other aspect of the game".

What I learned from the Brother Belgium card was the power of allowing game effects to mess with these "needed rules". It's tempting to focus on the things that are at the forefront of the game, but tweaks to the grist can offer a meaningful advantage to one player. It's important for a bidding game to have cards that offer such a notable advantage, to create competition between players who want the advantage and players who want the card for it's victory condition.

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Being designed for fans of the webcomic, the SatW game is going to include a number of jokes or references for that audience. These cards don't have a lot of room for flavour text, so the references have to come across mechanically.

Sister Estonia is a card I've had some consternation over. In the comics Estonia wants to be considered a Scandinavian country and thinks of herself that way, but none of the other Scandinavian countries see her as one of them. In the card game her "desired item" is a picture of her holding hands with Sweden and Finland and skipping merrily onwards. This desired item is listed as having a value of 4 coins, though item values only go up to 3. Of course, this is because the card for her acceptance isn't in the deck, Estonia will always be alone.

The worry for me is that people who pick it up in order to play the game but who haven't read the webcomic will be confused or cheated by this. They'll think there's a card missing from their deck, or they won't "get" why there's a reference to a card that doesn't exist.

What I learned from Sister Estonia is that I shouldn't underestimate my audience. In testing a fair portion of groups simply don't notice anything is wrong - there's a big item deck and it's not that surprising if one for a particular character doesn't come out. Others recognised the four coin cost as being unusual and flicked through for it, but seemed delighted to find it wasn't there. Perhaps pleased to have noticed something unusual and worked out a secret from it? A few got interested and looked up the comics about Estonia to see what was going on.

Nobody was upset as I'd predicted. A secret, with some clues and the option to find out the truth of the matter, seems to be a powerful thing. Of course I'll still mention that it doesn't exist in the FAQ of the rules, but it's been surprising how well received it was for a factor that I thought I'd have to balance between comic fans and game fans. Maybe some less explicit hints about setting would give future games more depth.

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While it seems a shame to end on a negative, I'd like to talk about something that didn't work, because the player psychology around it is interesting.

Some cards are based around adding mechanisms for properties that I want the game to have. For instance the desirability of a catch up mechanism means that there are cards along the lines of "Steal a thing from the player with the most satisfied characters"

One of the "not particularly interesting" dominant strategies was to accumulate items every turn without ever bidding more than zero - until a character comes up that you have the item for - then bidding so heavily that you can't lose. The consequence of this was that the core of the bidding game didn't function because all bids were either "0" or "MILLIONS" so there were no close decisions or times people were wishing they'd decided to bid a couple more that are the bread and butter of bidding games.

My ultimate solution to that problem took a different form and is perhaps worth an article at some point, but an intermediate solution that didn't work was to include characters that punished hording items - in this case by swapping hands of items. In the end that didn't work out because no matter how many such cards I included players would continue to hoard and attribute failures to "bad luck that the hand wipe card came up when I had a big hand".

The moral is that most players don't study the make up of the deck - I might know that in 98% of games each player should expect a hand wipe - but if the game doesn't flag this for the player it happening is a "feel bad" moment that seems like sucky luck or an unbalanced card - which is something to be avoided.

And perhaps there is a happy ending: Sister Mexico got to stay in the game because testers liked her for other reasons. When you're choosing what to bid she generates an interesting decision: You would like to bid enough to leave you with the 2nd largest hand, so that the player who selects her does not steal it from you - but you do not know what everyone else will bid, so the correct bid to leave yourself in that position is based on your mutual expectations of each other. Of course you could just bid everything in order to obtain her and swap your newly empty hand for an opponent's - but you have to be confident of having the most valuable hand or else you may be giving up everything for nothing.

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SatW has been a blast to work on and is maybe less crunchy than other games I've worked on because of it's theme and target audience - but that doesn't mean it's not presented a medium to try some new things and has shown me some interesting things about design along the way. Hope that it has some value to you, until next time: Happy gaming and maybe see you at MCM or UKGE
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Fri May 26, 2017 2:15 pm
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One card, two choices

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"Games are a series of meaningful choices." - Sid Meier

Today I'd like to think about games that give a player a card (or other component) and the opportunity to play it in two qualitatively different ways. Under what circumstances is this a strong mechanic? Where does it fail to carry its weight?

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The most direct implementation of this is simply to have a card that explicitly offers a player two (or more) options. This is a very powerful approach as it allows for extreme differences of kind between the two options, in which they could bear no resemblance to each other or even other mechanics in the game, enabling a choice that obliges a player to think in a new way. However the downside to this is that the abilities must both be described on the card which means that they either have to be simple or they risk turning the card into a wall of text.

The example above is from Viticulture (Though I think it is from the Tuscany expansion) and I've picked it because it shows something nice about how this mechanic can be used. This card offers a bonus for each empty field or a bonus for each non-empty field. At the moment that the card is played there's unlikely to be a meaningful choice between these two things - in most game states the best choice will be pretty obvious.

The meaningful choice that it creates actually occurs before the moment it is played. In this instance the choice offered on the card ensures that it stays relevant at all stages of the game, so at any given time when considering your hand and deciding what to play it's a viable option. If all of the cards in your hand are viable options, "which card to play" is an extremely meaningful choice. I feel that this is a neat reminder to look beyond the obvious for why something works or where a solution might be found. It tickles me that a card offers two options that will often fall short of producing a real choice but that this substantially improves he choices the game has to offer.

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Another option is to take an approach similar to Race for the Galaxy. In this game a card can be played for its face effect or can be discarded as a resource (to power a different card). This generates a lot of meaningful choices as not only can each card have a lot of detail on what it does, but it also involves closing off a greater number of equally detailed options. If playing a card requires the discarding of two others and you have five cards then there are 6 times as many possible choices as you'd have under a simple "play one card" model.

(Note the above line had an error Russ corrected in the comments in which I claimed 12 times as many options, based on an erroneous calculation that made the order of discards relevant)

The weakness of this kind of approach is that it requires the alternative use of the card to be the same for all cards. That alternative use needs to be attractive enough that a player would regularly consider it as an alternative to the more unique effects that the card face has to offer. It seems to be strongest where the alternative use is not merely something that is useful, but that is absolutely necessary. RtfGs example of "discard cards to power other cards" is great.

Scandinavia and the World runs into the opposite problem here - the discard mechanic is critical, but the face powers aren't different enough. They all boil down to "Get a point towards winning the game if you have the right character." As a result the tense choices do not emerge. This put me in a tight spot as a designer in that I'd like to add a little complexity to the items in order to add a lot of depth to the game in a trade-off that I'd usually take without blinking. However this game is intended as much for fans of the comic who aren't hugely into games as it is for fans of games who aren't hugely into the comic so the line for the ideal depth-complexity trade off is shifted somewhat compared to a normal game.

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The final type of choice on play is the context dependent choice. I've used the example of the Throne Room from Dominion because it was an image that I could find easily - but as we get into discussing the strengths and weaknesses of this approach you'll see that it's actually not the strongest implementation.

With this method a card nominally has one effect and can be played in only one way, but the effect is so context dependent that it's a way to include a great many very different effects on a single card. Cards that do this tend to have meta-effects such as rerolling dice or adding to all numeric variables on another card or something like that.

The strength of this approach is that it allows for a card to have many many many possible effects, rather than just two. This creates a broader decision tree and hopefully in doing so produces a more meaningful decision. The limitation is that it doesn't matter how many contexts that there "might be" what really matters is how many contexts that there are. So throne room often fails to provoke such a choice because it is often drawn with a very limited number of other action cards and which card to pair it with is often obvious (that is not to say that it's not a great card to include in the game in other respects, just that it does not produce this particular effect).

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Having discussed that there might be more than two choices it seems time to render the title "one card, two choices" a complete lie by pointing out that the card is optional. Any game component can be made to serve double duty and produce meaningful choices by having the specific use to which it is put as a decision for the player.

Here we see a Twilight Imperium player deciding that they don't need the strategy allocation to take many secondary actions and that they only fancy moving a couple of times in exchange for being permitted a really big maximum fleet size. So if you are using a counter, model, dice or anything else as part of your game, there's always the option to have it double as a completely different thing.

Happy or Challenging or Exciting Gaming!
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Tue Apr 4, 2017 2:51 pm
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Scandinavia and the Theme

Greg
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Today I am preparing the Scandinavia and the World card game files for printing reviewer copies. Looking for spelling errors, instances of "player" that should say "opponent" and other such grist. In doing so I'm re-experiencing how the mechanics and theme interact. It's particularly important in a game that is based on a webcomic, as it needs to carry the theme of the existing material strongly enough that existing fans recognise and enjoy it, introduce that material to people who have shown up for a game but don't read the comic and not to let that get in the way of the game itself.

So today we're going to talk about how mechanics and theme interact in card games, both in this game and in others, to deliver the best possible effect.

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So this is what I have to work with for each character card: Their name, flag and gender - which are pretty much set by what is established in the web comic that is the source material for this game. An image of them and some items that they want. The name of their ability and the effect of that ability (including an icon to indicate its type).

There are elements on there that have no mechanical impact and that exist purely to carry the theme - the name and image for instance. It is good for cards to have elements like this to reinforce what the game is about and to try to make the interactions in the game feel more meaningful - but they will fall flat if the game itself doesn't back them up.

Imagine playing a game in which you played "Summon a horde of dragons to reign fire down on your foes" and the effect of that was to roll a die and on a '6' kill one of their forty pieces - your dragon would feel more Puff than Smaug. A name and image can give a set up that makes someone interested, but the mechanic has to deliver or the overall effect would be worse than if the game had remained abstract.

This leaves the ability itself as my primary area for establishing the loves, hopes, personality, dreams, fears and more of entire countries. Tricky.

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Very often, the title of a card or ability is the glue that holds a mechanic and theme together. Here we see a mechanic of "Get an opponent's creature and use it for a turn" tied to an image of an angry angel striking someone on their knees. The title connects the thematic payload and the mechanical payload. Thematically I am casting a spell to manipulate your follower into an act of treason. Mechanically this creature that was yours a moment ago is now attacking you. The two sync up neatly creating a card that feels "complete" even if a player wouldn't consciously think about what makes it feel that way.

There is a reason for titles having this kind of impact.

Rules text is necessarily dry, sprinkling the "what to do in the game when this is played" bit with adjectives is a great way to confuse your players and have them asking things like "This card says eviscerate rather than kill, so can I use my 'prevent a kill' card on it or not?" Almost by virtue of being rules text it can carry only very limited thematic information.

Pictures are necessarily rich. Even a very simple image can contain a lot of nuance and it's not clear what matters most. In the image above, what's important? That the attacker is an angel? That the background is an angry colour? That the person is already on their knees? That the attacker is behind them?

The title tells you what aspect of the image to pay attention to and how the mechanics should be interpreted in terms of "what is actually happening" in the context of the game.

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Cards in SatW rely on this principle as well. The ability "Choose two opponents, they each steal a character from the other" is carrying a lot of weight mechanically. If a player is coming second, then the best way to use it is to force the winning and losing players to steal from each other - the losing player will typically steal something better than the winning player does (Since the winning player has better things) which allows the person who played the card to gain some ground on the current winner.

This is also one of the cards in the game that acts as an implicit catch up mechanic. It is very rare for it to be played in such a way that the weaker player in the pair won't gain more from it than the stronger one - but as it is a bidding game any player can make an effort to win the card and can therefore decide which two players are effective. As such it feels "fair" - a winner who is knocked down a peg by it has less of a "I hate that the game punishes me for doing well" reaction and experiences something more akin to "I made a mistake by not bidding higher for that card".

Thematically however the "mutual stealing" ability needs to sit with a particular country or character and needs to be tied to that somehow. Brother Turkey felt like the reasonable choice since a full half of the comics that feature him are in some way about Turkish Oil Wrestling. The "Wrestle" ability gives some indication of why a conflict between two people with some give and take has started and related cards (such as the oil) can have extra information to flesh out the thematic interaction for players to discover as they play the game.

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On some occasions the mechanic can be the theme all on its own. Consider "Decoy" here - it costs two mana to play and when it's revealed it's destroyed and you get two mana back! What a bargain. Right up there with buy one, get one.

The purpose of the card is to allow a player to con an opponent into thinking that the face down card is something meaningful. If the card were not titled "Decoy" and continued to have an image that as far as I can tell has nothing to do with decoys I think that players would still experience the card as "a decoy".

Assisting here is the physicality of the thing. When this card is played it is physically placed somewhere on the board (or on another card). There is no greater way to carry the idea of "This thing is here. You should pay attention to it." than to physically place the thing on what is essentially the display that tells you what is going on in the game.

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I've written before about divisive cards and how the inclusion of something like this will be optional so that players that love this sort of thing can enjoy it without ruining the game for people who hate this sort of mechanic with the burning passion of a thousand suns.

However, whether you like it or not, there is an emotional impact to a card that has a physical delivery as this one does. A country posturing with their air force is a theme that has some weight - perhaps more so in the current political environment than when I first wrote the card - but the act of physically dropping the thing onto your targets yourself lets the mechanic carry more thematic weight then comparable abilities without that sort of physicality.

I've deliberately picked quite extreme examples here, but this idea is really more of a continuum. Activities like drawing or discarding a card may not feel like they apply in the same way, but they are physical acts. A game could create a divide between sacrificing one of your own things and having it destroyed by an opponent simply by shifting whose job it is to physically put the card in the discard pile (If other ergonomic issues of the game didn't interfere) - A "physicality carries theme" approach is possible without needing people to throw cards at each other.

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Another way to have a mechanic carry a theme is through consistent usage. The Javelin offers +1 in battles against animals. So does the spear. And the legendary black spear. Basically if it's long and pointy you get +1 against animals.

The strong point of this approach is that once you've established a pattern it locks in your theme and it makes it possible to reverse it. This allows you to use "+1 against animals" to carry the notion "spear" which saves you the space of writing it explicitly and frees up that useful useful title for something other than describing the object's physical form.

It also makes the thematic choice feel stronger than it is. When every spear behaves the same way then "Spear" starts to feel like a meaningful class of thing - because the mechanics are treating it this way. The mechanic can't be at odds with what the thing is, but even if it's not that strongly connected it'll start to feel like it is as people play the game and the pattern becomes established.

In short, if you want your spears to feel "speary" include a few in the game and make them all do the same thing, what that thing is does not particularly matter.

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There are six abilities on Scandinavia and the World characters that allow you to steal another player's character:

Shared Pleasures (Sister Sweden) Sexy but not Vulgar (King Europe) Classic Seduction (Sister France) Naive Lover (Sister Iceland) Seductive Vampire (Count Romania) and Misunderstood Artist (Brother France).

The astute reader should notice a commonality in theme between these abilities that explains how it is that a character who was previously loyal to your opponent is now more impressed with you. Brother France is the odd one out, but this should have implications for how exactly he is behaving as an artist.

A seventh card allows you to nominate a character to be stolen by a third party - Seating Plan (Brother Sweden) - which is again is a nod to the ulterior motives that sometimes drive his seating plans.

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Now this post has focused on cards going into the game, as I happen to be in the process of arranging them they're particularly salient to me today. However we learn as much from our failure as our successes so it's worth a quick look at some of the attempts to harness mechanics to carry theme that didn't make it out of playtesting.

Sister Germany previously had a "You Dare?" power which responded to any loss by making an opponent lose the same amount. The theme this is trying to carry is that she doesn't take any nonsense from anyone (though again, I hear that it is a trying time to a prominent female German politician). The problem was that once people had the card they would do things like using cards that obliged them to pay opponents and then destroy the payment as cards they had lost. This made her more about "not paying debts" than "not putting up with this shit" and undermined the theme. It is important to consider the interactions between your thematic abilities, not just their impact in isolation.

Christiana previously held a "The Good Stuff" power, which resulted in shuffling some cards together and giving them to players at random. This was supposed to establish a pattern of "Drugs cause randomisation" similar to "Spears kill animals" but one by one the randomisation cards were deleted as playtesters didn't enjoy them and soon it stood alone and made little sense. It doesn't matter if something lands the theme if it's not fun as a mechanic - obvious really - but it's easy to fail to see the wood for the trees when you're close to a design.

King Europe used to have an "Aggressive Recruitment" power in which he stole a character from the poorest opponent. This was supposed to be in line with the comics about him trying to recruit Norway into the EU but failing due to oil making Norway independently wealthy. However because "steal a character" was already being used elsewhere in the design and it couldn't pull double duty without weakening the both abilities. Fortunately King Europe has already been shown to resort to alternate tactics. The takeaway is to try to keep things clean. Well, not clean clean, but consistent.

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So there you have it! Three techniques for making card games carry their theme and three ways to make that fail by undermining yourself. I'm looking forwards to announcing the SatW launch soon, though as it's a lighter game I'm not sure how many people that read lengthy blog posts on design theory will enjoy it, but please let people who might be interested know.

The game aside I hope it was helpful to dive into this exploration of mechanics and theme. It's nice to talk about ideas, though this is a huge huge area and there are easily another dozen posts in it to write sometime. Happy gaming and look out for animals.
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Tue Mar 28, 2017 2:45 pm
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Engineering Standoffs

Greg
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An exciting point during a game is the moment after each player has had some opportunity to make strategic choices and build up their position, but before a decisive conflict that will reveal which of the approaches that the players have taken will triumph.

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These moments don't occur by accident. If a designer doesn't consider their game the natural tendency is for the player with the advantage to push the conflict immediately while they're sure that the situation still favours them. To create a tension between players getting ready to act it's necessary for the designer to take steps to ensure that there's a motivation for the standoff to persist, at least for a little while.

The design question boils down to "How do you have a game in which a player can ultimately initiate a conflict and emerge victorious, but will be unable to do so until they've manoeuvred themselves into a significant (rather than mild) advantage?"

Some games simply don't care, their moments of tension and excitement aren't vested in this moment, that's fine. Those that do have a variety of different design decisions that let them capture this element in different ways. Today I'll take about five approaches: Risk, Obfuscation, Defenders, Revelation and Asymptotes.

Risk

I really wanted to use Risk as my example for this one, but it's actually relatively weak in this regard (when we get to defenders in a minute you'll see why). So I'll go with Prophecy - in this game you're wondering around the board, killing monsters to grab equipment and skills. When you think you're ready, you ascend to the astral realms to challenge guardians and steal their legendary items, the first player to get four of these items wins.

The standoff occurs when a player is powerful enough that they *could* defeat a guardian but not powerful enough that they definitely would. Combat is determined by a die roll so there is an element of uncertainty in how something will play out. Coupled with relatively severe penalties for failure (If you manage to get your character killed you start again from the very beginning) it creates a situation in which a player might have a slight advantage, but would be reluctant to progress to the final confrontation without doing more to shore up their position.

Obfuscation

In Ninja one player is using hidden movement to infiltrate a stronghold while the other openly moves a great many guards to try to stop them. At some moment the ninja must attempt to complete their objective, but in doing so reveals something about their location (a space they passed through this turn) to the guard player.

The standoff occurs while the players jockey to find the right position to make their move from. The ninja doesn't know exactly where in the stronghold their targets are and so has incomplete information, similarly the guards have no idea where the ninja is. In the moments leading up to the burst of activity provoked by the ninja's first search one player might objectively have a clear advantage, but the game's information is somewhat obscured making the right moment to strike more ambiguous.

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Defenders

How many games have a rule along the lines of "Highest score wins, defender wins in a tie"? The effect of this rule is to create a margin of power within which neither player can attack - as they're sufficiently evenly matched that the defender's advantage will be sufficient to swing the conflict. I'm going to use Magic as an example here because it's defender advantage mechanic is less obvious than in some other games and has some neat emergent properties.

In Magic both players can summon creatures. When creatures fight any combatant with a strength equal to or higher than the other creatures toughness kills it - otherwise they do nothing at all. There is no "defender wins in ties" the creatures kill each other if they're both capable. The defenders advantage instead occurs implicitly because the defender gets to choose whether their creatures intercept an attacker or not, which in turn decides which fight takes place. This creates all sorts of stand off situations. Suppose one player has a 5/1 creature and the other has a 1/1 - a clear disparity in power. If the player with the better creature attacks it will be blocked and killed, trading its life for a much weaker creature - but if the player with the weaker creature attacks it will be ignored and deal minor damage to the player while leaving them open to a counter attack from a much harder hitting creature.

Revelation

Traitor games come by this idea from a different direction. In The Resistance players select a group to go on missions - the members of that group then play success or failure cards to determine the outcome of the mission. The traitor team wants 3 missions to fail, the loyal team wants 3 to succeed. If a mission results in failure, it is obvious that at least one person in that group was a traitor (the loyal team isn't even allowed to play failure cards).

The standoff occurs because the traitor needs to determine when to throw in a sabotage card, in this case the situation is known and the outcome is predictable - but what the other players will do with the information that you reveal to them is the unknown factor. Where a game based on obfuscation may create a standoff based on players being uncertain as to the state of the game, a social deduction game can create the same effected based on players being uncertain as to how the social dynamics of the group will play out.

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Asymptotes

What if your game is cast from the euro mould and doesn't allow direct conflict? As is always the case with euro games, math has you covered. By which I mean thinly stretched metaphors using slightly misinterpreted mathematics. In Dominion players purchase cards which can enable them to purchase more cards or provide victory points necessary to win the game. However cards that provide victory points enter that players deck as "dead cards" and make it harder to purchase further victory points.

In this sort of system a standoff exists because there is a band between the point at which a player first could start taking decisive actions towards ending the game and the point at which its desirable to do so. By ensuring that progress towards victory slows the engine making that progress a tension is created between a desire to make progress now and to hold off starting the end game for a little while. While there is no direct confrontation the choices of the other player(s) factor heavily into when launching into the final sprint is a wise choice.

Summing Up

There are many more ways in which a game can create interesting stand offs, but the key ingredients to all of them are these:

A decisive action that shifts the game from build up to action. Whether that's buying victory cards, searching the first tile or simply launching an honest to go attack an identifiable moment where the stand off is broken is needed to define it.
A reason for players to be in the situation in which they could take the decisive action, but would not want to.
Some degree of uncertainty about the future following the standoff being broken, whether that comes from randomness in the game, unpredictability of player's actions or information that's not available to the player.
Not every game needs this element, but games that use it well can produce memorable experiences. Happy gaming and don't blink first.
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Tue Mar 14, 2017 12:25 pm
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What's Wrong With Me?

Greg
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Context: Infinite Legacy (but lets be honest, it applies to everything)

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It's generally not the done thing for creators to talk about this kinda stuff, but for the second time over the course of this thing I've disappeared for a few weeks with no notice. In designing games I'm often asking people to trust me with their money, whether through board games Kickstarters or the Infinite Legacy Patreon (when I finally launch that!) so I think you've got a right to know why I vanish, what the odds of it happening are and how it impacts projects that you've paid for.
This post may be a bit tl;dr for some so I'll summarise: Sometimes I'm broken. Stuff may be late, but it'll never be more expensive. When I'm not working on stuff I don't charge for it.

I'll go light on the medical detail partly because what matters for the purposes of this post are the impact on game design more than the nitty gritty detail but mostly because I am not a doctor (of medicine) and so there may be some slight irregularities in my understanding. Let's give it a paragraph anyway though:

The spiny squidgy bits in between the bony bits got squigied more than they were supposed to and made a bid for freedom. Two of them started to escape - lets call them Jean Valjean and Pascal Payet (my back is French now because England's prison escape stores, both real and imaginary, are less evocative). Jean's escape was nice and orderly and he was well reluctant to hurt anyone on the way out. Payet's was all spectacular and involved elbowing some nerve clusters. From time to time he gives 'em a good squeeze and they say "Well fuck this then lads, we can't work under these conditions. Tell the boys downstairs that we ain't getting any instructions from the brain and send a note to the brain saying that the lads are reporting constant pain. Then we can all take the day off while they fight it out with each other. Who's for tennis?"

In practical terms this means that I lose the ability to walk, basically at random. When it goes, it goes for a period between two hours and two months, again pretty much at random. So any project you support in which I'm a key member of the team might get a two month delay.

Where I can I hand my work off to other people. If I'm working with a company, as it was with 3DTotal or The People's Orchestra this tends to be pretty practical. If I'm in a smaller team it might be that the work needs to pause until I recover. The stage of the project also has an impact - if something is in the playtesting and improvement step it has a different impact to if something is in the layout and artistry step.

There's a cost associated with delaying projects, but I never want to pass that cost on to the player. Ideally the government that's taking my taxes when I can work will properly discharge its responsibilities and cover my living costs when I can't - but at the end of the day I'd rather suck up the loss myself than pass it on to you (which seems more likely in this day and age, though political rants can wait for another day).

A Kickstarter might be late, which might increase our operating costs, but I never want to charge a backer more for their game. The reason that I'm doing a dry run of game development via Patreon is to iron out bugs and one of the things that's come out of that is that I want it set to "custom charge" rather than "monthly charge" so that I can hit the button every month that I'm well enough to work, rather than every month come rain or shine.

The condition isn't degenerative, ironically if it was they could fix it (Apparently they couldn't identify a surgical target and act on it before the flare up is over, particularly with the unpredictable lengths of the issues), so there's no reason to expect that it'll ever lead to a project failing to be completed.

So in a nutshell that's why I've not been posting for a while and why all of the projects have been paused. I hope it gives you confidence that all of my projects will happen (Alongside my past record of delivering all of the games that've funded ) and makes it a little more understandable where there are blips in communication.

There's still room for improvement there, getting someone else to post an update when it happens would be a good working practice to get into, though this doesn't happen often enough for me to ingrain it as a habit. It's always good to look for ways to improve
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Mon Mar 6, 2017 1:38 pm
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How Many Cards?

Greg
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Context: 3DTotal

I saw a post on BGG today with a new user asking "How big should a deck of cards be and how many cards of each type should go into it?" This has correctly been answered with "It depends" - but what does it depend on and how do those dependencies work? Let's dig in!

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Let's start with the size of the deck: How quickly are we drawing cards and what happens when the deck runs out?

If the game is going to end when the deck runs out then we can use the intended length of the game and the draw rate to derive the ideal deck size. If a deck running out triggers some important event (e.g. The overlord gaining threat when his deck is reshuffled in Descent) then the desired frequency of that event becomes something we can use. If the discard pile is simply going to be reshuffled then we need to consider other factors.

A hard minimum on a deck size is the number of cards that will simultaneously be out in the most extreme situation. If your game has five players and each has a five card hand and there are ten upgrades that'd increase a players hand size by one then your deck can't be smaller than 5x5+10 = 25 cards. It sounds silly, but I've been at playtests where a prototype has ground to a halt because a deck that was still in testing ran out of cards in an infinite loop of shuffling an empty discard pile into a deck in a never ending attempt to draw one more card.

Another factor is how predictable you'd like a game to be. There's an interesting comparison here between Magic and Hearthstone (Yes I know, the latter is a computer game, but it's a computer game of a board game so we can analyse it). In Magic you have a sixty card deck with no more than four of each card. In Hearthstone you have a thirty card deck with no more than two of each card. Initially the chance of drawing a maximally included card is the same in both games (1 in 15) but this changes over time. A smaller deck creates a more consistent and predictable game, because while the average number of draws needed to achieve something remains relatively constant, the probability of this game being similar to the average is higher. If you need an intuitive illustration of this consider the following: How many copies of the target card will you see in the first 30 draws of a Hearthstone game compared to the first 30 turns of a Magic game?

However there is a factor tensioning in the opposite direction: How fine a probability do you want to be able to model? If you've got something that you want to have a 1 in 10 chance of happening, you're going to struggle if your deck has less than ten cards. It's all well and good to suggest that 2 cards a in 30 card Hearthstone deck is the same as 4 in a 60 card Magic deck - but what's the Hearthstone equivalent of 1 card in a Magic deck? Half a card? How are you going to do that?

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Another factor regarding deck size is how probable you want a particular combo to be. This sounds like it matters most in something like Magic, but it's a much bigger impact on say Fluxx - in which drawing an objective and the card(s) needed to complete that objective together can all but end the game. Of course here you need to think carefully about what constitutes a combo - there's a difference between the probability of drawing "All you need is love" and "love" and the probability of drawing "Any card that lets you draw more cards" with "Any card that lets you play more cards".

Finally - how impactful is each card? If every card drawn has a tremendous impact then a deck doesn't need to be particularly big. Consider the objective cards in Kingdom Builder. They completely redefine the game, causing a player to adopt an entirely new strategy to deal with them. As such very few are drawn per game (Three at the beginning) and the overall quantity needed is not particularly great Conversely, if each card isn't individually doing much you'll need a larger deck and more draws for it to have the desirable aggregate impact on the game.

Moving on to the multiples question - suppose we've fixed our deck size at 50 - how many do we want of each card?

Well again start with what happens when a type runs out - decide how desirable that is and set the quantity accordingly. Note that this can be a direct or indirect effect. So in something like Dominion the game explicitly ends when three stacks are empty, so the size of a stack needs to be set carefully to be in balance with the desired end of the game. However it can also happen indirectly - I've been playing a lot of Steam Works lately and there are some noticeable soft effects when the deck runs out of something important like Upgraders or Automations. Knowing "They're both gone, besides the one on the table this will be the other players only choice for an extra action." affects how the second Automation tile is played. Watching your playtesters for reactions as particular things come out and deciding when you'd like that reaction to occur can help to set the number of instances of something.

An extremely obvious measure is how many times you'd like a thing to happen. If you're running through a deck once then that's a 1:1 mapping with the number of copies of that card. If you're going to reshuffle the discard pile then you need to do some maths on the average number of turns the game is intended to last - but ultimately you can set a relationship of "This should happen X times per game" if you so choose.

A third important factor is to consider the consequence of drawing multiples of the same card (either consecutively or as part of the same hand).

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This can be desirable or undesirable from the perspective of the player, depending on the game being played, but that's not as relevant as you might suspect. The real question is whether it's desirable or undesirable from the perspective of making he game fun. Does a repetition generate interesting new strategies or make the game stale? Does it generate a heavy skew in who's likely to win and does the game have mechanisms to support this? How does it feel to draw a hand like this and is that a feeling you want people to experience during your game?

Finally, what relative probabilities do you want out of your design? Depending on the game you might want a degree of "filler" if your deck is essentially a way of going "There is a chance of notable thing happening and it will eventually happen". Something like Exploding Kittens takes this to extremes, with the win card (well the lose card, but one person's loss is another persons win), being the notable event and relatively large portions of duplicate cards being used to space those out.

If you're considering publishing, then the constraints that provides should also be considered. Bigger decks cost more money (per game) and more cards with unique art costs more money (once only). It's not good to sabotage the quality of a game in pursuit of publication, but sometimes the answer will be "It doesn't matter between X and Y" in which case you should usually go for X.

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With all of these questions and requirements (and more considerations I've not covered - it's a super broad question!) there are bound to be contradictions. Where two requirements are in opposition the game designer has only one option left: Compromise!

Wait no - I mean Shenanigans!

Suppose you've got 4 events that you want to happen 25% of the time but with deck reshuffling and a chance for the same event to happen three times in a row - what's the minimum deck size?

If you answered 12 you forgot that the last card before a reshuffle might be the first card after it, you should've answered 8. If you answered 8 you forgot that the end of a deck doesn't *have* to be the only time you reshuffle. You can get away with 5 - one of each card and a fifth card saying "Reshuffle the deck and draw again". I think a lot of Game of Thrones players overlook how great that winter is coming card is as something thematic that also allows some probability manipulations that'd usually require a larger deck.

Suppose you've got a 60 card deck that contains Key Card (tm). You want the odds to favour it coming up in the first 20 cards, but you can't have it happen more than once so don't want to include multiple copies. Do you have a solution that doesn't mean compromising on the deck size you've picked for perfectly legitimate reasons?

Yeah! Of course you do, we talked a few weeks ago about how deck search affects card probabilities. You can throw in a few "Search the deck for any card" cards, which let Key Card (tm) come up earlier but don't act as duplicates. Other solutions including having Key Card (tm) have a different effect based on how many Key Card (tm)s are in the discard pile and including multiples to make sure Key Effect (tm) happens roughly when it's needed without Key Card (tm) having to be unique.

I have not actually trademarked the phrase Key Card (tm) and have no idea where this compulsion has came from.

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Another trick is to split or combine cards. In 404: Law Not Found action cards can each be played for one of two effects. This was actually a dodge to make hand sizes more manageable while still offering a reasonable number of options - but it would serve just as well as a means to manipulate towards an intended deck size. Conversely the effects of several cards can sometimes be combined as in Blackbeard which uses the same cards to determine what sort of ship you find, the consequences of losing a duel, if your crew feel like a party, what sort of random event is coming up and more depending on the context in which they're drawn.

So - that's my whistle stop tour of things which impact on deck size - and tricks to nudge the edges of those limitations when they're inconvenient. With such a broad subject matter I couldn't really hope to cover it all in one blog post, but hopefully it's a good start position for thinking on the subject

On a side note - just for the BGG blog - I think I might've just tagged more games in a post than I ever have before. When I asked for feedback at the start of the year I got asked "Give more examples from games we've played" so hopefully this sort of thing is hitting the spot
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Tue Feb 14, 2017 2:43 pm
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Board Design

Greg
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Context: Infinite Legacy

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Last week I expanded the infinite legacy playtesting to a larger group to try to get some broader feedback. That was a nerve wracking excercise that deserves a detailed write up at some point, but it did not happen immediately because my spine promptly exploded leaving me stuck in bed for the next six days or so.

One of the reasons for running the Patreon for a year before asking for any support is to work out kinks, I'm pleased that I've got a system in place to say "I was injured this week and didn't do any work, so nobody pays anything" and confident it'll stand up to such problems once it's launched. Anyway, this week I was recovered enough to do more work and wanted to talk about it because it touches on a really important part of board game design: Board design!

You can play a lot of games without ever really thinking about the layout of the board. How many spaces are there on the Small World board? How many of those are magic spaces? How many are field spaces? How many are magic and field spaces?

At some point the designer of any board game has had to make decisions like that and there isn't always a mathematically obvious solution. To some extent the goal is symmetry: You don't want your game to be unfair, so putting too many of one resource type together will benefit solutions that exploit that particular resource. Always having the same combination of things occuring together means that comboing them is disproportionately powerful compared to combining other resources.

However you also don't want it too symmetrical. When a board is identical in all directions, it's boring. It also robs the player of meaningful choice - part of how players choose a Small World faction is to look at the least defended routes onto the board and see what sorts of resource they're rich in. Or to consider what opening might maximise the things that they score for. A perfectly symmetrical board with exactly balanced resources would take away a meaningful decision leaving all approaches equally valid.

There's also the need to constrain the board to generate the sort of game play that you're looking for. In Infinite Legacy playtesting has revealed that the sweet spot for spaces between cities is three. At two spaces cities can expand once each and come into contact immediately, which feels too fast and robs players of agency to avert a war if that's what they're aiming for. At four spaces cities can expand twice each without coming into contact - given only five moves are made in a game that's almost half the game!

This sort of spatial consideration affects a lot of different types of board game. Consider something like Ninja: Legend of the Scorpion Clan, the fundemental challenge is to move onto the board, get to a spot and move off without being caught (or to catch the person doing that if you play as the guards). The distance between things is a *huge* factor for that game. Why are the spaces in the fortress smaller than the ones around the edge of the board? Because that's where the interesting gameplay happens - there needs to be enough space for evasion to be possible in the key objective areas, but not so much that it's guaranteed. There needs to be enough distance to make crossing that area meaningful, wheras walking around the edge of the board isn't intended as a meaningful challenge or a game focus.

A lot of the time there's a degree of theorycrafting that's possible. Smallworld can say "If all the players have a race down of average size I want there to be 8 too few spaces for them to all spread out", Infinite Legacy can say "I would like the first conflict to be possible by turn 2 and likely by turn 4", Ninja can say "I would like the direct route away from a successful objective to be three turns of movement" - but playtesting is always necessary to refine exactly how a board should be laid out.

As you may have noticed (If you've been following this project) I've been using the Smallworld board to playtest, but moving the city locations around each test to try out different configurations and distances and concentrations of resouce. That's been great for getting a feel for how these things impact gameplay - but I'm getting a good enough feel now.

It's time for the game to have its own board and for that to start being tested and mutated depending on what awful things players decide to do to it.
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Fri Feb 10, 2017 6:03 pm
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Enough Rope to Hang Yourself

Greg
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I'm very interested in the self-destructive part of the human condition. We are in the process of making our environment uninhabitable to humans, have devised increasingly sophisticated means to prove it beyond any reasonable doubt and are doing it anyway. We're hilarious. So most of the games that I design contain some means by which a player can make everything terrible and then finds ways to make that choice seem compelling.

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Wizard's Academy is probably the most obvious example, which frequently offers short term relief by creating a long term problem. The room is on fire? Open a hole to the water dimension! That'll be a bigger problem in a few turns, but that's a few turns away, something will come up by then.

The general pattern of this sort of system is that the player is presented with a choice, which they make. The situation then changes or new information becomes available. The consequence of this is that the earlier choice is now detrimental in terms of the objective for which it was originally selected.

As a game designer, why do this? What does it offer to the player?

Let's talk about a few examples and games that pull them off:

If the downside is appropriately telegraphed it can contribute to the role of skill over random chance in a game. Being able to recognise the choices that will come back to bite you in the arse over the genuinely good ones becomes a part of the game - players who play games in order to hone their own skill (or to contrast it with others) get something out of that extra layer of thinking.

This can be a work of profound subtlety or it can be something so critical that once someone recognises "the mistake" they'll never do it again. Something like Dominion contains both, there are plenty of subtle interactions and then more obvious things like new players buying copper to get more money and discovering that their average turn results in less money because copper is poorer than the average money card in their deck. The key to making this work is to avoid "dead options" which are essentially traps and always a mistake. A game becomes complex without very much depth if players quickly learn, you need to know the rules for A, B, C and D - but only B is worth doing. Dominion dodges this by having other interactions that make it sometimes advisable to buy copper (or more subtlety self defeating cards) so that the option remains worth considering once a player has got the hang of "Devoid of context, this is a bad idea."

I described our self destructive nature earlier as hilarious - but actually that's not too far from the truth. People find it funny to watch other people suffer (In Stranger in a Strange land Heinlein has his alien observer that all humour is rooted in pain) but it's funnier if they do it to themselves.

Consider nudging someone in RoboRally. Pushing someone into a pit is satisfying - but pushing them off course so that they drive themselves into a pit is even more satisfying. This functions best when the game has a fair play element - in which a person might reasonably have seen the consequence of their action and considered an alternative - rather than just being defeated by some unknowable unpredictable thing. Robo Rally achieves this by making individual moves relatively predictable (The other robot can go 1-3 spaces in a straight line, the further it moves the more likely it is to move before me) so that a player has some capacity to predict where they might be nudged and plan accordingly.

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Incidentally this is somewhere that I feel that I didn't nail the design of my first published game - 404: Law Not Found - as well as I might. Moving action programming to a smaller environment seemed like it would have more interactions and avoid the situations Robo Rally can have where other players aren't within move distance and it's not so interesting - but having it such that on any given turn you could be knocked in any number of ways from any number of directions undermined the predictability of those moves, which cut out a part of what makes them effective. I'm quite impressed by how Colt Express nailed the action programming in a small environment by making the range of actions that immediately affected other players more limited and having shared open planning for greater predictability.

Going back to giving people the tools to make life terrible - another advantage that it can provide is repeated high points. It's good for a game to have high points that feel like "This is it - this move will make or break the game", however they can't be that frequent because otherwise the game is inevitably going to break. Essentially big stakes can only exist by comparison to small stakes - you can't make your game higher stakes by just multiplying every victory point output by ten.

Future self sabotage makes repeated high points a more achievable goal. Consider something like Space Alert in which everything feels like it's going to explode and doom you all continuously. You wind up being able to go "Well I'd like to deal with it this turn, but I'd also like to leave a gap in case that last move broke the elevator. I can have what I want now or I can be sure that I'm not making a mistake that ruins everything - but I can't have both. Games are series of meaningful decisions so that sort of decision tree is compelling and it can make decisions feel high impact where it's possible that either decision is fine (or either decision is doom!)

Here Space Alert has an advantage in not having the outcome of the decisions revealed until all subsequent decisions have been made. It also benefits form a series of individually achievable objectives, but arranged in such a way that achieving one may be an impediment to achieving others (by virtue of people being in the wrong place, or power being used, or shields being depleted etc.)

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There are, of course, downsides to this kind of design. Most players viscerally hate being stymied by a game or the feeling that the designer is willing to "cheat" in order to make them lose. Giving people enough rope to hang themselves is fine, but failing to telegraph the possible consequences of their actions and providing some meaningful way for players to discern between their options means that they'll blame the system rather than themselves.

That changes "I can't believe I fucked it up that way, I'm gonna do something different next time." to "Nothing I do matters, this game sucks, let's not have a next time."

It's not for every game and it's not for every group, but there are times to give players more power and let them use it to destroy their greatest enemy - themselves.
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Wed Feb 1, 2017 12:01 pm
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The interconnectedness of all things

Greg
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The new Infinite Legacy prototype is assemebled and has seen a little love, but the changes proved more extensive than anticipated. Reducing the number of tokens on the board by changing the way that resource tokens are placed is all well and good - but it had knock on effects in other parts of the game that weren't immediately obvious.

This is likely an issue for games with exception based gameplay in general. If you're not familiar with the term, it's games that have (relatively) straightforward core mechanics that are elaborated on by cards. So a rule might say "You place one resource token on a space" and a mine card might say "Whenever a city with a mine places stone on a space, place metal as well" - the card is the exception to the rule.

The consequence of this is that changing the base rule means that all exceptions linked to that rule need to change - and it's easy to miss them. The mine is a nice obvious example, but realising that the reward for having a hero with the heroism special interacting with an ambitious leader is harder to spot.

I am curious if anyone else has tools or systems they use to keep track of this sort of thing? Do other designers go through every card by hand every time they change something? Go CTRL+F for relevant keywords? Actually remember everythign they've done reliably? Use some sort of specialist software to track all cards relevant to a particular thing?

In any event, progress on Infinite Legacy goes forward, but some relatively straightforward updates broke a lot of other things so the playtest and improvement cycle isn't as rapid as I might like.

The new city strips do feel nicer to use though
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Thu Jan 19, 2017 11:15 pm
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Card Probabilities

Greg
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Context: 3DTotal

I've been playing a lot of Magic: Duels lately and consequently have been spending a certain amount of time swearing at the frequency with which I get hands that either consist entirely of or are entirely devoid of lands. Thinking about how likely that is opened the floodgates to a ream of ideas about card games in general, so let's dig in:

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Before I get too far into this topic, let's do a little bit about Magic to contextualise it - you can skip this if you're a Magic player (And if you're not, don't worry, we'll talk about other games in a bit). The important thing to know for our purposes is that your cards are divided into lands and spells. In order to win you'll generally want to play lands in order to be able to play spells. A hand with only spells is bad because you cannot play any of them, a hand with only lands is bad because they can't do anything to help you win on their own. Depending on your deck you might be hoping for 2-4 lands in your starting seven card hand.

For this example I'm assuming a deck with 23 lands and 37 spells, which is reasonably typical. So looking back at the graph you can see the most likely outcome is drawing 3 land (at 30.29%) followed closely by 2 and the extremes are vanishingly unlikely.

So how does this compare to dice? Suppose I'm not drawing seven cards from a sixty card deck, but instead rolling three sixty sided dice - what happens?

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The shape of this distribution is totally different! The move from cards to dice has left us...actually that's pretty similar.

There are differences though - it's more obvious in some places than others, but you can see that the central results (2-3 land) are a little less likely with dice and the extreme results are a little more likely. What's going on with that?

It's simply a consequence of removing cards from the deck as they're drawn. If you've rolled all land on your first six dice, dice seven is still just as likely to roll land. However if you've pulled six land cards from a deck, only 17 remain, so the odds of the extreme result are reduced. Essentially using cards over dice will produce more consistent results.

(Though after the fifth "no land" hand in a row it doesn't fucking feel like it.)

The difference in an initial hand of magic is quite subtle, but they become more pronounced as decks get smaller. Let's consider the same comparison, but for copper in the opening hand of a game of Dominion:

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In dominion you have a deck of 10 cards, 7 of which are copper and you draw 5. As such you can't possibly draw only 1 copper (since you are drawing 5 cards and there are only three not-copper) so comparing the deck of 70% copper to the dice of 70% chance of copper shows some divergence pretty early on. This sort of divergence is great for balancing games in different ways, the card based version of Dominion gives players a more even start than its dice based equivalent.

Always remember that a fairer game is not always more desirable - the game needs to have the right attributes for its goals - but it's good to know how changing your tools gives different opportunities. So is that the limit of what we can do with cards?

No! Of course it's not

Let's consider the impact of drawing a card vs drawing a card that lets you search the deck for the card that you want. Consider two situations in Last Night on Earth - I'm doing the quest involving rescuing all of the NPCs. There's a card called "Just what I needed" which lets me look through the deck for anything I want and take that.

Suppose there are 20 cards left in the deck and I'm going to manage to get 10 of them before being eaten by zombies. I need to find two more NPCs, which is more desirable: A deck with 2 NPCs and 2 "Just what I needed" or a deck with 4 NPCs?

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The difference in success between these scenarios is a little over 5%. The 4 NPCs situation will end well 70.9% of the time. The other scenario ends well approximately 65% of the time.

The reason for this is because of how deck searching cards alter the deck. Consider what happens if you get an NPC on your first draw (in either scenario) - there are 3 cards that will help you left in the deck so your odds on rescuing the town on your next draw are 3/19. However if you drew "Just what I need" and searched out an NPC the deck now only contains two cards that can help you - the remaining "Just what I need" and the other NPC - so your odds are only 2/19 of managing that on the next draw.

(Edit: A reader below points out it is in fact 2/18 because an extra card has been removed form the deck. This is correct, though does not change the conclusion of the paragraph. It does draw attention to the fact that it's a good idea to understand the underlying principles of a thing rather than blindly trusting what a stranger on the internet writes though )

The fact that deck searching works in this way makes it something that we as game designers can use. For the alert player being able to search something out can be a reward or penalty (depending on the context of the game) which can allow some sneaky balancing choices and a high skill ceiling in which players are taking quite subtle effects into account.

It's also something that can be used to generate a desired emotional impact without throwing off a balanced element. Consider an effect in a cooperative game like "Search the deck for the biggest monster, it attacks!" this can be great for creating a feeling of tension or danger or appropriately punishing a poor choice - but at the same time it also ensures the necessary downbeat for players to recover from the tough encounter by making the upcoming cards friendlier.

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Trashing (permanently removing cards from a deck) works in broadly the same way, but without the card taking effect first - it's not worth rehashing similar calculations to show it's value, but it deserves a mention as something that we can do with card based randomisers that don't work for dice.

Something that does deserve a deeper look is the notion of shared decks vs individual decks. In most deckbuilders each player has their own deck - in a lot of adventure games players draw from a shared deck. Let's say we're heavily modifying Talisman and have decided to monkey with the adventure deck.

The adventure deck can be really swingy, sometimes it'll give you a fantastic treasure that really boosts your character. Other times it'll give you a monster that you can't possibly beat, leaving only wounds and pain. To abstract the process we're just going to call each card good or bad and consider them in those terms.

Let's consider three systems:
1. The players share a central 60 card deck, evenly containing good and bad cards.
2. Each player has their own personal 20 card deck, again, evenly divided.
3. We have a good and a bad deck. Players flip a coin to decide which to draw from.

Suppose each player has five adventures in the early game - how much difference should we expect due to random chance?

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In all cases we're more likely to see one player getting more good cards than the other than a balanced outcome. There's not as much to show between the coin flip idea and the shared deck as I'd have predicted - a shared deck feels unfair as if another player draws a great card they've not only had a lucky break but also increased the chance of bad draws for other players.

The effect exists - a fair or 1 pt difference outcome is 0.4% more likely with the coin flips than a shared deck - but that's quite a narrow margin. The impact of splitting the deck into smaller solo decks is much more pronounced.

From a design point of view it's interesting to think about the point at which the differences between cards and randomisers start to become pronounced. With large decks there's not much distinction (with an arbitrarily large deck there's no distinction at all) so lets look at how solo decks play out over a variety of deck sizes:

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The difference between using a 10 card and 20 card deck is quite noticeable, but everything above that becomes an indistinct smudge. There is still an effect there of course, but it's much diminished.

This bears some thinking about, in terms of whether there may be times that an illusory effect exists, in which an initially small deck generates a very tight start, but as they bloat chance becomes more of a factor. This would allow a game to give an impression of containing less chance than it does, which could be desirable in some types of game.

Though of course abstract mathematics is just that - abstract - until it's considered in the context of some particular game then all we're looking at here is general patterns. Nonetheless, there's a lot to love about how cards behave differently to dice as randomisers and all of the delicious options that provides for getting new types of game to behave in interesting ways.
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Tue Jan 17, 2017 1:45 pm
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