Monday, December 30, 2013

Grokkable Moment

I have been thinking a bit about good games to introduce people to Eurogames. Settles of Catan was my introduction to them and was my go to for sharing Eurogames with others. Recently, I acquired 7 Wonders and feel I have had more success with it. My friends ask to play 7 Wonders more often than any other game. In thinking over the differences between the games a few things pop out, namely the length of the game and the complexity of the rules. These features end up combining in such that new players grok 7 Wonders just as it ends, so they are ready to play again and use their new found understanding. Whereas in Catan, new players tend to grok the game when it becomes obvious they are going to lose. This usually leaves a good 15-30 minutes of them playing a game where they know they are completely irrelevant, which is a decidedly un-fun experience.This leads me to believe that the best games to teach people about Euorgames are shorter games where the moment of grokking occurs just as the game ends.

I am sure that not everyone is familiar with the word grok. It loosely means "to intuitively understand." That light bulb that just went off in your head where you "got" what grok means is what if feels like to first grok a new concept. It is that experience that helps draw people into a game. When a person learns something new, they immediately want to apply it. The moment when a player sees a new strategy or how the rules interact clicks is one of the times when that player will be most engaged with the game. They will want to both test their knowledge and show off their new understanding.

Capitalizing on the desire to try new knowledge is one way to draw people into a game. One way a game can use this feature of human psychology is through presenting players with same situation repeatedly. This way players can immediately make use of knowledge gained in the previous iteration. Another use, and the point of this post, is to structure the game so new players grok the rules right at the end of the game. This way the players will immediately ask to play again to use the new knowledge from the first play.
 
7 Wonders does this by having most of the points scored in Age III. Most new players are confused in Ages I & II because they mostly setup Age III. Once the player sees the value of the Age III cards and how expensive they are everything falls into place for them on how the game should flow. The rest of Age III tends to be spend gathering more information by reading up on what different cards do so the new players have a more complete picture of what to anticipate in Age III next game. Luckily each age is fairly quick so new players don't have time to get bored or discouraged about losing as they are still actively learning. Add in that each play of 7 Wonders is about 30 minutes and you have a perfect receipt for how to make new players want to play again.

In contrast, Catan has a much longer end game. It could easily be 15-30 minutes from the point at which a player is inevitably going to win and the game actually finishing. When this point arrives, most new players realize the large mistakes they made in the early game which constrain them from wining now. Moreover, there is little learning for new players at this point as only extremely tight play can save them, which they are not experienced enough to preform. Combine this with an average game of Catan taking a hour or more and it is easy to see how 7 Wonders provides a nicer new players experience.

I think these differences in the moment of grokking a game plays a large role in new players asking to play again. From my limited sample, everyone immediately asks to play 7 Wonders again, whereas I usually have to prod for the second game of Catan. To me this means that 7 Wonders and other short games with late moments of grokking are the best to teach on. These games will end up in more people asking to play again which results in more long term casual gamers.  So while I do like Catan, I don't think that it will be my go to game for introducing players to the world of Eurogames.

Friday, December 20, 2013

Catan No Trade Theorem: Take 2

Yesterday I posted about how the Milgrom-Stokey No Trade Theorem applies to the Settlers of Catan game. It was a little technical and very stream of conscious, so I wanted to take another crack at it after thinking about the problem some more and coming up with some interesting implications. Including not only a new No Trade Theorem variation and the result that trade is possible in Settlers, but also trades can occur where everyone knows that one player is getting screwed over! In covering this ground we see that one of the rules of Settlers that looks like it restricts trade is actually key to enabling it.Well done Mr. Teuber, well done!

Though first I have to admit I made a mistake in applying the theorem yesterday. One big difference between the Settlers' universe and the Milgrom-Stokey theorem is player's utility depends on the players' hands and buildings in Settlers, but this is not allowed under Milgrom-Stokey. I gave a convoluted argument about how to fix this in the previous post which is wrong. Luckily one can simply expand the Milgrom-Stokey setup to include utility that depends on the other players' consumption and all the math still works. Overall not too big a deal.

This extension does limit the potency of the resulting theorem though. For example, consider a trade between 2 players that they both agree to. In the Milgrom-Stokey world, the other players are indifferent between this trade happening and not because it doesn't affect their utility. Therefor all players approve of this trade, which means that neither of the two players involved in the trade actually benefit. In the standard setup this result has a lot of bite. Now consider the same 2 player trade, but in a Settlers' world where this can affect the the utility of players not party to the trade. Here we don't have that the other players must be indifferent. Moreover if at least one of the 2 players that are party to the trade is made strictly better off by the trade it must be that one of the players not party to the trade is made strictly worse off. This is a directly implication of the No Trade Theorem in this setting as if some player was not made worse off, all players would agree to the trade and hence no player is made better off.

The insight that both players involved in a trade in Settlers could be made better off, but make some other player worse off is key to understanding how trade could exist in the game. For example consider a trade between players 1 & 2 in Settlers where player 1 gives 2 an Ore in exchange for a Wheat. As a result of this trade Player 1 builds a city on his turn and during Player 2's turn she also builds a city. It is not hard to imagine a board setup where this would put both players far ahead of the remaining player or two not part of this trade. Granted this is a pretty rare occurrence for a trade to so clearly benefit both parties at the expense of the other players. But this partly explains how trade could occur in Settlers even if players are perfectly rational and have perfect understanding of the game.

Personally this is not a fully satisfying answer. Particularly because of how much weaker the no trade theorem is in an environment where utility depends on all players' consumption. A No Trade Theorem which applies to trade that any number of players approve of would be closer to the spirit of the Milgrom-Stokey result. One of my colleagues suggested how to do this. Consider a trade in Settlers that benefits both players and hence harms a player not party to the trade. Assuming he is not budget constrained, this 3rd player would be willing to offer a trade to one of the two players considering trading that would cause him to be hurt less and the other player to gain more than she would under the current trade on the table. This trade then blocks the original trade as one of the players who was part of the original trade prefers it. Clearly if one can construct such a blocking trade for any trade, no one can trade because it will always be blocked. In the language of cooperative game theory the core of this game is empty.

A theorem of this form would prevent trades which don't involve all players as the other players could find a way to block it. Such a theorem would be a true analogue to the Milgrom-Stokey result. At the moment I haven't proved that such a theorem is true, but lets assume that it is and applies to Settlers. Would this theorem actually imply No Trade?

As hinted at in the introduction, such a Theorem would not be able to prevent trade in Settlers. In the motivating example we had the 3rd player offering a different trade to one of the two players involved in the trade on the table. There is nothing that says which of the two players this 3rd player could present an appealing trade to. It could be that the only trade the 3rd player could use to block the trade on the table is with the non-active player. This would violate the rules of Settlers. Only trades in which the active player is one of the parties are allowed. Thus a rule that restricts the possible trades actually breaks a No Trade Theorem, which enables more trades to happen!

The forward thinking reader might object citing the possibility of this blocking trade happening on a latter players' turn. There are two key features which might inhibit the promise of future trades. First and foremost the rules of Settlers explicitly state that agreements are non-enforceable, only spot trades are recognized by the rules. The 3rd player doesn't have to follow through when time for the blocking trade comes around, especially if the blocking trade is harmful to him but was simply less bad than the trade on the table. Secondly, the state of the world has changed by the time the blocking trade is available. Players possibly have new resources and structures. This changes their incentives possibly making the blocking trade unattractive at the future date. Given players are risk averse there are very strong incentives pushing them to accept the trade on the table instead of a future blocking trade.

I promised that I would prove that trades actually happen in Settlers where every player knows one is getting screwed over and can do that now. As motivation, I am sure we have all seen a trade about to happen then some 3rd player makes a better offer out of the blue. For example player 1 is trading two Bricks to player 2 for an Ore and Player 3 offers 1 Ore for 1 Brick. He is not doing this because it a good trade. But he knows that player 1 is going to city and player 2 is going to road and settlement and simply wants to block one so he doesn't fall even further behind. In addition this is a better trade for player 1 because she keeps one brick and doesn't give a road and settlement to player 2. This is exactly the original blocking argument where the 3rd player offers a trade that is harmful to block an even worse one. Therefore by using a one trade to block another, we can actually have trade occur where everyone knows that one of parties to the trade is screwed.

Veterans of Settlers will note that the active player will always benefit from a trade on her turn, assuming perfect playing and knowledge. The only way to get trades which negatively impact one of the parties is when they block another trade. The active player must be party to both the original and blocking trade due to the rules, so must always be made better off by such trades. This means that if you trade when not the active player, odds are you are the sucker. Though if players are budget constrained due to having small hands it is less likely that a block trade could be found, implying that a non-active player could benefit in addition to the active player from a trade.

Between this post and the previous, we have analyzed in detail the classic Milgrom-Stokey No Trade Theorem in the context of Settlers of Catan. With a minor tweak the theorem applies, but doesn't have the same bite as the original. In particular, we don't get that there is no trade, but that any trade which occurs must harm someone, and not necessarily one of the players party to the trade. We also looked at a possible stronger No Trade Theorem for Settlers using a blocking trades argument. Fortunately for Settlers, the rules restricting who can trade cause such a theorem to fail. But using this logic we uncover some interesting implications about trade in Settlers, including the fact that there can be trade where everyone knows the non-active player gets screwed.

Thursday, December 19, 2013

Catan No Trade Theorem: First Blush

A very common question that comes up when I play with my friends is "Why do people trade in Settlers of Catan? Shouldn't some No Trade Theorem cover it?" (I am sure this says I play with too many Economists...) We tend to puzzle over it for a bit, but never reach a true conclusion about if there is a No Trade Theorem that applies. In this post I will look at why, or why not, a No Trade Theorem applies to the Settlers of Catan universe.

To do this we are going to start at the beginning with the Milgrom-Stokey No Trade Theorem. No I don't expect you to read the paper to understand what follows. Though I will be relying on many concepts in economics and will link the Wikipedia articles on them when they first appear. This theorem has a couple of parts.
  1. Utility function depending on the state of the world and one's consumption
  2. Agents are risk averse
  3. Beliefs are updates from a common prior
  4. Initial endowments are Pareto Optimal
  5. Agents observe some private information
  6. There is a "trade" preferred by all agents after they receive the private info
If all 6 conditions (plus some more technical conditions) hold then the "trade" preferred by all agents provides identical utility to the initial endowment.

The first thing to look at is a technical  issue condition 6, which is why "trade" is in quotes. The reason I didn't say trade is the "trade" in the paper is more complex than those defined by the rules of Settlers. In Settlers a trade is between 2 players and must include each player giving some amount of resources to another. The "trades" in the Milgrom-Stokey are far more general and could involve resources moving between multiple players. This really isn't a huge issue as we could construct a sequence of Settlers trades that result in the Milgrom-Stokey trade, and this could certainly be done to satisfy the constraint that only the active player can trade. I will return to condition 6 later, but need to examine the other conditions first.

Conditions 2, 3, and 4 are clearly satisfied in Settlers. Most people are risk averse, which satisfies condition 2. Condition 3 essentially says that everyone has the same model of how the world works. There is no reason that players should disagree on how things in the game work or the likelihood of events because everything in a board game is completely defined, assuming that people know the rules of Settlers and understand probability. Condition 4 is true because players utilities can be thought of as their probability of winning the game. These probabilities must sum to 1. Hence anytime one player's probability improves another's must necessarily decrease. Therefore every endowment must be Pareto Optimal because any change in endowments that positively effects one agent must negatively effect another.

Condition 1 is the most technically difficult to translate. I think there might be way to apply it to Settlers, but there are 2 big issues with condition 1 relative to the Settlers of Catan universe. First, Settlers is not a one shot game like the Milgrom-Stokey theorem. Players take turns until one wins, so even the length is endogenous! Normally I would just suggest that everything could be considered an Arrow-Debreu securities but the other issue with utilities would prevent this from working and also suggests an alternative way to utilize the Theorem.

Utilities only depend on the state of the world, essentially on how the rolls dole out resources which affects who wins. But the state of the world intimately depends on the resources and buildings each player has. Buildings directly determine most points in the game and alter resource production. Resources change what actions players can take by affecting the available buildings. So there is a feedback loop that depends on how players play the game, which is affected by the trading! Essentially this means that an agents' utility depends on his endowment and the endowments of everyone else. But on any particular player's turn, the other players' can't buy anything so the cards in hand only affect utility through future actions and the buildings on the board make sense as the state of the world. Hence we can apply the theorem to each player's turn individually and simply use backwards induction style argument to calculate utilities from the continuation game. This means that trade should never happen in Settlers... or would mean that if not for issues with the other conditions.

Condition 5 is very odd in the Settlers of Catan world because there is actually very little private information. Any resources rolled are known by all as we can see the numbers and where all the buildings are, even though you may not look at other player's hands. Really only when the Robber moves so a player can steal from another or a Development Card is drawn is there any private info. So most of the time trade occurs in Settlers after not new private info, but new public info! This is even weirder than trade after new private information because every agent already knows how their probabilities of winning have been updated, so there is no information revealing effects of trade to leverage in these cases. Any explanation of trade in Settlers much account for this weird feature.

Condition 6 is where everything breaks down in the Settlers world. We already saw that Milgrom-Stokey "trades" could be reproduced by Settlers' trades. This is not the problem with the condition though. The issue is all players must agree to the trade. In Settlers only the two players on either end of the trade must agree. Hence we could see trades in which the players not party to the trade wishing it didn't happen. Moreover any "trade" that all players agree to must not shift the probabilities of winning because one player would have to be worse off and disagree if they did. This means that the theorem applies, but uses the word "trade" in a different fashion than Settlers does! (Yep, kind of a cop out...)

Overall the Milgrom-Stokey Theorem is very general and flexible. It just takes some work to transform the situation into one that matches the conditions. The truth about Settlers of Catan is the environment does satisfy the conditions of the No Trade Theorem. Unfortunately the theorem does not exclude trades which fewer than the entire set of agents are party to. Thus making it useless for answering the real question of "Why do 2 players ever trade in Settlers? Isn't one of them getting a better deal?" Exploration of this question will have to wait for another post, as this is long enough already. If you have any ideas on how to answer this revised question please let me know in the comments.

Saturday, November 30, 2013

Game Expansions: Greedy or Optimal?

One near universal constant in both physical and virtual games is the expansion. Especially in realm of board games it is hard to think of ones which don't have an expansion. And most of those are probably flops or too new to have an expansion out. Often these expansions completely alter mechanics in the basic game. For example the new expansion to Pandemic, the In the Lab expansion, completely reworks the mechanics for curing a disease. It changes it from simply turning in 5 matching cards to manipulating the infection cubes in a lab to sequence the disease. The new mechanics are super thematic, but also add a lot of additional complexity to the game. The expansion forces the players to do things that are unlike anything in the base game.

Pandemic is not an isolated incident. 7 Wonders: Leaders, King of Tokyo: Power Up!, and Wiz-War: Expansion Set* each introduced brand new mechanics which add complexity to the base game. In all these cases the new rules in the expansions could have easily been included in the base game. For some of these games the expansion tends to be a critical part of experienced players enjoyment to the point where they won't play without the expansion. Personally I consider the Cities & Knights expansion key to interesting play in Settlers of Catan.

The question is why weren't these expanded versions of the games simply the base game? It is not just that they were developed later in response to fan demand. I remember reading that Klaus Teuber intended ships and sea exploration to be part of the initial release of Settlers of Catan. But this feature was not added until the Seafarers expansion. So why was Seafarers not included in the base Settlers game? Are all these designers just money hungry wanting you to buy multiple $40 to $60 boxes to have the full game? Or is there a reason why releasing a simpler game could be better?

The obvious answer is of course it is about the money. But it is not as simple as simply wanting a reliable revenue stream with yearly expansion. Releasing a simple base version of a game actually increases the rate of adoption and reaches a wider audience than releasing the full game in all its complexity. Not everybody is a hard core gamer and wants to spend 30 minutes or more learning the rules and setting up the board to then play for 2-3 hours. Especially when they might find themselves in a helpless position a hour in and have to suffer through the rest. Arkham Horror, I am looking at you. This lower barrier to entry will make people more willing to try it as the rules are both more understandable and there is less risk of wanting to quite before the game is over.

Having this lower barrier of entry through releasing a simpler game increases the spread of the game through 2 mechanisms. First more people are willing to purchase the game to try, reaching a more casual audience. The last time I was in Target, they had Settlers of Catan, Pandemic, and Ticket to Ride base games. This is a huge recent development. Games like those used to only be found online or in hobby gaming stores. Now they are main stream enough for big retailers to carry. What is notable is the expansions are usually not found at big box retailers. This implies that it is the simplicity of the base games which attracts customers, not the depth found in expansions.

The other way a lower barrier to entry helps is through providing an easy way to teach non-gamer friends how to play. This might not seem like a big deal, but presenting people with something they can easily grasp in one play is huge. People then feel like they get it and want to play again. I think this is a huge reason 7 Wonders is such a favorite with my more casual gaming friends. The base game is simple and fast so it tends to click quickly and make people want to play again.

Most games I will teach without the expansions because there is no reason to add the complexity for new players. This is especially true with Settlers of Catan, which has a surprising complex base rule set. There is a lot going on to acquire resources and then build more of your colony. Compare this to the simplicity of matching cards to build routs in Ticket to Ride and it is easy to see that the addition Knight mechanics and city improvements are unnecessary complications when teaching the game.

Clearly starting with a simple base game is the optimal way to release a board game. This is not just from a money perspective but also from an enjoyment perspective. Game designers, in general, want to share their creation with as many people as possible and want to see that people are engaged and enjoying themselves. It is this passion to create things that brings people together that really makes a designer great. Note that the simple versions have a bigger penetration than the expansions because they are easier for players to digest. Which is fine. If a casual gamer just plays the basic version and doesn't have interest in the extra complexity of the expansion that is one more person enjoying time playing than if the game had been released as one big compilation. And the hardcore gamer is happy because he has the extra rules to add depth for him to analyze.

*Yes I did reference the original Wiz-War game and not the recent 8th edition by Fantasy Flight Games. The reason is 2 fold. First there are no expansions for the new version. Second the first expansion for the early editions of Wiz-War added creatures, the upcoming expansion for the 8th edition does not. I am still super excited about getting my hands on a copy of the new edition, but it didn't work as well for this example.

Wednesday, September 18, 2013

Using Evolution to Keep PvE Interesting

One of my friends and I were talking about how to make PvE more interesting in MMOs. Right now things get pretty repetitive in many MMOs because PvE doesn't tend to vary that much. After running through a mission or raid a few times things become predictable and known. Granted some have extreme variance in spawn composition but this tends to be very swingy or requires lots of developer time to balance. To make truly interesting PvE without requiring each instance to be individually balanced by hand one needs to leave the paradigm of fixed distributions and allow the game to evolve.

I know that evolve tend to quickly enter the realm of unbeatable by human players, which is completely contradictory to the idea of PvE. One needs players, of appropriate level and properly equipped, to be able to consistently conquer PvE content. Further they should be able to do it in a reasonable amount of time for the type of mission or raid it is. So instead of optimizing the computer to kill the player, each PvE event should try to optimize itself so that the player leveled & geared for the content finishes the event in a specified amount of time on average. Essentially the computer is trying to optimize what spawns to get as closed to the desired experience as possible which still having some variation to keep player's on their toes.

Lets look at an easy example from EVE Online: Incursions. In particular consider the Vanguard Incursion sites. These are high level raid events requiring around 10 people to complete. Vanguard sites require a mix of 2-3 Logistic Ships, the healer ships in EVE, and the rest are Damage Dealers. Right now they take about 10 minutes per site for a fleet of minimally skilled and equipped pilots. The problem is Incursions are very predictable. There are only 3 types of Vanguard sites and the spawns in each site have a fairly constrained set of possibilities. It is clear that right now each wave always has certain NPC ship types and simply chooses a random amount within a specified range for each.

Incursion sites become very mechanical after awhile. After enough sites one can call targets before a new wave spawns and an experienced fleet doesn't even need target calling because of how predictable things are. Overall this is a poor state of things as a top level event in EVE can be explained by a simple kill order list looked up online. Some variance to get players thinking and adapting would make Incursions more interesting and something that players actually want to keep doing instead of burning out an only using them to make ISK, the EVE currency.

Using an evolutionary program to alter the spawns and tactics of the NPCs would be a good way to add variance without having to hard code each possible spawn. The game should monitor the composition of each fleet that does a site, keeping track of relevant skill levels, ship fittings, and NPCs spawned in each wave in addition to the time the fleet takes. Then the game can preform a standard numeric minimization algorithm to generate spawns that it thinks will keep a minimally skilled fleet busy for 10 minutes. (This is done my minimizing the absolute value of completion time minus 10 minutes.)

To illustrate consider a simple Incursion site with 3 waves of NPCs where each spawn has a fixed point. Then the evolutionary algorithm is given a set of NPCs that may be used in this site. Every time a fleet enters an Incursion site it generates a set of three waves from the NPCs it is allowed to use. Given the large number of times fleets do these sites, it will allow the game to quickly go through the search space and find the collection of waves which, on average, take 10 minutes. To keep things interesting the algorithm would also do a certain amount of random experimenting which will enable it to eventually catch up with any new tactics the players devise. Thus forcing the players to keep experimenting and not rely on simple online guides.

I know that this post is a bit on the vague side and just provides a lofty overview of the idea. Over the next few posts I will try to unpack the idea more and go into the details of how it could be applied in practice.

Sunday, August 4, 2013

Dungeon Run Review Part 2

I was thinking more about my Dungeon Run review and something was bugging me about the suggestions I made. Overall my impression of the PvP portion of the game was that the incentives were horribly off and it should be removed. Though I am not sure that what is left holds up. A game that is a simple 15-20 minute dungeon crawl doesn't really sound that exciting and probably doesn't have too much replay value unless there is a large variety in the monster and treasure cards. Even adding an escape from the dungeon probably won't quite have the needed feel as it would be hard to do the monster control and attacks well without a GM. So in retrospect the PvP should be the selling point of the game, unfortunately I found that the weakest aspect. Which means a way to fix it is in order.

Before getting into concrete suggestions for fixing the PvP I wanted to talk briefly about a way to test balance and why. The best way to test PvP is to skip the first part of the game and just playtest the end game. This is the part that needs to be working first as you can always tone the monsters and traps to the appropriate level of challenge based on where the PvP balance ends up. (See slide 96) Simply let each player pick their character, give them 1-2 levels, 2-3 random items and then have them quickly build a map just by moving through with no monsters. Once the map is complete, randomly give a player the stone and start the endgame. This way you can get lots of iterations of the PvP, which should be the strongest point of the game, as it is in Betrayal at House on the Hill.

Now the question is, how to both encourage PvP and make it fun in the endgame? Honestly I think the basic PvP combat system is solid. It is resolved with two simple roles and the attacker has an advantage as they are the only player who can assign dice to block. This incentivizes attacking over defending. Further the way the first player is always the one with the stone and that player controls the monsters helps focus attention on them and gives them and edge when everyone is gunning for them.

In the last post, I talked about how the characters really are not equal in terms of stats or abilities, which clearly needs to be fixed for the end game. Further all characters gain a super ability when they have the stone, which usually means they are far more deadly than the Boss. These abilities should be toned down, if not removed as the player with the stone already goes first and controls the monsters.

There also needs to be more ways to restrict movement. Both by removing the ability to move that extra square and through some system to make leaving a player's square hard if they don't want you to move. I suggested that some roll based on the Skill stat should fix this and provide an incentive to choose high Skill characters for the endgame PvP. Map size and the type of tiles might play into this. They should be distributed so that all areas are reasonably reachable when the end game starts, but getting to the entrance should take multiple turns to prevent people simply running away.

The other big problem is there is no reason for the person holding the stone to engage in PvP, as they win if they reach the entrance. Something more needs to be added to the game so they have a reason to attack. Maybe they need to get to some other tile to activate the stone or each player gets some sort of key and multiple are needed to escape. The one thing to watch out for is requiring a death match as this will result in very degenerate behavior during the PvE portion of the game. Honestly the first thing that I would try is to have the Stone drop in the Boss Room when the Boss dies, instead of directly from the Boss. This adds more strategy to the game, ensures that the player with the stone has the maximum number of tiles to move, and that there is at least on choke point due to the Boss room having one exit.

Overall I think the PvP in Dungeon Run deserves to be explored more. I think the incentives in the current iteration leave a lot to be desired, but am optimistic that they can be improved with appropriate testing.

Saturday, August 3, 2013

Dungeon Run: The Case for Playtesting

Recently I was gaming with some friends and one of them brought out Dungeon Run. As it is a Dungeon Crawl of the most classical form and we were all fans of D&D, we decided to give it a shot. (The rules being relatively short and straightforward helped too.) After a quick read-through we selected out characters and began the crawl.

The map of Dungeon Run is formed by drawing new tiles as the heroes explore. It is very similar to Betrayal at House on the Hill in that aspect. With every new tile there is a chance for a monster, trap, or treasure for the hero to kill or take. Combat and other skill checks require one or two rolls that are easy to calculate and compare. Once the stack of tiles runs out the game shifts from exploration to combat. At this point the Boss, carrying the Summoner's Stone, spawns on the map. The goal becomes to kill the Boss and then be the Hero who leaves the dungeon with the Summoner's Stone. That is right, once the Boss is dead the game becomes a free-for-all where Heros battle one another for the Stone. Unfortunately this portion ends up not being as fun as it sounds.

Both games of Dungeon Run progressed about the same way. Each hero split off into their own piece of the Dungeon and, barring something like a Magic Immune Troll, handled all the encounters and picked up all the treasure in their portion. Overall there was almost no cooperation unless the game forced it. Further there was no reason to trade because no one had any real trouble (unless the monster was built to hose that class) and we all knew the backstabbing would commence as soon as the Stone dropped. The Bosses were surprisingly easy overall, usually just requiring two characters supporting each other to kill.

In both games the real play ended when the boss died. Someone had chosen Vargagg, the Orc Barbarian, in both games and he dominated the post-Boss PvP. Not only is he very powerful in combat, he also can gain the ability to move an extra space on leveling up. This made it so he could simply out run every other hero and escape unchallenged. His utter dominance was a big factor in the groups eventual disinterest in the game.

My impression of the game is it has some very solid core mechanics but is very poorly balanced. In addition there are some issues with who controls the monsters as there is no GM and the end game PvP in general. Really the game needed a lot more play testing before being released as there were some obvious issues that our group noticed after just a few play-throughs.

The combat system is very elegant and only requires two rolls to resolve. Further the game places the player squarely in control of the combat. They roll second and can use their dice to either block the monsters hits or damage the monster. Everyone in the group picked it up fast and seemed to enjoy the system. The issue with combat is it is strictly better to have a single high attribute because it gives you more dice. This wouldn't be too bad, except the characters have a fairly wide range of max stats and overall start with too many dice diluting the challenge and reducing the incentive to team up.

Overall the character stats were completely unbalanced. First having a high Brawn or Magic is dominant in the game. Not only does it make killing monsters easier, but can often be used in place of Skill to avoid traps or board impediments, essentially rendering the 3rd stat of limited use. On top of this the total starting stat points is not uniform across the characters. In fact both magic users have the lowest sum by 2 and neither has Brawn stat above 1. The first thing the game needs to do is bring the characters into better balance by equalizing the total stats more and reducing both the average sum and the max possible starting value of each stat. This will both make all the character more playable and facilitate more cooperation as the characters will be weaker.

The other issue with the characters is the vast power discrepancy in starting and level up abilities. We found the most powerful abilities were the simple always on modifiers. The subtler abilities like long range trading or leveling up faster from certain monster types were never relevant due to the length of the game. The most potent ability, which should not be in the game unless all the characters have access to a form of it, is the ability to move an extra square in a turn. This is essentially a 50% increase in movement as normally players can only move two squares in a turn. A player with this ability can arrive at the center of action much faster and evade any pursuers in the end game.

A big issue in the end game is how easy it is to avoid PvP. Not only can one character move faster than the others, but there is no way to stop people from moving through or leaving your square. With monsters you have to roll to leave their square, else they get a free attack on you. Players have no such ability and cannot restrict each others' movement. This makes the end game a mad dash for the exit, rather than a strategic move through the dungeon to evade capture. An easy fix for this would be to have the Skill stat affect your escape ability against players if they don't want you to leave their square. Maybe something like you roll yours skill stat and the target number is anything greater than the opponent's stat. This would give high skill players an edge in map management, which seems fitting.

The monsters themselves are reasonably interesting. In addition to their differences in attack and defense each has a special ability which forces different tactics and spices up play. The monsters range from very easy to moderately challenging, which is about right for a casual game. The sole exception to this is the Ice Troll. This monster is immune to Magic, so characters must use their Brawn stat to attack it. Unfortunately this is a very tough monster in general and no magic user has a Brawn stat above 1, leading to running away being the only option. This issue is partly fixed by re-balancing the stats, though I think that Immunity is very powerful in this game and should either be removed or placed only on weak monsters. It is very disheartening to have the boss spawn with an immunity because then the only thing a player strong in that stat can do is wait for the others to kill it. A better ability would be <Attribute> Resistance X, where if you attack with that attribute you remove X dice from your pool. This allows for more fine grained control of difficulty and can allow players to be at least marginally useful against such a monster.

Traps seemed very lack luster in this game. I think that there were two things wrong with them. First most could be overcome by Skill or another attribute meaning most players could power through on Magic or Brawn and shafting the usefulness of the Skill characters. Second traps don't persist, they trigger once and then are gone. It would be more interesting for them to stick around inhibiting movement and giving Skill characters more options for leveling up.

I almost thing that taking out the endgame or significantly changing the goal would make this game more enjoyable. The pace and timing of the game through the Boss seemed about right. Each player would gain 1-2 levels and have 1-3 items, which was sufficient for killing the Boss. Even if the power of the characters is toned down a bit everything in the game is doable if the players cooperate. The problem is running is a better strategy than fighting especially as the character with the stone gains some very powerful abilities. I think that if the game ended with the Boss it would be about perfect, as short dungeon run that you can play multiple times in a sitting. After thinking about it for awhile I am not sure there is a good way to create the endgame PvP because that tends to drag it out and make people wish the game had ended once a clear frontrunner appears.

One possible way to add more to the endgame is to have the players have to escape the dungeon with the Stone. Maybe every turn a monster spawns on the square with the Stone if there is none, else it spawns in the boss room. And have players re-roll every time they enter a room for new monster and traps but not treasure. To keep the pressure on it might be worth either making all the monsters have a 2nd ability after the Stone drops or not provide experience after the Boss dies. This would force a lot more cooperation and really emphasize the idea that the dungeon doesn't want them to take the Stone.

These sort of mechanical spawns also removes the GM issue that appears with monsters when no player is designated GM. Honestly the game has a very elegant first player system which makes it hard to get stuck and clear who is the arbiter on monster movement at that moment. Even in the endgame, this part of the game works well, though doesn't compensate for the bad PvP.

Overall I think the core of the game is very solid in concept but not execution. It uses a classical exploration system and has an intuitive dice system for resolving everything. Even the pace of play and power progression through the game seems very close to correct. The real issue is character imbalance and poor incentives for PvP in the endgame. These show the game needed more play testing and probably should jettison the current endgame for something that encourages players to be less assholes to each other.

Tuesday, June 25, 2013

Public Good Provision in 7 Wonders

7 Wonders is a classic Eurogame. It requires resource production to build upgrades which give the player points towards winning the game. In addition there are is a trading mechanism so you can utilize resources of other players. The interesting thing about 7 Wonders' resources is they act more like public goods than any other Eurogame I have played. This can result in massive underproduction of resources. Let's break down the mechanics and player incentives to see why this happens.

In 7 Wonders players each receive a hand of cards, they choose one to build, and then pass the remainder to the player next to them. This process repeats until the hand is exhausted, then a new hand of more expensive cards is dealt and the drafting continues. The game consists of 3 ages or rounds of drafting. At the end of the game points are totaled to determine the winner.

The catch with building cards is the player must be able to pay the cost listed on the card, usually some number of resources. Resources are gained in one of two ways. The first is through the cards a player has already built or as an ability of the Wonder the player is playing. This method of producing resources is permanent and usable in every build phase. So if the player can produce 1 Wood due to having that resource card, every time they build they can use that 1 Wood. But if the player has a card that costs 2 Wood, they would need access to two different sources of Wood. In later ages, cards can get very expensive requiring access to many types and large quantities of resources. This is the main incentive to drafting cards the produce resources as none of the cards give players points directly.

The second way to gain resources it to purchase them using gold from a neighbor. The twist in 7 Wonders over usual trading mechanics is this one is both non-exclusionary and non-rivalrous. This means that the player receiving the gold can't reject it and prevent the other player from using his or her resources. Further even if a player is using a resource, a neighbor can still purchase it from them. So if a player has 1 Wood that they are using to build this turn, their neighbor can also pay gold to use that Wood on that turn too.

It these interesting properties of trade that can result in a game being completely resource starved in the last age, where no new cards produce resources. In Ages I and II there is a disincentive to taking resources early  because that guarantees a higher quality of cards which actually affect points at the end of the game though having more options. Plus a player following this strategy can simply buy from those that do draft the resource cards early gaining the double benefit of more resources they can access and a better quality of card choices through the resource cards being removed. And if people are at a table were everyone else is taking non-resource cards first, then it is optimal to do that too in order to maintain card quality parity and not feeding others the best cards when you are taking only resources.

When all players follow this take resources late strategy it often ends up that there are fewer resources on the field than needed for the more expensive building because the last card of an Age is discarded instead of drafted. Which leads to relatively depressing Third Ages due to everyone being resource starved. The interesting thing is this is actually optimal! It is clearly better to buy resources from others to get more scoring cards than buy resources. And any player building resources is clearly the sucker in the game as the other players use his production and snap up all the good cards. The only thing that might temper such a trading strategy is running out of gold, which is possible if the other players are not also trading due to the lower velocity of gold in such a game.

This is the only example I know of where the existence of trade and a reliance on it leads to the players getting locked out of upper tier parts of the game. It is definitely worth digging deeper into the mechanics to determine if trade having this harmful effect generalizes or what the key component of the system that makes trade harmful is.

Monday, May 6, 2013

Pandemic: The difference a rule makes

Recently I got to try Pandemic. In this game four diseases threaten to wipe out mankind. The players must work together to keep the plagues from spreading while racing to find a cure before time runs out. Each player can be one of five roles (7 roles in the new version) which grant them special abilities. Like the Researcher who can give any card in any location, instead of just the card corresponding to that location. This is important because a set of 5 (or 4 for the Scientist) cards of the same color are needed to cure a disease. It is a very good game and I recommend that you give it a try when you have the chance.

When I was playing with some friends, they were playing that you could only give cards on the giving player's turn and were finding the game quite challenging. Most of that first game with them was spent figuring out how the receiver could end up in the correct city to be given the card they needed. This made the game more an exercise in creating board moving than actually about stopping pandemics and it wasted a lot of turns, which are really the limiting factor in Pandemic.

After some rules discussion, we played the next game by relaxing that giving cards could be done on either the giver's or receiver's turns. The difference in difficulty was astounding. We won easy without a sweat, whereas before it was more like a coin flip. The other big difference to me was the type of discussions we were having. Instead of trying to go through weird gyrations to pass cards, we talked more about stopping diseases. Now we debated the trade-off of heading off the spread of a plague or getting a cure for another sooner. The focus had returned to what the designers had in mind, instead of trying to go through the gyrations of a small rule.

This was a very nice example of how a very simple rule change could have a dramatic impact on how the game is played and really the quality of the game. The lesson I took away from this is when most of the discussions in a game are about how to work within one rule, unless that rule is central to the concept of the game, there is probably something wrong. And then letting the players do what they want to, give cards on any turn in this case, can make a more enjoyable experience as then the players' focus is not distracted by obtuse rules.

Sunday, April 7, 2013

The CSM Memebers live in EVE's Hinterland

[Null Sec] importing  goods from Jita and exporting harvested materials to Jita, Elise argued, was a bad design. [CCP] Grayscale agreed...
This line in the CSM minutes really frustrated me because it show a lack of understanding in both why EVE Online is an interesting game and how economies work. I believe that what Elise is observing is evidence of good design. The shear volume of trade passing through Jita, the main trade hub in EVE, shows that EVE has a deep and highly connected economy. Further the exporting of raw materials and importing of finished goods indicates a large degree of specialization, which is evidence of a highly developed economic system.

Elise & CCP Grayscale don't see that they would have to turn the entire EVE world on its head to achieve a higher level of industry in Null Security Space and less reliance on High Security Space. The full exchange on page 45 discusses changing industry incentives and resource distribution to make Null Sec look more desirable misses the logic completely. Higher production efficiency and more abundant resources would have lots of trouble off setting the inherent locational  and security advantage of High Sec.

High Sec is the only region of EVE where NPCs police behavior. Any crime, like blowing up another ship, will result in speed retribution. To the extent that it is impossible for a player to keep his current ship once he has committed a crime. This makes it really easy to move items and materials around. Especially low value to volume items which can auto-piloted to the destination, leaving the player free to do other things too. On top of the level of safety, High Sec is also the central region of space. Meaning it is easier to move good where ever they are needed as opposed to an operation on the far side of EVE's galaxy.

Null Sec is space that can actually be owned by players. It forms the outer ring of the galaxy. Also there is no police response of any kind, so your ship is not safe. Granted a player that is part of the alliance which own the space will be very secure there. There are also certain logistics structures which makes moving things around fairly easy for those that inhabit the space. The issue is any independent player will not be able to gain a market foothold without becoming part of the alliance and subject to its rules & taxes. Further any moving requires an active player, auto-pilot is certain death in Null Sec.

The real issue is Null Sec would not be Null Sec without the features mentioned above. But it is these very features which make the space undesirable to industrialists. So I see no way to improve Null Sec industry without turning the game on its head, or providing very extreme incentives to make players to what they don't want to. Which is bad design because player's don't enjoy being forced to do things.

To make a historical analogy, High Security is the center of a strong empire. People are free to come and go as they please and are relatively safe. Null Security is the hinterland or frontier of the empire. It may be ruled by local strong men demanding tribute or even be completely lawless. Often this hinterland contains materials which the central empire needs, but rarely is any actual production of finished goods done there. It is too easy for the local strong my to extort away all profits and too much output is lost in transport to thieves.

In this light the truly strange thing is the CSM is composed mostly of these frontier strong men with very few representative of the strong central empire. This seems like a case of the fox guarding the hen house.

Friday, April 5, 2013

The Experience of Design

I started reading The Art of Game Design: A Book of Lenses by Jesse Schell recently. So far it is a pretty interesting book. Some of the information is stuff I have come across in other readings, which is a good thing as this is supposed to be an introductory textbook for game design.

Chapter 2 of the book focus on how a designer is not creating a game but an experience. The game is just a medium for the experience. At the core this seems approximately correct for what a game is. Most video games seek to let you experience some story. Even board and card games often strive to create an experience. For example Magic attempts to simulate a wizards duel. This lens certainly provides focus  for a designer as she can constantly evaluate the components of the game against the criterion of how they contribute to the experience she is trying to evoke.

On the other hand focusing on just the experience is limiting and would seem to reduce the depth of the game. Evaluating the concept that a designer creates an experience through the lens of Mark Rosewater's Psycographic Profiles, this focus leads to just designing for Timmy. Johnny and Spike are not drawn in by raw experiences, they have other base needs that drive them. A game that simply provides an experience has little replay value for them because Johnny can't express himself and Spike can't prove himself just through experiencing what the designer had in mind.

I think that Schell's focus on the experience because that is an actual starting place. Starting with either of the other two's desires would be extremely tough. The need to express oneself or prove something makes more sense in the context of experience or existing game, but not much on the blank slate that is the start of design. While I think it is necessary to have Johnny & Spike elements in any game to give it replay value these add to the Timmy experience which starts the creative process.

Monday, April 1, 2013

Measuring Meat lost to Pirates

A friend of mine pointed out this article to me. It is written by Tommy Refenes, one of the developers of Super Meat Boy, on the joint topics of losses due to piracy and consumer confidence in a game studio. His points on the value of consumer confidence are spot on. Having a good reputation with your customers is key for them trying new games you produce & continuing to support your current offerings. Tommy considers keeping consumer trust as far more valuable than worrying about pirating. I completely agree with him on this. My disagreement with the article stems from his reasoning on why piracy is not a problem.

Essentially Tommy believes that piracy is not a problem because we can't precisely calculate the loss. As we can't pin it down exactly ever, we shouldn't even try to estimate it. An implication of this logic would be we should not come up with theories to try and figure out any counter factual. The problem is that coming up with theories, working out their testable implications, & then testing them is the basis of the modern scientific method. That is why to me his main argument can be summed up as giving up.

Really anyone can come up with rough bounds on the loss due to piracy, [0,Price*Pirated Copies]. The power of theory is then tightening these bounds, especially the lower one, as that is more relevant to the DRM worst case cost-benefit analysis. Granted the theory is only as good as you think the assumptions are. But we can compare games with different pricing strategies & types of DRM to try and separate competing assumptions. For example, comparing a game with a fixed price to one that has periodic, but randomly timed sales, which should allow us to understand how sensitive piracy is to price. I am sure with the data most companies collect quite a bit could be said about the true costs of piracy.


Returning to why piracy is less important than consumer trust, essentially piracy is a good problem to have. If people want to pirate your game, they must find it fun enough to want. So if people want to pirate your game, you clearly have some player confidence that you are delivering a quality experience. Granted you can have cases where the reason to pirate is the DRM is invasive and it is easier to play without the DRM on. But these are cases of companies throwing the baby out with the bathwater due to not understanding user issues and being overzealous in piracy elimination. So barring MMOs, which almost have perfect DRM by definition, there must be an optimal level of piracy & DRM where one balances increasing trust with providing just enough barriers to piracy to deter some people.

Thursday, March 28, 2013

Seagull Droppings

I have been doing some catchup reading on the CSM minutes. (The Council of Stellar Management is a player elected group which CCP consults on design focus & decisions for EVE Online.) One of the most interesting sections, and the section that has made me the most hopeful for the direction of EVE Online, was the session titled EVE Online - The Next Decade. This section was lead by CCP Unifex and CCP Seagull.

I was extremely impressed with CCP Seagull's comments on how the company is starting to analyze new features for EVE. The biggest contribution seen in the CSM minutes is her additions to the EVE developer lexicon. She identifies 5 major types of players:
  • Instigator: Players with ambitions who inspire groups to act.
  • Enabler: These players run the logistical side of large groups so that things function smoothly.
  • Lurker: Solo players who have little contact with others.
  • Group Player: Players that want to engage socially with other though joining activities.
  • Small Scale Leader: These players put together activities for others to do. They differ from instigators in not having as large a scale, more an evening's activity verses conquering an empire.
The objective behind defining player types is so that CCP can get into the mind of the players better. In particular, examine the question "What do I do now?" from the players' perspective. EVE is an incredibly open ended game and figuring out what to do when you play is often a more daunting prospect than how to do something.

To me the fact that people in the company are starting to definite types of players and design specifically for those types of players shows that CCP is maturing. This shows a better understanding of their game and more focus in improving EVE. In reading the minutes it is clear that CCP Seagull it talking on a level above the CSM and even most of the other developers in the meetings. This terminology and way of thinking is clearly very new to many people are still adjusting to it.

There is a similar evolution in vocabulary and way of thinking that happened in Magic: the Gathering, most of which was driven by Mark Rosewater. I have blogged a bit about the Psycographic Profiles before. It is interesting to see that both CCP and Magic created terminology to talk about different types of players after about 10 years of existence. This seems to be a natural evolution of game companies as their products age they develop a lexicon to facilitate thinking and discussion of feature.

The last thing worth pointing out is the 5 player types CCP Seagull defines are categorized by what role they play in a group. The Psycographic Profiles of Rosewater are about why people play. These two different systems don't compete with each other as they define different parts of the player. In theory one could use both systems to construct a more detailed profile of a player. Though that is an exercise for another blog post.

Thursday, March 14, 2013

Social Games are not designed for Spike

I just read this blog over at Gamasutra and my impression is that the author is a type of Spike. He wants to demonstrate mastery through goals in game and doesn't understand how games like FarmVille can be appealing. Essentially these games are not designed for him but a very different market segment.

The way these social games work is people have their space, in FarmVille a farm, which they can customize & use to produce things. These products can be used for further customization or traded with other players. Also each player's space can be view & discussed by their friends. In truth, this is not much different from having a flower garden in one's yard. It provides a topic of conversation among friends and complementing the garden is a compliment to the gardener. In essence the garden is an expression of the gardener's self, just like the farm in FarmVille. Which is what Johnnies are all about, expressing themselves.

This isn't to say that Spikes and Timmies can't enjoy the game. Timmies love the experience of hanging out with their friends and bonding over a shared interest. Some Spikes will relish mastering the production method in FarmVille to create the most productive farm. Granted once a Spike masters the game and proves that he has mastered it he will probably get bored. But this does not mean social games suffer from poor game design, just very targeted design.