Dice Mechanic

Savage Worlds rates skills and characteristics in terms of dice. The better the skill or characteristic, the more sides the die has, 1d4, 1d6, 1d8, 1d10 to 1d12. Very high level characters can increase abilities beyond 1d12, but the result is a bonus to the die roll adding either +1 or +2, depending on how far the skill is increased, to the roll. There are also some “edges” that give bonuses to specific skill rolls regardless of the skill’s die size, but these are discussed in their own section. There is also a penalty for characters that are untrained in a specific skill. The smallest die is a 1d4, and this is the minimum for a characteristic. However, someone completely untrained in a skill rolls 1d4 and subtracts 2 from the final result as a penalty for lacking the skill.

A further wrinkle in the dice mechanic is that the dice “explode”. When a die rolls the maximum for that die size, 4 in the case of 1d4, 6 in the case of 1d6, etc, the die is rolled again and the new roll added to the previous roll. This continues as long as the maximum is rolled. For example, if a 4 is rolled on a 1d4 the die is rolled a second time. If that roll is also a 4 then that 4 is added to the first 4 for a total of 8 and the die rolled again. If the next roll is a 3 then that would be added to the total for a roll of 11. If the third roll was a 4, the player would continue rolling and adding. The exploding die makes the probabilities a bit tricky, for example a 1d6 can never roll any number divisible by six as the die would simply be rolled again. However, the probabilities really become odd when the “wild die” is added.

The Wild Die

Player characters in Savage Worlds, along with some important NPCs, are referred to as “Wild Cards”. One of the big advantages of being a Wild Card is the wild die. This is a 1d6 that is rolled along side the normal dice whenever a Wild Card makes an ability roll. The wild die explodes just like the ability die. The player then uses the best roll. For example, if a Wild Card with 1d8 strength was trying to lift something they would roll 1d8 for the ability and a 1d6 wild die. If the 1d8 came up a 3 and the 1d6 came up a 5 they would use the 5. Note that any bonuses or penalties apply after the die roll. Thus a Wild Card with no pilot skill trying to fly a plane would roll 1d4 for the skill and a 1d6 wild die and take the better roll. They would then subtract 2 from the final roll for the unskilled penalty. To make things a bit more complicated, the wild die is not always a 1d6. Once a character has increased an ability to 1d12 +2 they can increase it a bit further to 1d12 +2 but rolling a 1d10 for the wild die rather than a 1d6. Figure 1 shows the probability of rolling a given number or better for each skill. As can be seen, the probability curves have very odd shapes due to the wild die and the exploding nature of the rolls.

Success

The most common roll needed to succeed in Savage Worlds is a 4. Sometimes characters will roll against each other trying to get the highest roll. Also, some situations use a different target number, most commonly hitting in melee combat. However, most of the time a player needs to roll 4 or better. As can be seen in Figure 1 there is a very large jump in the probability of success from unskilled, 1d4 –2, to the lowest skilled level, 1d4. The increases in the chance of success then get smaller and smaller as the character moves to larger dice, until shooting up again at the 1d12 plus bonus levels only available to high level characters. As a result, for a basic success, skills at 1d10 and 1d12 are not much better than a 1d8. This provides an interesting combination with the skill advancement system.

Skill Advancement

In Savage Worlds every skill is associated with a specific characteristic, for example shooting with agility and repair with smarts. It cost twice as much in terms of original character creation or character advancement to raise a skill above the associated characteristic than it does to raise it to below or equal that characteristic. So for a character with smarts 1d8, raising their repair skill from 1d8 to 1d10 costs twice as much as raising their repair skill from 1d4 to 1d6 or from 1d6 to 1d8. The average starting characteristic is 1d6, so it is relatively rare for a character to start with better than a 1d8 in any characteristic. This means that getting skills above 1d8 becomes very expensive. Combined with the fact that 1d10 and 1d12 skills aren’t much better at most rolls than a 1d8, many people question why anyone would increase a skill above 1d8. This is actually a bonus of the system. For most things characters don’t really need a high skill level and can get several skills at a useful point during character creation. However, there is a reason to have higher skill levels, raises.

Raises

While a 4 or better is all that is usually needed to succeed at a task, if a player rolls 4 better than they need for a success, usually a total of an 8, they get what is called a raise. In some cases raises provide defined bonuses. In combat a raise increases the damage done to an opponent. For spell casting, which also covers weird gadgets, psionics, and super powers, many spells gain extra effectiveness if the character gets a raise. GM’s are also free to assign bonuses to any roll that generates a raise. For example, you don’t just talk your way past the bouncer, but also get told about the private party in back. Looking at Figure 1 shows that the probability of getting a typical raise, rolling an 8 or better, doesn’t improve all that much going from 1d4 to 1d6 and actually goes down moving to 1d8. The big increases start coming with 1d10 and 1d12. The result is a slick little system where being broadly competent is easy but if a player wants to be really good and consistently roll raises then they need to specialize a bit and buy the more expensive larger die skills.

Bonuses: Fantastic, if you can get them

In addition to the straight ability die, characters can also have “edges”, special abilities, some of which give a bonus to certain skill rolls. For example, the edge “Ace” gives a +2 on all boating, driving and piloting rolls. Unlike the legendary level skills of 1d12 +1 and 1d12 +2, these bonuses apply to any appropriate skill roll regardless of die size. In a game where a roll of 4 is usually needed for success and the minimum die roll is a 1, having a +2 on the roll is a huge bonus. This can be seen in Figure 2 which shows comparisons of a 1d4 +2 to 1d6 and 1d8, 2A, and 1d8 +2 to 1d10 and 1d12, 2B.


With the +2 the chance of failing to get a 4 or better becomes very small. A 1d4 +2 is much more likely to succeed on a basic roll than a 1d8. Also, remember Figure 1, 1d10 and 1d12 aren’t much better than a 1d8 for rolling 4 or better. So for a basic success the minimal skill with a +2 bonus is better than the best skill available to most characters. Even for rolling raises 1d4 +2 is better than a 1d8. Edges cost the same as increasing a skill above its characteristic, i.e. twice as much as raising a skill to low levels. So, if the associated characteristic was 1d8 or better it would cost just as much to raise a skill from 1d4 to 1d8 as it would to purchase the bonus edge. Given a choice between increasing the skill or taking the edge, take the edge every time. The situation shown in Figure 2B may not seem as clear-cut because for some of the higher rolls a 1d12 has a somewhat better chance than a 1d8 +2. However, those higher skill levels will likely cost the same, rather than half, of the cost of the edge. But even if the associated characteristic was 1d12 so that the cost of going to a 1d12 skill or getting 1d8 +2 with the edge were the same, the minor increased chance of getting a high roll doesn’t make up for the smaller chance of succeeding at all. Take the edge, every time. This wouldn’t be so bad if every skill could reasonably get that +2 bonus, but one of the most poorly thought out and irritating aspects of Savage Worlds is that no, not every skill can reasonably get that bonus.

Table 1 shows the skills available and the bonuses that can be acquired by purchasing edges.

Table 1 Available Skill Bonuses

The majority of skills are normal skills, an edge giving a +2 bonus can be reasonably purchased. They are always available and have no or reasonable requirements. For example, Ace has no requirements and gives a +2 to boating, driving and piloting while Scholar requires two knowledge skills at 1d8 or better and gives a +2 to those skills.

There are two favored skills, persuasion and streetwise, were just absurd bonuses can be purchased if desired. Granted, the cost would be high and the utility low unless the GM made good use of raises or had them roll against an opponents roll. Still, the bonuses available for these two skills dwarf those available to others. Sophie suggests that this might be to encourage characters that aren’t just combat machines, though if that were the case some suggestions as to how raises might affect these skills would be useful.

Then there are the disfavored skills, where the edge requirements are obnoxious. Alertness only applies to one skill, notice, and can only be purchased at character creation. If a character doesn’t start with the bonus they can never get it. Mr. fix-it is just ludicrous. It requires that the character have another edge, Weird Science, which is a special power only available at character creation and not present in some campaigns. In addition the character needs smarts 1d10 and repair 1d8. The result is that basically no one can take the +2 to repair, a roll made far less often than driving or piloting.

This is nothing compared to the red-headed stepchildren of the skill set, the disowned skills where a bonus is simply not available. An argument could be made for the esoteric skills that are used to power special abilities, like sorcery or weird science, as they are a case by themselves. And even a big time fan of Johnny Weissmuller’s Tarzan films is unlikely to base a character around the swimming skill. But why can a character get a +2 with boating, driving and piloting but not riding? This is especially strange in a game that started as a Western. And what about gambling? Didn’t they ever see Maverick? Then there is guts, the roll to avoid fear. Apparently amongst all those heroes no one is particularly brave or fearless. The most egregious though is fighting, the skill for any sort of hand-to-hand combat. Why a +2 for shooting but not fighting?

Fighting versus Shooting
Range

In Savage Worlds ranged, though not thrown, weapons use the shooting skill while melee attacks use the fighting skill. Ranged attacks have the great advantage of… range. A character can attack opponents when they might not be able to attack back and doesn’t have to waste time moving up to an opponent to attack them. Occasionally, the fight will be over before melee characters can even close to attack range.

Hitting

At melee range both ranged and melee attacks need to hit the target’s melee defense. This is based on the target’s fighting skill and is at minimum a 4, 2 for completely unskilled characters. The higher the fighting skill the higher the number needed to hit. For example, someone with a 1d10 in fighting has a melee defense of 7. There is also a penalty for being unarmed and fighting an armed opponent. Once beyond melee range melee attacks can’t hit at all, they’re out of range, but ranged attacks need a 4. So unless the opponent is unskilled or unarmed melee attacks usually have to roll higher to hit than ranged attacks. As an added insult, the marksman edge gives a +2 to shooting if the character takes only one ranged attack, often there is no option to take more, and doesn’t move, they don’t need to as they have ranged attacks. This means that typically a marksman needs a 2 or better to hit while a melee fighter needs a 5 or 6. A glance at Figures 1 and 2 will show how significant is this advantage.

Initiative

Savage Worlds uses an unusual initiative system. Most games use a roll plus some modifier representing the character’s penchant for getting the first move. As the dice can rarely be seen across the table and there is math involved, each character’s initiative has to be written down generating a certain amount of bookkeeping. Instead, Savage Worlds uses a deck of playing cards including the jokers. Each character or group is dealt a card and initiative is in order of the card’s value. Jokers allow a character to go at any time and give a +2 bonus to actions that round. See Figure 2 as to why this is so desirable. The deck is not reshuffled until a joker is drawn, forcing a joker to come up on a regular basis. Many people dislike the system as it uses a completely different randomizer than skills, cards instead of dice. However, it works quite well as with decent sized cards they can be seen across the table and don’t require bookkeeping.

It does present an interesting problem for characters with high initiative, though. The system can’t use adds, as that would defeat the purpose. Instead there are several edges that improve a character’s initiative by changing the card draw. Quick allows a character to discard any card lower than a 6 and draw again. Level headed allows a character to draw two cards and take the better card. The advanced version allows for three cards. Also, level headed and quick can be combined. Once again, the probability changes are not necessarily obvious, making it difficult to decide whether to take one of these edges. The chance for drawing certain cards obviously changes as the deck is depleted. However, to get some idea of how useful these edges are Figure 3 shows the likelihood of drawing cards of a value or better from a fresh deck for each of the edges and combinations.

As can be seen, the system works. The edges generally increase the character’s initiative. Interestingly, level headed and quick, which have basically the same cost, are about equally effective, even though the effects are slightly different. Taking two edges, either basic and advanced level headed or quick and level headed, are also about the same. Obviously, having all three gives the biggest initiative boost. It should also be noted that they all increase the likelihood that that character will get the eventual joker draw, gaining the round bonus and causing the reshuffle. There are certain edges that give even more bonuses when the character draws a joker. This results in synergy between the joker edges and the initiative edges, and the joker edges are probably not worth it without some kind of enhanced initiative.

Experience

The experience system is a very simple level system. The game master gives out a small number of experience points (xp) for playing and every five xp causes the character to go up a level. Gaining a level generally lets a character buy one increase in their abilities. However, if the character is raising skills up to or below the controlling characteristic they get two increases. While a level system, there are no classes. Within certain limits a character can buy anything. The main limits are that certain edges can only be purchased if a character has attained a minimum number of levels while others can only be purchased during character creation, primarily representing innate abilities.

The former is a nice use of a level mechanic. For example, only very high level characters can purchase abilities at the 1d12 +1 or better level. This keeps beginning characters from being the best in the world at a skill. Similarly, beginning wizards don’t have access to the most powerful spells, though there is some debate about how much better some of the advanced spells really are. The result is that the general outline of character development is controlled while allowing very broad choices.

Limiting certain edges to character creation does not work as well. The primary reason for the restriction is that some abilities seem more inborn rather than something a character would develop. For instance, while someone might be lucky it is unlikely that someone would become lucky after several adventures. However, this is pretty much an esthetic choice and situations could arise that would explain gaining some of these restricted abilities later on, like say gaining “Noble” if the character were knighted and given a fiefdom. In the case of mystical powers there also seems to be a sort of character balance/ niche protection aspect requiring that a character be dedicated to those powers early on. Given the large amount of character ability that needs to be invested to actually be good at a mystical power, this seems unnecessary. Fortunately, waiving these restrictions is a trivial fix. Older versions of the system had “bennies” also affecting the amount of experience a character gained. However, this has been removed from the Explorer’s Edition.

Bennies

“Bennies”, basically a nickname for benefits, are similar to hero point or fate points from other systems. They are points that a character can spend on things, primarily rerolling a poor dice roll. This allows the GM to easily reward players for exceptional play, just give them an extra benny. It gives players some guard against bad luck killing their character. Importantly, it also gives players input into what rolls they feel are important to their character or the story. If a player feels that their super spy really shouldn’t fail that seduction roll they can spend bennies to help this come about.

Starting with Advanced Characters

Savage Worlds is really set up to start with a starting character and have them advance with time. However, characters can be made at any level of ability by simply creating a starting character and giving them some levels during character creation. Unfortunately, due to level restrictions, limiting characteristics, etc., it has to be done in that order. Make a beginning character and then increase them level by level. Rolfe has an excellent description of why this is a serious pain.

Starting Costs Versus Advancing Costs

One common annoyance in games is having things cost different amounts to purchase during character creation compared to character advancement. This opens the door to some serious optimization abuse for people familiar with the system. Fortunately, Savage Worlds has very little of this. The largest factor is that some edges are only available during character creation and so these have to planned out for a character from the beginning. The other difference between beginning and advancing characters is the cost of new skills. During character creation increasing a skill from non-skilled, 1d4-2, to skilled, 1d4, costs the same as increasing a skill up to or below its governing characteristic, like increasing shooting from 1d4 to 1d6 if the character has 1d6 or better agility. During character advancement new skills cost twice as much. The end result is that one should try to have all the skills the character will really need at the beginning, even if this means that they are only 1d4. For example, giving a character 1d4 stealth and 1d4 climb during character creation will usually cost just as much as giving them 1d6 stealth but no climb skill. However, raising both 1d4 stealth and 1d4 climb to 1d6 later will usually cost less than adding 1d6 climb to the character, even though the final result is the same.

Conclusion

Savage Worlds is a reasonably mechanically heavy system that has more than its fair share of quirks. Both the dice rolling and initiative probabilities are odd and take some getting used to. Certain rules, especially skill edges, seem poorly thought out and it’s a shame that they weren’t tweaked in newer additions. Overall, though, it is a solid, flexible, and enjoyable system that works well for many genres.

A previous post discussed the mechanics of Risus, a free, simple RPG. It showed that skill differences were very stark in combat and an opponent was highly unlikely to beat someone of higher skill. This might give the impression that Risus has no way of dealing with such situations, but it does. Risus has rules for teaming up on an opponent.

The basic team rules are pretty straightforward. One character is designated the leader. They roll their dice as usual. Other characters can join in as members of the team, assuming that they have an appropriate cliché to use. For example someone with 3d6 swordsman could team up with someone with 2d6 Viking and someone with 3d6 wizard to fight a powerful troll. The team members also roll their dice. However, team member dice only count if they roll a 6. Thus a team member with 2d6 skill could contribute 0, 6, or 12 points to the overall roll, depending on the number of 6’s they rolled, but no other values are possible. This means that on average the leader’s dice contribute the average for a d6, 3.5, while follower’s dice on average contribute only 1. Of course, by only counting 6’s the variance of the roll is quite high even though the average is only 1. Given that the average for follower’s dice is about 1/3 that of the leader’s, one would expect that every three dice of follower skill would be roughly the equivalent of adding a die to the leader. As can be seen in Table 1, this is basically the case.

Table 1. Percentage Chance of Winning a Single Die Roll

Combat

However, there is more going on than just a better average roll. Combats are not contests of a single die roll but involve multiple die rolls and damage. While the average roll of 4d6 is about the same as a team of two 3d6 characters, the 4d6 skill is eliminated after four points of damage while it may take as many as six points of damage to eliminate the team. So how does the damage get allocated in team combat? The usual way is for every character to roll their skill dice again and the character with the lowest roll takes the damage. For example, if two characters with 3d6 skill each are teamed up and take a point of damage, they both roll 3d6. Whoever rolls the lowest total takes the damage. In addition to being able to take more damage, it should be noted that follower’s dice are not as valuable as the leader’s dice. So if the damage falls on the followers it isn’t so bad. These factors should combine to make a team of two characters with 3d6 cliché better in combat than one character with 4d6. This is born out by Table 2, which shows the results of one million iterations of a Monte Carlo simulation.

Table 2. Percentage Chance of Winning a Combat

The first section of Table 2 shows the likelihood of teams of one, two, or three characters with 3d6 clichés beating opponents of different skills. The blank cells were not determined. Despite the fact that on a single roll a team of two characters with 3d6 is slightly worse than a 4d6 (see Table 1), thanks to the damage effects the team has a better–than-even chance of defeating a 4d6 in combat.

It should be noted that the values in Table 2 are likely to be ever so slightly too low. In order to make the calculations easier, it was assumed that if the leader’s cliché went to 0 the team would lose. This comes from another rule of team combat. If the team breaks up all team members suffer a point of damage. If the leader is defeated then the team automatically breaks up, causing damage to the entire team. Having lost one member and then suffering the damage from the break up, a team would have a tough time coming back to win the fight. So why take damage for breaking up the team? It prevents players from constantly reshuffling the team. Because the leader’s dice are more valuable than a follower’s, without this rule the team would immediately reform with a new leader if the leader’s cliché ever fell below that of another teammate.

Because of the value of the leader’s dice and team damage if the leader dies, victory is heavily dependent on whether the leader takes damage early on. A casual examination of the detail of several simulated combats between a 3d6 two-man team and a 4d6 opponent supported this conclusion. Most of the defeats came from the leader taking damage in the first or second round. Once the leader took damage it significantly increased the likelihood of taking more damage as well as that damage falling on the leader. The resulting death spiral was quite steep.

Sacrifice

This brings up the second way to allocate damage in team combat, sacrifice. A teammate can volunteer to take the damage for the team. That character then takes the damage plus another point of damage. Under most circumstance this is two points of damage, reducing their cliché by two. Given that a single leader’s die on average contributes more than three follower’s dice, this is useful. In addition, if a character does sacrifice  for the team this inspires the team so much that on the next turn the leader rolls double the normal number of dice.

For example, if a two-man team with 3d6 clichés takes a point of damage the follower can volunteer to take the damage. Their 3d6 is reduced to 1d6. However, on the next turn the leader rolls 6d6, for a total of 6d6 plus 1d6 that only counts if it rolls a 6. Given how significant an edge extra dice are, this produces a very good chance of wounding the opponent on the next round if they have 5d6 or less. This may seem a great deal like “pumping”, exchanging a wound for at best a wound on the opponent. However, the larger number of potential wounds that a team can take combined with the lesser value of the follower’s dice should make it a very powerful option. Also, the damage is applied to only one character so if that character is already at 1d6 the extra damage is meaningless.

To test the effectiveness of this option, the Monte Carlo simulations were rerun assuming that the followers would always sacrifice themselves. The results are shown in the second half of Table 2. It is clear that this tactic greatly increases the odds of victory. It does, however, guarantee a fair amount of damage on the followers. So the utility of sacrifice may also depend on how healing is being run.

Doing Things

Skills/ abilities in Risus are called clichés. They range from 0, no ability at all, to 6, with starting characters having no cliché higher than a 4. When a task is in doubt a player rolls the number of 6-sided dice for the appropriate cliché and adds up the total. If the total equals or exceeds the difficulty, they succeed. Table 1 shows the difficulties and likelihood of success for 1 to 4 die clichés.

Table 1. Task Resolution

The first thing of note is that a cliché of 1 represents pretty minimal ability, the rookie or intern, but it is still supposedly better than someone without any skill. However, a 1 can only succeed on easy tasks. Many GM’s pretty much stick to moderate or hard difficulty numbers, feeling that they shouldn’t even bother with the really easy stuff. But that makes clichés of 1 nothing more than a placeholder to try to increase with experience as they will then always fail. A GM that doesn’t intend to make much use of easy difficulty tasks should really warn the players so that they know just how useless clichés at 1 will be. It’s also worth noting that the chance of success falls off very rapidly with higher difficulty, quickly going from almost certain to almost impossible. Understanding where to set the difficulties is important to avoid the game becoming just a fail fest.

Combat

Combat in Risus covers everything from courtroom drama, to horseraces, to actual physical combat. Opponents roll their appropriate clichés and whoever rolls higher wins the round. The looser has their cliché reduced by 1. On ties nothing happens. The combat continues until it can’t go on, say one of the characters flees the scene, or someone’s cliché is reduced to 0. There are some rules for teaming and the like as well as optional rules, but that’s the basic mechanic. The first section of Table 2 shows the likelihood of beating an opponent on a single roll.

Table 2. Chances of Winning a Round of Combat

Just as with task resolution there is a quick fall-off in the likelihood of success. Even a one die difference is very large. This has lead to people making house rules. Sort of silly to house rule a system as simple as Risus, but some people really hate that steep fall-off.

The simplest house rule is to take the highest of the dice as the result. So a roll of 4 dice resulting in 1, 3, 3, and a 5 would be read as a 5, the highest roll. This system is shown in the second section of Table 2. The fall-off, while still significant, is not as steep as the original system. However, the chance of ties goes up dramatically. This is because there are now only six possible outcomes and the more dice that are rolled the more those outcomes cluster at the high numbers.

An alternative, more complex, house rule is shown in the last section of Table 2. It is intended to keep the shallower fall-off of the highest die rule but reduce the chances of ties. This rule involves taking the highest die roll, but matches are added together. So a roll of 1, 3, 4, and a 5 counts as a 5, the highest roll. However, a roll of 1, 3, 3, and a 5 counts as a 6, the two 3’s are added together to get 6 which is higher than 5. As expected, the fall-off is steeper than the take the highest rule, but not as bad as adding all the dice, while the chance of ties is somewhat reduced. Overall the statistical differences don’t seem to be worth the added complexity.

Another thing to keep in mind is that combat tends to favor higher skills more than single rolls do. The likelihood of winning an entire combat, rather than just one round, is shown in Table 3.

Table 3. Chance of Winning Combat

Notice how drastic the fall-off becomes for the base system and the steepness of the death spiral. If two characters with 4 die clichés fight, the character that is wounded first goes from a 50% to a 10% chance of victory. Either house rule gives a lesser opponent a decidedly better chance.

Pumping

One optional rule is the ability to “pump” a cliché. This allows a character to increase their cliché for one round by a number of dice in exchange for taking that many points of damage to their cliché. So a character with a 3 could go to 5 dice for one round but at the end of the round reduces the 3 by 2 points to a 1. Under basic combat this option is useless. Since the minimum damage a pumping character takes to their cliché is 1 while the maximum damage the can inflict is 1, the best that can be obtained is keeping the same difference in clichés as at the start. Given the advantage of higher dice there is no reason to pump if your cliché is higher. If it is lower then pumping just guarantees loosing. If the skills are the same you go from a 50% chance of a win to a tie being the best that can be hoped for.

However, under some very specific circumstances pumping can be useful. If an inappropriate cliché is used in a conflict, say hairdresser to win a horserace, then the damage inflicted for a win is 3 points. Of course, one needs to come up a pretty impressive excuse as to how the cliché applies. But that gives the possibility of doing more damage to the opponent than the character takes by pumping. Also, if a character has more than one appropriate cliché they can switch back and forth between them each round. This opens up the possibility of pumping with one cliché to inflict damage on the opponent and then switching to the other to finish the fight.

Healing

As appropriate for a simple system, healing is basically left up to the GM. Someone using lawyer to fight a court case may loose, but will probably have their lawyer skill back at full once the case if over. Though if they suffered some massive blow to their self-confidence or reputation the damage might be longer lasting. Given the steepness of the death spiral, healing really bears thinking about. If physical damage takes some time to heal, the characters will either need to face progressively easier foes or retreat to heal up between fights.

Final Thoughts

There are other aspects of the system like fighting as groups and other optional rules, but this commentary is already about as long as the rules. Overall, even very simple systems seem to have their share of unexpected complications and pitfalls.

First of all, this is not about the Rules restaurant in London. Though I’ve eaten there and the food is excellent.

No, this is some thoughts about game rules. John has been writing a series on game design for this site and much of game design is really about rules. Some games also provide interesting settings and characters, but so do good science fiction and fantasy authors. What makes it game design is that it has rules.

I’ve been gaming a long time and have seen, played and run many different game systems. I also have a fairly easy time with math. As a result I can figure out most rules systems pretty quickly, they are usually just variants of something I’ve seen before. As you might imagine, I’ve been called a rules lawyer, and less pleasant versions thereof, on many an occasion. Now a player obsessing about the rules, especially during a game, can be really annoying. But I would argue that there are some good reasons to understand the rules of the game and how they are supposed to work, illustrated in the following gaming anecdote. (Ok, as a gamer I’m probably writing these things just to tell gaming anecdotes, sue me.)

One of the best games I’ve ever played in was a Runequest game. Runequest was one of the earliest RPGs (1978) and definitely shows its age. The system has plenty of things it doesn’t cover, is somewhat clumsy, and has a fair amount of crunch. You not only had overall hit points but also hit points for each limb, your head, and your torso. So you could loose an arm without dying or die with many hit points left by loosing your head. Each section of your body could have different amounts of armor. There was even one god whose worshipers could do things like swear to never wear armor on their left arm allowing them to do extra damage to other people’s left arms. See, crunchy. Anyway, I actually felt more freedom to try whatever I wanted in that game than many newer, more elegant systems because of the GM. Being a good GM he was good with NPCs, stories, etc. But what allowed all that freedom was his knowledge of the rules. He knew them inside and out, backwards and forwards. So no matter what I threw at him, he would think for a bit and then come up with a way for the rules to take care of it. I was leaping around, swinging on chandeliers, fighting on top of runaway carriages, and all sorts of stunts that the game hadn’t been designed to handle. But he came up with ways that were fair and worked smoothly with the rules. Sometimes I’d succeed, sometimes not, but it was fun trying. I felt more freedom to try stuff than in anything I’ve seen outside of rules-light systems, and Runequest is not a rules-light system.

Anyone who has gamed for a while knows that these things come up. Someone will want to do something that isn’t covered by the rules, or not covered directly. Maybe the rules themselves are so bad that they need to be worked around. I remember being at a convention and attending a demonstration game of Superhero 2044. The combat rules were so bad that the guy giving the demonstration, from the company that produced the game, said that no one used it and he used house rules for the demo. Some people also like tweaking systems, adding house rules or adapting them to different settings. Then of course, there is the advantage of not realizing that the power combination you gave the bad guy is unstoppable halfway through your climactic fight. All of these have something in common. Fewer problems arise and the results are usually better when you really know the rules and how they work, or don’t work. So time to put in one last anecdote.

I played in a Shadowrun game over several iterations of the rules. At one point my character was Feedback, an insane rock star turned shadowrunner. Feedback had maximum human, 6, Dexterity and Body, a stat covering things like endurance. She also had close to maximum Strength, as well as a high skill, 6 dice, in Athletics. In short, she was an Olympic athlete with cyberware. Our group at the time also had two physical adepts, basically magically-powered martial artists. Their physical statistics were about what Feedback had but they had no Athletics skill. What they did have was one level of Athletics auto-success. This cost a bit of their magic pool, but not tons. A beginning adept could, though they had better things to buy, get something like 12 auto Athletics successes.

How the system works is you roll a pool of six-sided dice equal to your skill and try to match a target number or better. Each die was counted separately and they “exploded”, meaning that if you rolled a 6 you rolled that die again and added it to the 6 and could keep on going as long as you rolled 6s. Each die that equaled or exceeded the target number counted as a success. As a result, rolling a 6 meant you automatically rolled a 7 or more, as the re-roll would add at least 1 to your original score.

For example, let’s say there was some kind of running task to outpace the boulder rolling at you through the ancient temple. The difficulty might be a 4. With 6 dice of Athletics, Feedback would roll 6d6 and count how many 4s or better were in the roll. The average would be three successes. The physical adepts, on the other hand, would roll their 0 Athletics, which meant that they could default to a characteristic like dexterity, but at a penalty of –2 on the rolls. So if they had 6 in dexterity they would also roll 6d6, but they would need 6s, giving an average of one success. They would then add in their auto-success for a total of 2 successes. You can see that there are three ways to adjust the difficulty in this system. You can increase the number of successes you need, i.e., you need three 4s. You can increase the difficulty number, you need to roll an 8 or better. Or you could do both, you need to roll three 8s. The thing is that how those different methods change the likelihood of success is not necessarily obvious. This brings us to the story.

Our usual GM was running. We were raiding an office building and needed to get to the top floor. Several of the players went straight for the elevators, which was apparently the way the GM wanted us to go. However, we had no hacker, the enemy knew we were in the building, and all elevators were computer-controlled. If I were those guys I would have taken us up to almost the top and then dropped the elevator down the twenty-some floors, killing us all. I suggested taking the stairs. But we were in a hurry. So the GM came up with his running up the stairs rule. For every two flights you had to roll Athletics. The target number was the number of flights you had gone up. Failure meant that you took a fatigue level. Given how the mechanics work, even 2 fatigue levels is pretty crippling in a fight. The early flights would be easy. You needed a single 2 after the second floor, a single 4 after the fourth, a single 6 after the sixth etc. But by the twentieth floor you needed to roll a 20. The chances of that on an exploding d6 are 5 in 1296, not likely even with a large pool. But since they had one auto-success, the physical adepts never even had to roll. The GM had just created a system where the adepts, with a bare minimum of Athletic auto-successes, would make it without breaking a sweat while everyone else, including my Olympic athlete, would pass out before getting there. And this was generally how he handled athletic stunts, you needed one really high number like a 20 or 30. This made my significant skill investment in Athletics useless while his buddies’ one auto-success let them do whatever they wanted, no matter how crazy. One of the many reasons I left that game.

So, why all this rambling about rules? As I said, I’ve seen many game systems and I like thinking about how rules work, interact, don’t work, or generally affect a game. So I hope to write some thoughts on different systems and types of rules. Maybe someone will find them interesting. Maybe they’ll even save someone from making a terrible house rule, though that is probably the delusions of grandeur talking.

This is the second supplement to the Variance and Game Design article. While there are some new observations, it covers much the same ground as the first supplement but for a different system, Spirit of the Century. So if you haven’t read the first supplement you should do that. If you have and are a glutton for punishment then this article is for you.

The System

For my first test I chose a system I was familiar with and had some old questions about. For the second test I chose Spirit of the Century (SotC) because it is a game I haven’t played but really want to, due to some cool sounding mechanics. My biggest reservation about the game, however, was that combat would be heavily influenced by skill level compared to non-combat rolls. So, I looked at SotC mostly to satisfy my own curiosity.

Spirit of the Century Mechanics

SotC has a much more complex combat system than Feng Shui. Skills are rated by descriptions but really translate into a number from 0 to 5. To make a skill check, you roll 4 Fudge dice. These are special dice that can roll –1, 0 or +1. Thus for four dice the roll will run from –4 to +4 with an average value of 0. This roll is added to the skill. For simple tasks, if the roll equals or exceeds the target value the character succeeds.

In combat, the attacker rolls whatever skill they are using for the attack while the defender rolls whatever skill they are using for defense. If the attacker’s roll plus skill exceeds the defender’s, then the defender takes damage.

Damage occurs in terms of stress and complications. Everyone has a stress track, basically a series of numbered boxes. For a basic character they run from box 1 to box 5. The amount by which the attack beats the defender is the damage and the box corresponding to that number is checked off.

For example, if the attacker wins by 3 then the number 3 box is checked off. If the attacker later wins by 2 then the number 2 box is checked off. Notice that checking off box number 3 had no effect on box 2, so when the 2 damage hit occurred box 2 got checked off. If the corresponding box is already full then the next highest empty box is checked off. So if the attacker gets a third hit for 2 damage, this would normally check off box 2. However, box 2 is full so we look to box 3, but box 3 is full so we look to box 4. Because box 4 is empty, box 4 is then checked off. If the damage goes past the end of the stress boxes then it results in a complication.

Under most circumstances, a character can suffer 3 complications. The first time the stress track is exceeded they take a minor complication, the second time a moderate complication, and the third time a major complication. If they take damage that would result in a fourth complication the character is taken out. It should be noted that the same mechanics apply to mental or social contests as well, though being a pulp game, most combats will likely be physical.

SotC also has Fate points, a limited supply of points that can be spent to reroll a die roll or add two to a result, and this can be done after the dice are rolled. Exactly when and how many Fate points can be spent for any die roll is entirely dependent on the character and the circumstances of the roll.

Assumptions and Simplifications

Initiative is much easier to handle in SotC, but I left it out to make things more comparable to the Feng Shui results. I left out “spin”, a rule where if someone’s defense roll is much higher than an attacker’s attack roll, the defender gains a temporary advantage. It would have been somewhat annoying to code and would just serve to make higher skills even more advantageous.

The big thing I left out was Fate points. There use should matter greatly, but because they are highly character- and situation–dependent, there is simply no way to reasonably model them. However, I do discuss Fate points later.

I assumed that both Pain and Suffering had 5 boxes on their stress tracks. Some skills can make this number go up, but that should just serve to make the combat longer and increase the differences between skills. So I decided to use the base 5 boxes.

I also assumed that neither combatant had any applicable combat stunts. Some stunts can affect combat, but not all characters have such stunts and certainly not for all types of combat, so I ignored them.

Finally, I assumed that each combatant’s offensive and defensive skills where identical. This is not always the case in SotC. The guns skill normally only gives offense, not defense, while athletics gives defense but no offense. However, skills like melee can provide both and, even if using different skills, they can easily be the same level. So for simplicity’s sake I assumed that they were the same.

Spirit of the Century Results

Again, I tested the model by setting Pain and Suffering to equal skill levels and running 50,000 simulated combats until one combatant, the other, or both were taken out. As before, the results showed Pain and Suffering with an equal number of wins and a small number of ties (Figure 1).

At first blush it might seem odd that the combats lasted much longer than the Feng Shui fights, tending to be around 16 to 19 rounds long rather than 8 to 10 (see supplement 1). After all, it takes only 9 minimum damage hits to take someone out in the SotC example while it takes 12 minimum damage hits in the Feng Shui model. Two things are causing this. First, in Feng Shui an attack causes damage if it equals or exceeds the defender’s defense. In SotC, only attacks that beat the defense total cause damage, so damage-causing attacks are less likely. Second, the stress and complication mechanics generally suppress the variation in damage results.

For example, imagine a defender hit by the following amounts over their defense, in order, 4, 5, 1, 1, 1, 5, and 4. In SotC this would result in box 4 being checked, then box 5. The third hit would check off box 1. The fourth hit would normally check off box 1, but it is full, so it checks off box 2 instead. The fifth hit would check off the 1, but it is full, as is the 2, so it ends up checking off box 3. The sixth hit, for 5 damage, would check off box 5, but it’s full, so it goes over the stress limit and causes a minor complication. Finally the 4 damage hit can’t fill boxes 4 or 5 as they are both full, and causes a moderate complication. Compare this to the result if all the hits did minimum damage, i.e., were 1 above the defender’s total. The first hit checks box 1, the second box 2, since box 1 is full. This continues until the fifth hit fills the final stress box. The two subsequent hits cause a minor and moderate complication, respectively. The end difference between a series of mostly powerful hits and a series of minimum damage hits is nothing.

If the same series are compared in Feng Shui, assuming our base damage of 3, the first series does a total of 42 damage, more than enough to defeat an opponent. The second series would do 28 damage, leaving the opponent standing. A couple of solid hits in Feng Shui can really shorten the fight.

But what about unequal skill levels? I had assumed that the results would look a great deal like those for Feng Shui (see supplement 1). My jaw dropped when I saw the results presented in figure 2.

When Pain was set to one lower skill than Suffering, out of 50,000 simulated combats Pain won once and tied once. Again, that is out of 50,000. In the absence of Fate points, a difference of a single level in combat skill is insurmountable! For what it’s worth a comparison to non-combat rolls is presented in Table 1. Again, I use the sum of Pain’s wins and ties, not that it matters much.

Table 1: SotC Combat Versus Non-Combat Results

These results have a couple of implications. First, Fate points aren’t an important mechanic. They are an absolutely critical mechanic. In the case of unequal skill levels, the only variation in combat results comes from the use of Fate points. Second, GMs really need to keep an eye on characters’ combat skills. An opponent with a skill of 4 would be zero threat to a character with a 5 combat skill but, barring Fate points, an unstoppable foe to a character with a 3 combat skill.

Why the difference?

Why are the results so different between Feng Shui and Spirit of the Century? Variance seems a likely explanation. A lower variance dice mechanic should exacerbate the problem of multiple rolls. However, comparing Feng Shui and SotC takes a little maneuvering. In Feng Shui, only the attacker rolls. In SotC, both the attacker and defender roll. Fortunately, with Fudge dice, unless there are rerolls, having the attacker roll 4 dice and the defender roll 4 dice is mathematically equivalent of having the attacker roll 8 dice and the defender not roll. So I compared the Feng Shui roll with a roll of 8 Fudge dice as shown in Figure 3.

Feng Shui does have more variance in its results, but not huge amounts more. It seems difficult for that to completely explain the difference. But remember that the stress and complication mechanics tend to reduce variance. In SotC a large hit like a 4 or 5 is at the end likely to be pretty much the equivalent of a minimum value hit. A couple of lucky blows by the underdog are not going to have much effect on the combat’s outcome.

Conclusions

The results here reinforce the finding that combat results are more consistent. But what really comes through is that the choice of mechanics has a very large effect on how much consistency is present in combat. The analysis has also given my some insights into how SotC would work if I ever manage to actually run it.

In my post about variance in game design I discussed the effect of rolling multiple times for combat resolution and how this reduces variability of combat results compared to non-combat results. This was supported by some simple logic and probability. However, I was interested in getting some actual numbers to back up that hypothesis. Herein I present the results of one of those tests. Now, the variance article was written to try to present the concepts of variance to a more general audience. No such attempt has been made here. You have been warned.

The System

In order to get a more accurate idea of how skill levels determine success in combat I conducted a Monte Carlo analysis of Feng Shui. I chose to look at Feng Shui because I have a fair amount of experience with the system and one of the things we always complained about was that a point of combat skill seemed as valuable as 3 points in a non-combat skill. Thus, I had some idea of how the results would turn out and was curious as to how close our gut interpretation of the difference between combat and non-combat skills would be to the numbers.

Feng Shui Mechanics

The basic mechanics for Feng Shui are relatively simple. You have a skill. To see if you succeed in a task you roll 1d6 and add the result to your skill. This die “explodes” in that if you roll a 6 then you add 6 to your skill and roll the die again and add that number to the skill as well. If you keep rolling 6s you keep adding 6 and rolling again. In this way it is possible, though highly unlikely, to roll a +100 or higher. You also roll a second “exploding” 1d6 and subtract that result from your skill. For example, if you roll a 4 on the plus die and a 3 on the minus die and have 15 skill your result is a 16, 15 +4 –3. Obviously, the average roll in this system is +0.

To succeed at a non-combat task you need to roll equal or better than a target number. This number is usually set by the game master but may also be someone else’s skill, such as rolling your intrusion skill versus someone else’s intrusion skill to see if you get past the security system they set up. In combat you roll your combat skill against their combat skill. Only the attacker rolls, not the defender. If you equal or exceed the opponent’s combat skill you hit and go on to determine damage. You can make yourself harder to hit by giving up some of your actions to dodge, which increases the number an opponent needs to hit you by 3.

Damage is calculated by adding your damage, which is either a straight number for ranged attacks or a number plus your strength for hand-to-hand combat, to the amount you exceeded the opponent’s combat skill and then subtract the opponent’s toughness. Thus it is possible to hit someone and still do no damage. The resulting damage is subtracted from their hit points. Almost everyone has 35. When their hit points reach 0 or lower they are out.

Model Assumptions and Simplifications

In order to be able to reasonably program the model, I had to simplify the mechanics a little. In addition, I was really only interested in comparing combat to non-combat outcomes rather than exploring all possible combat outcomes. So I made certain assumptions and simplifications for the model.

First, I ignored initiative. Initiative in Feng Shui is somewhat complex in that it gives you a certain number of actions per round and different things like dodging and attacking cost different amounts. In addition, the costs can change depending on circumstance. That was just too annoying to put in the model, so I didn’t. However, if I assume that both combatants, let’s call them Pain and Suffering, have the same initiative bonus then given the multiple rounds of each fight and the fact that I’m simulating 50,000 combats initiative should really just fall out in the wash. It does have a couple of implications for the results though. Ignoring initiative allows for ties, Pain and Suffering could both get reduced to 0 or lower hit points on the same round. In play this can’t happen because one or the other would go first and the opponent wouldn’t get to carry out their attack. Assuming that they both have the same initiative bonus then in an actual game Pain would win half of the “ties” and Suffering would win the other half. It also means that when I talk about rounds I’m really talking about one exchange of attacks rather than a Feng Shui turn, which can often contain 3-4 or even more attacks.

I set the base damage, the damage done by a character minus the toughness of his opponent, at 3. Feng Shui is a combat-heavy game and people tend to have decent toughness scores so this is a not unreasonable choice. A smaller base damage would be expected to make the combat last longer, and thus have more rolls, and thus favor higher skill levels even more. A larger base damage would be expected to make combats shorter, and thus have fewer rolls, and thus favor higher skill levels somewhat less. I did run single simulations using base damages of 1 and 5 and the results were exactly as expected, though the changes in the win/ loss outcomes were actually quite small (data not shown).

I also assumed no dodging. The dodging mechanic is tied in with initiative and so can’t be modeled exactly without it. I did run one simulation assuming that both opponents would dodge all attacks. As expected, the combat lasted much longer and the higher skill level character was slightly more successful than without the dodge (data not shown).

I left out the various combat stunts that characters might have, they would be often difficult to model and there are just too many of them and they vary too much between characters. Needless to say, a character with combat stunts will have an advantage over a character without such abilities, but examining this is beyond the scope of this analysis.

I also left out Fortune points. Fortune points are a limited supply of points that can be spent to add one, non-exploding, d6 to a skill roll or active dodge. Most characters have few, if any, Fortune points and in our games we tended to roll many combat rolls. So overall the effects of Fortune points were minimal for most characters. However, some characters have a fair number of Fortune points, and if they know that this is the last combat of the session they might as well use them fast and furiously. In addition, while most combat stunts just amplify normal combat parameters, i.e. you do more damage or attack more often, some stunts can very seriously inconvenience an opponent. For such stunts Fortune points can become quite powerful. For an example of a Feng Shui combat with stunts and Fortune points see Sophie’s write up.

Feng Shui Results

In order to test the model I set both combatants, Pain and Suffering, to the same combat skill level and ran 50,000 simulated fights until either Pain, Suffering, or both collapsed. The results are shown in Figure 1.

If the model is working, then two combatants with equal levels of skill should have equal numbers of wins as well as a few ties. As you can see, this is the case. It can also be seen that the typical combat length is around 8 to 10 rounds. This is 8 to 10 attacks and with Feng Shui turns being about 3 to 4 attacks per turn, the combat should last about 2 to 3 turns. This is in keeping with my personal experience with the system and made me more confident of the model.

To test the effects of skill difference on combat outcomes, I ran tests setting Pain’s skill at 1 to 3 points lower and 1 to 3 points higher than Suffering’s. Unless something is wrong with the model, the results should be symmetrical about the even skill result. The results for Pain at one skill lower than Suffering should be the same as the results for Suffering at one skill lower than Pain. This was the case. Also, the 2 points lower result was intermediate between the 1 point lower and 3 points lower results. So Figure 2 only shows the results for Pain at 1 and 3 points lower than Suffering.

As expected, with a lower skill level Pain is much less likely to win the combats than Suffering and that chance decreases as Pain’s skill is reduced. The combats also tend to be a little shorter, typically about 7 to 9 rounds for one lower skill and 6 to 8 rounds for three lower skill.

But the real question is how this compares to the chance of success with non-combat skill. This poses a slight problem. Non-combat success is obtained by rolling equal to or greater than the target number. Basically, ties go to the player character. However, combat would not normally have ties, but it does because I ignored initiative. Assuming equal initiative bonuses, the player would only win half of those ties in an actual game. However, in order to make the non-combat, player wins ties, more comparable to the combat results I added together both Pain wins and ties. This is the equivalent of the player winning all ties. This isn’t quite accurate, but seems a fair way to compare the two. Additionally, the number of ties is relatively small and this decision does not change the final numbers by that much. The results are presented in Table 1.

Table 1: Feng Shui Combat Versus Non-Combat Results

You will notice that even being generous to Pain by granting him all ties, the success rate falls off quite dramatically as Pain’s skill gets lower, proving the hypothesis that combat results are more consistent than non-combat results. Another interesting result is the chance of success at 1 skill higher for combat is about equal the chance of success for 3 points higher on a non-combat skill, my Feng Shui group’s gut reaction was pretty accurate!

Conclusion

I feel satisfied that combat results really are more consistent than non-combat rolls.

How Common Is Average Anyway?

Introduction

Most games incorporate an element of chance, usually with dice, though others use cards, coin flips, etc. While we are familiar with the concept of mean or average of a roll (a measure of central tendency), one aspect that often seems overlooked as designers search for a cool or easy to use mechanic is the question of variability, or how often do you get the same or similar results from the mechanic. The most commonly used measure of variability or dispersion of results around the mean is the variance. I think that it is easiest to look at an example.

Figure 1 shows the resulting distribution of four mechanics with very different probability curves but very similar average values. The possible rolls are given along the bottom while the lines show the percentage chance of rolling that number. The famous twenty sided die, 1d20, is shown in blue and every result on the die, from 1 to 20 has an equal possibility of occurring of 5%, resulting in an average roll value of 10.5. Two d10 added together are shown in red, with average total of 11. Three d6 added together are in green, average total of 10.5, while the black line shows a mechanic where the value is “Always 11″, thus the average is also 11.

It should be obvious that despite the fact that their average values are roughly the same, these different mechanics have very different probabilities of rolling at or near the average. The likelihood of rolling a 9, 10, 11, or 12 on a 1d20 is 1 in 5. For 2d10 it is more than 1 in 3, for 3d6 it is almost 1 in 2, and always for 11. The d20 is the least predictable , i.e. rolling near the average is less common than with the other mechanics. The “Always 11” mechanic has no randomness at all, it always generates an average result.

Variance and the game

Why do we care? First, the distribution of the chosen mechanic can have a dramatic effect on the style of a game. For example, let’s say that Lance Armstrong is rated as +10 bicycling skill and that we will add this to our die roll. A random fan from the audience has a mere +0 skill. If they race and the fan needs to beat Armstrong’s roll to win the chance goes up tremendously with mechanics that have a very wide distribution, i.e., a higher variance. The fan’s die roll needs to be 11 higher than Lance’s die roll, 10 to overcome the skill difference and 1 more to make the fan’s total higher.

Because none of these mechanics can roll lower than 1, the fan has to roll at least a 12 to have any chance of beating Lance. If the fan rolls a 12, a 1 in 20 chance using the 1d20 mechanic, then Lance has to roll a 1 for the fan to win, also a 1 in 20 chance using the 1d20 mechanic, for a 1 in 400 chance of the fan winning. If the fan rolls a 13, again a 1 in 20 chance, then the fan wins if Lance rolls a 1 or 2, a 1 in 10 chance, for a 1 in 200 chance of the fan winning. If we add up all the possible ways the fan can win using the 1d20 mechanic the fan has an overall 11.25% chance of winning (Table 1).

Table 1: Ways of winning for Fan:

Because the other mechanics favor average numbers, the possibility of the extremes — Lance rolling poorly while the fan rolls well — becomes lower. Using 2d10, the chance that the fan wins is 3.3%; with 3d6, it is 0.45%; and with the “Always 11” mechanic, the fan always looses.

A mechanic with higher variance allows more surprise upsets with the underdog winning. This means that players have a chance against better opponents, though worse opponents have a chance against them. Stylistically, this could work well for a more realistic World War II game as even the best soldier can go down to random gun fire. It would also work well for comedy where the random chance can fuel all sorts of jokes.

A mechanic with more closely grouped results allows more confidence in the expected results. Players can take on people they are much better than, confident that they aren’t going to get trounced due to a poor roll. Stylistically this fits things like classic samurai movies where only someone of roughly the same or better skill can possibly beat a samurai. Neither high or low variance is “better”, they just give a different flavor to the game.

Different levels of variability

Real life is also full of things with very different levels of scatter and variability. Drawing for high card is completely random and no amount of skill will help you unless you cheat. A bicycle race is much less variable, however — much more predictable. Lance Armstrong will certainly have some day-to-day variation but barring a major catastrophe will always win except against other high-end professionals. This can cause problems when your mechanic has much, much higher variability for certain tasks than the real world.

Games generally do not address of the question of variance directly. Though sometimes they do: one old miniatures game used d6 for resolution but veteran troops counted 1s as 2s and 6s as 5s. So novice troops could roll the extremes, 1s and 6s, but veteran troops could not, making the performance of veterans more consistent. However, all games have to deal with this in some way.

The old school method was to simply not bother rolling for things that everyone assumed should work. People always rolled for direct conflicts but not necessarily for driving to the mountain chateau, or even trying to get into the chateau. Even during a fight, some game masters might make players roll to leap the railing while others might not. This handled most things reasonably well, but there was always a question of where to draw that line. Once you decided to roll for something, it went from 100% chance of success to a significantly lower chance. Also, the person’s skill didn’t come into play unless you rolled. Either no one had to roll or the very skilled and the unskilled had to roll.

A modern modification to this technique is the idea of “Take 10” or “Take the Average”. This allows the randomness to be taken out of certain tasks by adding a static number, the equivalent of our “Always 11″ example mechanic. However, it also incorporates the character’s skill. If the 10 or average value that is added to the skill is sufficient for the task then no roll is necessary, otherwise you roll. This allows highly skilled characters to avoid certain failures from poor luck but leaves less skill characters with an opportunity to succeed.

Of course, these techniques still give only two types of variance: none at all, or whatever the ordinary mechanic produces. Now, some games do use multiple different mechanics depending on what they are trying to resolve. Old school DnD used 3d6 for generating characteristics, 1d20 for armed combat, and percentile dice (1 – 100) for unarmed combat. However, the different mechanics seem the result of other design decisions rather than an attempt to model different amounts of randomness. Also, some games have mechanics such as using different dice to represent different skill levels, so variability can change with skill level. Again, this seems to be an unintended consequence of the mechanics rather than a deliberate change of variability. Trying to add multiple levels of randomness may simply not be worth it in a game design. Still it is something that can at least be considered.

Other ways to change consistency

So far the examples given have been about changing the amount of variance by changing the die mechanic, but this is not the only way to alter the distribution of results. One can also adjust the values of the skill added to the die roll. The examples had no skill = 0 and high skill = 10. If this were changed to good skill = 50 and high skill = 100 then the choice of dice mechanic for generating numbers 1 to 20 would mean very little. The size of the skill would swamp out the value of the die roll. No matter which mechanic was employed or what the outcome of the die rolls were, a highly skilled character would always beat a moderately skilled one. Likewise, if skill values were very small, for example, a high skill = 3, then the die roll becomes incredibly important with high chances of upsets using all but the “Always 11” mechanic.

Requiring that the player make multiple rolls to succeed can also change the variance. If in our cycling example the fan has to beat Lance four times in a row to win, then the chance of success when rolling 1d20 drops from about 1 in 9 to less than 1 in 6000. After all, multiple rolls will tend to converge on the average. One of the interesting upshots of this and the way most games are put together is that non-combat actions are often resolved with a single roll, while combats are often resolved with a series of rolls. The end result is, barring instant death rolls and the like, that the outcome of the wild, woolly, and chaotic combat is more foreseeable than what should be more reliable and predictable tasks, like picking a lock or repairing a car. As a result there are many systems where an increase in combat skill makes success much more likely than the same increase in a non-combat skill, despite the fact that they often cost the same in terms of character advancement. Mechanics like “Take 10” can help to alleviate these problems somewhat, but designers really don’t seem to think these things through.

Beyond dice

This discussion has been presented in terms of dice rolling mechanics; however, the same ideas apply to any sort of randomizer. For example, a big problem with many card-based systems is their over-reliance on suits. A poor example was a game where cards of the proper suit, say spades for combat, counted at face value with Aces being 14 giving a number from 2 to 14. Cards of any other suit counted as 1. These systems usually give people a hand of cards, but if you are doing the same type of action several times in row then the appropriate suit gets used up quickly and it then basically comes down to drawing cards for the value. This gives a number from 1 to 14 with an average value of 2.75 and a 3 in 4 chance of getting the minimum value of 1. The result is that continuing tasks in such games become incredibly unreliable. Such a set up can be worked around, the GM just has to make sure that the same type of actions don’t occur several times in a row. But the mechanic really forces the GM to compensate for the mechanic.

Conclusion

Obviously, there are many other considerations in the choice of mechanic, such as ease of use, but giving some thought to how much variability a designer wants and how much is produced by the mechanics could make games flow more smoothly.