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.

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