Theory: Mitigating Randomness

So you’ve decided to use dice, or some other randomizer, to help shape your game experience. You’ve thought carefully about what the odds of success for different actions should be, and have calibrated the randomizer accordingly. However, you’re finding the results unsatisfactory; perhaps the occasional bad roll is too devastating, or players are getting into unwinnable positions early through unlucky dice rather than bad play. Below are some tools you can use to mitigate the effects of randomness, keeping the excitement of an unpredictable outcome without the risk that dice will dominate the game.

Change the odds for key rolls

If something is critically important—because it’s the culminating move in a strategy, for example, or because it’s necessary for the game to progress—shift the odds so that that specific roll is more likely to succeed. Players naturally get frustrated when a game’s randomizer undoes their hard work at the final moment, or even worse when it stymies the game completely (the “I need to make this Investigation roll to find the clue, but I keep failing” problem). Twisting the odds toward the players at key junctures retains the tension inherent in the possibility of failure, but makes it unlikely that an actual failure (or worse, repeated actual failure) will inhibit their fun.

Broadly speaking, there are three ways to push the odds in the players’ favor:

  1. Roll more dice

As you roll more dice there are more opportunities to outweigh bad results. The average result when rolling two dice is 7, but if one of those dice comes up as a 1 the total result is probably going to be low. By contrast, rolling three dice means that even if one of them lands on 1 the other two will probably still get the total to or above 7. Rolling more dice while looking for the same end result thus leaves open the possibility of failure, but makes it less likely.

Warmachine implements this concept to great effect. It allows players to expend a resource to roll more dice when trying to hit a target, without changing the math that determines the total the player needs. This allows players to improve their chances on vital rolls, reducing the risk that a single unlikely fall of the dice will decide the game while promoting simplicity by keeping the math consistent.

Adding dice to control randomness works even in systems that don’t rely on totals. For example, role-playing games sometimes count the number of dice that meet or exceed a certain threshold value—say, one might roll ten six-sided dice and count all the dice that came up with a 4 or better. Even though there’s no totaling of values here, rolling more dice still helps, since one has more opportunities to get those 4+s.

  1. Roll the dice more times

One’s odds of succeeding on a roll go up substantially if one is allowed to roll the dice again, especially on “easy” rolls. Allowing the players to roll a second (or third, or fourth . . . ) time can thereby act as a safety valve against unexpected and/or undesirable results.

Heroclix uses this approach. The results of an attack in Heroclix are based on a single roll. Each roll can lead to a hit, or a miss, or an unusually damaging hit, or a miss so severe that it reflects damage back on the attacker! As one can imagine, the outlier results can be devastating, especially “critical misses;” wasting a turn setting up an attack that instead results in damage to one’s own piece is often a game-ending setback.

To limit how often those crushing failures occur, Heroclix is liberal about allowing players to re-roll their dice. There are many ways to get the ability to do so, or to get access to a limited variant (e.g., the ability to re-roll a die that lands on 1). Critical misses therefore end up being very rare. Furthermore, when they do happen they are usually the result of a strategic decision to forego re-rolling in order to get some other advantage, so they feel like a justified outcome rather than being struck down by random chance.

  1. Change the goal

Perhaps the most obvious means of shifting the odds in the players’ favor, this may also be the most dangerous. It’s easy enough: if the players normally need to roll a 7, make it so that they need to roll a 6 or a 5.

Unfortunately, this seemingly simple approach can be complicated in play. First, it can introduce memory issues when the change is not directly followed by the roll. This issue comes up in many miniatures games: piece A can increase the defense of one of its friends, B or C. By the time it comes to the opponent’s turn it’s not always easy to remember whether A made B harder to hit, or C, or neither of them. By contrast, picking up an extra die or re-rolling a bad result both happen at the moment of roll, and so memory issues generally are not present.

Second, changing the goal can significantly add to the game’s mental overhead. It’s much easier to look at a lousy roll and decide to re-roll it than it is to do math. Adding a step to calculating the goal—or even worse, making the players calculate the goal when normally they wouldn’t have to at all—can be trying.

Changing the goal, then, is a technique to use with caution. Forego it if the game already involves significant calculations, or if the game otherwise involves no calculations. Outside of those circumstances, think about whether another solution would provide the same in-game benefits.

Remove the worst results

If a certain possibility is going to be bad for the game, consider removing it entirely. There’s no need to be content with “this unfortunate thing won’t happen often;” as the designer, you can make it happen never.

The example of this that sticks out in my mind is the Combat Resolution Table in Avalon Hill’s classic wargames. CRTs generally looked something like this:

Roll 1-1 2-1 3-1
1 A eliminated A eliminated Exchange
2 A eliminated A back 2 Exchange
3 A back 2 Exchange D back 2
4 Exchange Exchange D back 2
5 D back 2 D back 2 D eliminated
6 D eliminated D eliminated D eliminated

The CRT’s X-axis is the odds in the battle, while the Y-axis is the attacker’s roll. Thus, if the attacker and defender are of equal strength (1-1), then a roll of 1 means the attacker’s entire force is eliminated while a roll of 6 eliminates all defending units. If the attacker has double the defender’s strength (2-1), the table changes so that there are more of the results favorable to the attacker, and so on.

CRTs could be a bit unwieldy; they changed the goal in a calculation-heavy context, with all the mental load that implies. One had to total up the attacker’s strength, then the defender’s, divide the former by the latter, and then check the table to find out how high one actually needed to roll to win the battle. Playing games with a CRT could involve a lot of basic arithmetic (which, in retrospect, may in part be why my father suggested them when I was little).

The trouble was worthwhile, however, because CRTs allowed the designers at Avalon Hill to encourage good play by removing the worst results. Attacking at even odds is easy, but the CRT allows an even-odds attacker to be eliminated wholesale. 3-1 attacks, by contrast, are rather trickier to set up, so players who manage it are rewarded by having the possibility of total defeat taken off the table.

Avalon Hill’s wargames were games of maneuver, and it would have been a problem if players had maneuvered skillfully and then been crushed regardless. They might have been confused as to what was expected, or even concluded that sound tactics were not to be used. By using CRTs that protected players from bad results after they managed their troops well, Avalon Hill’s designers made sure that the game was consistent in encouraging strong play.

Put outlier results behind multiple rolls

Sometimes a game would benefit from an outcome being rare—rarer than one can achieve through a single roll. In that case, it can be useful to require multiple rolls to get that result. With each successive roll that needs to succeed (or fail), the odds that a player will get through all the rolls diminish.

Warhammer 40,000 uses this technique to give battlefield primacy to important models like unique characters and giant futuristic battle-robots. It needs to be possible to take these centerpiece models off the table, but 40K’s designers have concluded that to emphasize their power and importance it should be quite difficult. As a result, damaging such models involves many rolls in sequence: one to hit, then a roll to see if they were hit hard enough to do damage, then a further roll to see if their armor saves them, and then a final roll for an “invulnerable save” to see if a force field or their own doggedness keeps them going. It’s very difficult for an attacker to get all of those rolls to work out as he or she needs—a friend of mine once had a character survive multiple turns of an opponent rolling hundreds of dice against him—and so these centerpiece models are subject to some risk while generally being very safe even when they lead from the front.

Choose from a pre-set list of results

It’s possible to manage, not just how likely a result is, but how often it can occur overall. For example, a game can produce random results by having players draw from a deck of cards rather than rolling dice. By adding and subtracting cards from the deck, the designer can control not just the odds of getting a 7 or an 11, but how many 11s it’s possible to have during a game.

Forbidden Desert uses this strategy. During the game a sandstorm swirls around the players; it gets worse over time, and will eventually bury them. If the storm rose too quickly it would be patently impossible to win—and not much fun. It’s easy to imagine that happening if, for example, the storm got worse on every roll of 6 on a die; inevitably someone will have the unlucky game where they roll a bunch of 6s in a row, and will walk away irritated.

The game avoids that problem by using a deck with a limited number of “Storm Picks Up” cards. Since the players will go through the deck multiple times during the game, and the storm can’t get too strong on any one trip through it, there is no danger that the storm-rises result will occur too often.

Choose from one of several lists of results

An outgrowth of the previous technique, here the game has different pre-set lists of results for different events/points in the game/etc. Players get a random result from a list appropriate to the situation.

Many games do this, but I think an especially strong example is Through the Ages. Through the Ages is a civilization-building game in which players buy cards representing noteworthy elements of their civilizations—inventions, an important person, etc. Each card is available in limited quantities, controlling how often it appears in the game.

Even that level of control, however, is insufficient for Through the Ages’ purposes; it would be frustrating if the random draw of cards gave a player whose civilization is in the 1900s options like basic agriculture and bronze weapons. As a result, the cards are subdivided into three decks, each appropriate to an historical era. This still provides a random draw, but the draw is guaranteed to generate options that at least have the potential to be impactful given the stage of the game.

Allow some tasks to be accomplished without randomness

If accomplishing something is absolutely vital to the game, should it be rolled for at all? It may be better simply to assume success and reserve uncertainty for matters where failure doesn’t bring the game to a screeching halt.

The GUMSHOE role-playing system follows this line of thinking to make sure that games simulating an investigation work. Essentially, GUMSHOE provides that player-detectives can never miss vital clues entirely; if something they need to know is present they will always find it, no rolling required. This ensures that, like a good mystery novel, the players get to the end with the all the pieces of the puzzle. Also like a good mystery novel, the challenge is in recognizing them for what they are, and putting them together correctly!

The problem of must-succeed situations can also be resolved in other ways; for example, players might be asked to roll just to see how well they succeed (the worst result of failure having been removed). However, assuming success and moving on will always have the benefits of simplicity for players and predictability for the designer. Neither of those should be undervalued.

Make failure as interesting and fun as success

The brass ring of randomness mitigation, here there’s no frustration because all possibilities are awesome. Randomness is still present, but there’s no need to go out of the way to control its effects; the effects are positive for the game as a whole no matter how the dice turn up.

Very few games even try to follow this road, but when it works the results are impressive. For example, the (sadly) short-lived Marvel Heroic Roleplaying used a system in which high rolls were more likely to result in success, but rolls of 1 could be a source of “Plot Points” which give the players extra capabilities. As a result, even bad rolls were good—just on a different axis.

Don’t leave fun to random chance

Adding an element of chance can do a lot for a game—but it can take over the game if incautiously implemented. The techniques above can help take control of randomness, mitigating its potential downsides. Give them a try when your game needs the Goldilocks amount of uncertainty–not too little, not too much, just right.

Theory: Rules for Player Powers

After hammering away at Lines of Questioning for a while, I feel that the latest variant is a great foundation for a “basic game.” However, it’s also incredibly difficult; saying that playtest victories have been elusive is somewhat like saying that one doesn’t often see a unicorn.

My thinking at the moment is that the core gameplay mechanics are solid, and that the difficulty issue can be addressed with role or power cards that give the player a little boost. Legal analysis teaches that a free-ranging quest for good ideas is less effective than following reliable guidelines, so I thought that as a first step I should try to create those guidelines. Here’s what I’ve come up with.

Player powers in cooperative games (which can include solo games for our purposes here) come in two types: weighting and unique. Both serve to make the game easier, and hopefully more fun as well. However, they accomplish these goals in very different ways.

Weighting powers make the player better at a game action everyone can take. The player might pay a lower cost for the action, or get a bigger payoff, or be able to take it when other players cannot. However it happens, the power weights the player’s choice; it puts something heavy on one side of the scale that balances the options.

Perhaps the quintessential weighting power is the Medic role in Pandemic. The Medic can do all the things the other players can do, but is the best in the game at treating sick people. Since treating sick people is absolutely necessary to win, and the Medic does it better than everyone else, the Medic player’s evaluation of how he should spend his turn is always going to be tilted in that direction.

Unique powers, by contrast, enable the player to do something outside the normal game rules. Instead of making a choice more appealing, as in the case of a weighting power, it adds a whole new option. Players without the power cannot replicate it, even inefficiently. Recent implementations of the idea include Forbidden Desert’s Climber, who cannot be buried under the game’s shifting sands, and Space Hulk: Death Angel’s squad-specific action cards.

Admittedly, the distinction between these categories is not always a bright line. Having a unique power does tend to weight one’s choices; the Climber can move to the same squares as every other Forbidden Desert character, but her additional safety can have a substantial effect on the choice of destination. Similarly, weighting powers can be considered “unique” insofar as they enable players to break the game’s normal rules.

I nevertheless feel that it’s useful to think in terms of powers as coming in two flavors, because they work out somewhat differently in play. Weighting and unique powers produce different behaviors in players and can be used for different purposes.

Weighting powers have subtle, but important, impacts. First, they provide guidance to the player. By making one choice more appealing, weighting powers signal to the player that that is a good choice and he should go in that direction as often as possible.

Think back to Pandemic. If you take a group of people who have never played the game and give them each a role, the players will naturally gravitate toward whatever their roles tell them they’re good at. The Medic will start treating the sick; the Researcher will try to get cards to the Scientist; the Operations Expert will build research stations. All of those are useful contributions, and so that inexperienced group will make progress in the game.

Compare that to what would happen if Pandemic had no role cards. Should everyone treat the sick? Maybe the best strategy is for everyone to build research stations all at once, and completely ignore the cards? Who knows! New players would be completely at sea, and might suffer through many frustrating games while they figured out a reasonable distribution of labor.

That thought experiment points toward another benefit of weighting powers: they are an easy source of player satisfaction. It feels good to treat sick people as a Medic, because each treatment is a little chance to be top dog. No one else can treat people like the Medic can.

As the game goes on those opportunities can even build into something especially satisfying, a reputation for competence and accomplishment. When the table comes to rely on the Medic, trusting him to keep them in the game while everyone else does their behind-the-scenes work, it gives a taste of what it’s like to achieve a position of responsibility in the real world.

By contrast, unique powers offer neither of those things. They do not generally help players decide what to do; if anything, they make in-game decisions more complex. In Space Hulk: Death Angel the purple squad has the ability to move the evil aliens around. It’s difficult to say whether and when that’s better than just attacking them; the choice is highly context-driven, and nothing about the ability itself signals which way the player should go.

Nor are unique powers always going to be wells of player satisfaction. Frequently they just create agita as players struggle to decide whether they should use a power now, or save it for later, or use the power in a different way. We have all seen people frustrated at the end of a game because they were so afraid of wasting their Cool Thing that they never actually did it.

Unique powers are nevertheless still valuable despite those weaknesses because they are an effective route to new decisions and different play experiences. As an example, take another look at Forbidden Desert. Most of Forbidden Desert’s players operate in an environment characterized by water scarcity. The Water Carrier, on the other hand, can have as much as she pleases if she’s willing to spend the time to dig a well; for her the game is all about opportunity costs. Having a unique power fundamentally changes the experience for that one player, which helps keep the game fresh and interesting.

These, then, are the rules I’ll be using as I design player powers for Lines of Questioning:

First, follow the rules here for when player powers are useful, and in what amounts.

Use a weighted power when (a) the power should help players, especially new players, decide how to approach the game; and/or (b) the power is meant to add satisfaction to the game experience.

Use a unique power when (a) the goal is to create a new set of decisions; and (b) the power will not frustrate players by being difficult to use correctly.

On Monday I’ll be back with first-draft ideas.

The Case Study: Player Powers, Take Two

Cooperative games often give each player a unique power: Pandemic makes one player a scientist and another a medic, while Forbidden Desert has one player be good at carrying water while another can dig quickly. Yet, it isn’t necessary for a co-op to do so; Space Alert is a great game, and all of its players are on equal footing. I’ve been interested in bringing unique player abilities into Over the Next Dune, and have even put forward some untested ideas, but before sinking a lot of time into it I want to figure out with confidence whether OtND is in the category of games that benefit from such abilities or the category that doesn’t.

When would one want to add unique player powers to a game? I’ve come up with a couple of possibilities:

1. The game benefits from a certain amount of something, but no more. Pandemic would be easy if everybody had the medic’s ability to cure lots of people in a turn. However, letting one person do that is just enough to keep the players above water when the cards flip the wrong way and disease suddenly spreads all over. A single medic serves as a safety valve without making the game trivial.

2. The unique abilities provide very different game experiences. Playing a Dwarf Trollslayer in Warhammer Quest has little in common with playing a Grey Wizard. Providing such distinctive experiences adds a lot of replayability, since getting tired of one of them doesn’t mean you’re tired of the game as a whole.

3. The unique abilities create new, interesting decisions. Playing the water carrier in Forbidden Desert is neat because in addition to the game’s usual decisions you have to decide how important it is to stay close to oases. Figuring out when it’s safe to go help the team and when you should to stay behind collecting water is tricky. The unique power is valuable in part because it brings that interesting decision to the table.

Looking at that list, I’m struck by the fact that it’s mostly about the powers rather than the game. Do the abilities provide different experiences? Do they create new decisions? It depends on what the abilities are!

We could come at the problem from the other direction. When would one not want unique player powers in a game?

1. Giving players unique capabilities would undermine the game’s mechanics. Diplomacy is a classic game of cooperation (and competition). It’s a wargame where the players’ strengths start out relatively even, so to make progress you have to cut deals. If the players had special abilities they could rely on it might make negotiation less important–and the negotiation is the reason to play.

2. The game is at a complexity limit. Space Alert is played in real-time on a 10-minute clock. Players make mistakes and overlook things, even without having to track the effects of special powers. If people were also trying to manage unique abilities the game could tip from “hilarious barely-controlled chaos” into “impossible and frustrating.”

Over the Next Dune certainly isn’t so complicated that it can’t bear the weight of unique abilities. I’m less certain whether player powers would undermine the game’s central challenge of tricking the searchers. On the one hand, the more tools the players have the less likely they are to take the risk of getting close to searchers to pull them around. On the other hand, it seems like abilities could be created that would increase rather than detract from engagement with the searcher-tricking mechanic.

The best way to resolve that uncertainty is with some testing. How about this as a starting point:

Pop a Tire: If this player token is adjacent to one or more searchers at the start of the Sneak Phase, that searcher is affected by terrain during the next Search Phase. (Any time during the next Search Phase that searcher’s movement would cause it to enter one or more squares with terrain in them, the searcher must expend two squares of movement instead of one. If it does not have enough movement remaining to expend two squares of movement, it stops moving.)

My thought is that this creates a new decision (whether and when to slow down a searcher) and a potentially different game experience (seeking out searchers instead of avoiding them), without adding complexity (players will already know the terrain rules) or undermining the central mechanic (since it increases rather than decreases the mechanic’s use during the game). I also like that, as noted in the first iteration of this ability, it doesn’t empower one player; rather, it helps a player assist the others.

That’s one power, but there can be five players in a game of Over the Next Dune. I’ll be back with more on Monday.

Theory: Simulation and Puzzle Pure Co-Ops

It’s an article of faith that a great opponent makes a game more fun. A good pure co-op game, then, needs a good AI foe to challenge the players. Designing that opponent requires, first and foremost, deciding what kind of co-op you’re creating: a stand-in or a puzzle. Mashing elements from both types together leads to trouble.

A stand-in challenges the players by imitating a living opponent. It tries to do what a human would do in a given situation. In essence, it simulates the experience of having a human sitting across the table (or on the other side of the internet connection) playing against you.

A puzzle challenges the players by presenting a problem for them to solve. It is not concerned with doing as a real person would do; its only goal is to provide an interesting dilemma, and it acts in whatever way the designer thinks will best achieve that. Puzzles may (should?) have a theme, and they may be good simulations of that theme, but they aren’t trying to simulate an opposing player.

Which category a game falls into has a huge impact on what kind of AI is appropriate. Stand-in AIs need capacities that puzzle AIs don’t. A human will respond to his or her opponent’s actions; to feel “real,” the stand-in needs to be able to do the same. It has to be able to find out what the players are doing, determine what an appropriate response might be, and implement that response.

Puzzles, by contrast, don’t have to care what the players are doing. In fact, they don’t have to do any specific thing so long as they’re interesting. The central question is what the game needs, not how a person would behave, and the AI needs only those capabilities relevant to the game’s particular answer.

Either choice can lead to a great game. Pandemic and Forbidden Desert, for example, are both great puzzles. The diseases to cure in Pandemic and the sandstorm to dig through in Forbidden Desert don’t act like human opponents–but why would they? Diseases and sandstorms aren’t sapient, and it would be weird if they could respond to the players’ actions. Instead they operate in ways that are both thematic for the natural forces they represent and interesting in play. For puzzles, that’s the gold standard.

As an example of a great stand-in I always go back to the Reaper Bot and Zeus Bot for the original Quake. (Wow. I’ve been playing FPS games for a long time.) At a time when a lot of people were on dial-up and internet play with other humans was a lag-filled affair, the Reaper and Zeus Bots were striking for their ability to navigate without bumping into walls, good aim, and consistent connection. Many real players, fighting against 300-500ms pings, couldn’t offer those things. The bots out-humaned the humans!

Designers run into trouble, however, when they mix the two categories. One sees this a lot with “cheating” computer game AIs (which are usually intended for solo play rather than co-op, but the issues involved are comparable). They look like stand-ins but are actually puzzles, and as a result they often end up being unsatisfactory.

For example, players often express frustration with the AI in the Civilization series of games. Civ’s AI promises stand-ins; the player controls one civilization and the others are guided by an AI that has each civilization pursue its own ends–just like they would if humans were guiding them. The goal is to beat the other civilizations, eliminating or outscoring each as though they were separately controlled by human players. The AI-driven civilizations sometimes cooperate and sometimes attack each other, imitating what humans do. It looks like a stand-in, it quacks like a stand-in . . .

. . . but it’s not a stand-in, and at least anecdotally it ends up irking many players as a result. Civ’s AI doesn’t get much smarter as the difficulty level goes up; it just gets more and more resources, far outstripping what the human player receives. Those resources enable the AI to challenge a skilled player, but they undermine the simulation; no human can do the things a high-difficulty AI can do. Ultimately the game becomes a puzzle in which the player must find optimal moves that will allow him or her to keep up with the AIs’ lead in technology and production. Players choose a higher difficulty level looking for a simulation testing their diplomatic ability and battlefield tactics, instead find an optimization problem testing their command of the math behind the game, and walk away aggravated.

(To be fair, some players greatly enjoy the higher difficulty levels. However, they’re usually knowledgeable about the game, know they’re in for an optimization problem, and are specifically seeking that experience.)

Civilization demonstrates–-has in fact been demonstrating for years–-that a really tasty apple is not a substitute for an orange. When designing a pure co-op, follow in the mold of Pandemic, Forbidden Island, and Quake’s excellent bots by figuring out whether you need a puzzle or a stand-in and then delivering fully on that experience. Slipping elements of one into the other is apt to confuse the game’s message and frustrate players.