Group Skill Checks as Dice Pool

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I tried something at my weekend Beyond the Wall game that may need to have a few more iterations before I’m totally happy with it, but seemed to work well enough to mention here.

I’ve never been a fan of using margin of success in D20. For one thing, it makes skills work differently than the other reasons you roll a d20 in the system. When you attack or save, you care about whether you met the target number or not, and often what number the die displays (for auto-miss or crit), but you don’t typically get any benefit from rolling significantly better than the target number. So having to track how much your result exceeded the DC for increased success immediately makes the skill system feel bolted on, like it came from another game.

And, in general, those other games that use margin of success for skill results have some kind of weighting to the roll, such as a dice pool or adding together multiple dice. In those systems, there is usually one level of success that’s much more likely than the others based on how the dice are weighted (e.g., in Fate, you’re very likely to get a margin of success equal to how much your skill exceeds the target, and much less likely to get four higher or four lower than that). But when you use a d20, there’s a 20-point range of margins of success that are equally likely. Particularly for non-iterated checks (like most Knowledge checks), the results can wind up feeling very swingy (e.g., “Sorry, you missed out on getting really useful clues because you rolled low and only just made the DC; you would have gotten much more information if you’d rolled higher.”).

So I was very interested when I noticed (via Shieldhaven using it in his game) that 5e had added* the concept of the group skill check. In the base rules, it’s something you can do when the whole group is trying to accomplish the same thing that requires a skill (e.g., stealth, climbing, etc.). If at least half the party succeeds, everyone succeeds (the higher-skilled individuals are assumed to cover for the lower-skilled).

As written, this is a useful addition that solves a lot of standard issues (such as always having to leave the armor-wearers behind when trying to sneak around). But the variation I tried goes even further:

  • Virtually anything that the whole group could work together on can be a group skill check (e.g., perception, knowledge, persuasion, etc.).
  • Instead of rolling, a character can Help another character, and share the results of that success or failure (in BtW, helping is a specific action that can only be done if you have the skill or spend a Fortune Point, but I don’t think it would break anything if you allowed your D20 variant of choice’s version of helping). You can’t combine helping in this way (i.e., you can’t pile help on the person with the highest skill check to push her to no chance of failure; at least half the party needs to actually roll).
  • Instead of requiring a simple pass/fail based on party size, before the roll the GM has in mind the general spectrum of what it means if no one is successful up to everyone being successful. Very difficult results may require the whole party, easy ones may only require one success, and more successes might grant a better result over the minimum pass.

This essentially winds up splitting the difference between a dice pool roll and a 4e skill challenge. And it allows the GM to give out better results for more successful rolls without any actual roll caring about anything other than pass/fail (and maybe crits, if you use skill crits). Importantly, it doesn’t incentivize low-skill players to avoid participating the way 4e skill challenges did (because each player only gets one roll, so you can’t sit out to let someone else go multiple times, and because helping is as good as succeeding yourself). My players seemed to dig it, so I’ll probably keep experimenting with it. I welcome thoughts on possible improvements in the comments.

* This is the first place I saw it; apologies if it originated somewhere else.

D20: Advantage as Caution

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The mechanic of rolling 2d20 instead of one is very helpful in both the newest edition of D&D (where it’s used for Advantage and Disadvantage), and for other games that use an uncurved die for a single roll. By rolling 2d20 (or even more), you’re essentially adding a curve to a roll whose results would otherwise be linear. Particularly if you read the dice independently, you’ve made the results much more similar to a dice pool or iterated series of rolls. This serves to reduce swinginess, by further reducing the chance of fluke successes or failures (I suspect most players are more likely to try rolls on their high skills when given the option than their low ones, so are going to have a roll swing into a failure on a high skill more often than it swings into a success on a low skill).

Ultimately, there are a decent number of traits on a character sheet that get rolled far less often than others (e.g., you make attack rolls and perception checks all the time, but other skills maybe only a couple of times a session unless you’ve really built the character to make use of it as part of a combat mechanic). For frequently-rolled traits, averages are likely to kick in, but for something you roll once a session, you could wind up having a disappointing tally of failures over time on something that ought to regularly succeed. Particularly when something important hinges on your once-per-session roll of a high skill, it might be preferable to have some way to accentuate the curve.

This house rule adds the following options to a D20 game (particularly low-powered, high-whiff stuff like Beyond the Wall):

A player may roll a single d20 normally if not acting particularly cautiously.

A player may instead choose to act cautiously, rolling 2d20. The player can only do this in non-surprise situations (e.g., not on saves unless the source is obvious and the target is not flat-footed, or on rolls to notice something if the character isn’t actively searching).

When acting cautiously:

  • If both dice are successes, it’s a full success.
  • If both dice are failures, it’s a full failure.
  • If one die succeeds and the other fails, it’s a partial success/success with consequences (glancing blow for half damage in combat, resist the worst but not everything on a save, etc.).
  • Both dice must be a critical result for the action to count as a crit (success or failure).

Essentially, acting cautiously means that you’re lowering your chance of a crit (from 1 in 20 to 1 in 400), reducing the chance that you’ll fail outright, but adding in a decent chance of partial success. For rolls you’d normally fail 75% of the time, you drop total failure down to a 56% chance (but most of your successes are only partial). For rolls where you’d only have a 50/50 shot, you change full failure and full success to both be 25%, with partial filling up the middle 50% of results. For rolls with only a 25% chance of failure (which is still pretty risky on a roll that a lot hangs on), you lower full failure to only around 6% (but move 40% of your successes to partial ones).

Two Fisted Fate

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Today’s idea is a quick, somewhat silly one that I had when traveling without my 4dF and thinking about running a game. Fate is rules- and trait-light enough that it would be a good game to run places where dice and even character sheets are hard to manage: camping, road trip, etc. With a background in LARPing, my group’s natural fallback for resolution in a diceless situation is Paper-Rock-Scissors. I realized that if you’re playing it fairly randomly, it actually generates three results, just like dF. The problem is that you’d have to iterate it four times to generate 4dF. If you do, the distribution of results should be pretty identical to 4dF (barring unrandom choices of signs), but that might bog the game down more than getting all the results at once.

Thus, use two fists at once (do not do this if you are the driver in the road trip!). Compare each hand independently to each of your opponent’s hands, and add up to the total results like so:

PP PR PS RP RR RS SP SR SS
PP 0 2 -2 2 4 0 -2 0 -4
PR -2 0 -1 0 2 1 -1 1 0
PS 2 1 0 1 0 -1 0 -1 -2
RP -2 0 -1 0 2 1 -1 1 0
RR -4 -2 0 -2 0 2 0 2 4
RS 0 -1 1 -1 -2 0 1 0 2
SP 2 1 0 1 0 -1 0 -1 -2
SR 0 -1 1 -1 -2 0 1 0 2
SS 4 0 2 0 -4 -2 2 -2 0

So, for example, if I throw Rock and Paper, and the opponent throws Rock and Scissors, my Rock ties his and beats his Scissors, for a net +1, and my Paper beats his Rock but loses to his Scissors for a net 0, for a total +1 result.

The numbers are much more contingent than normal dice rolls, so the probabilities are a little skewed and notably lack +3/-3 results:

Result Standard RPS
-4 1.2% 3.7%
-3 4.9% 0.0%
-2 12.3% 14.8%
-1 19.8% 14.8%
0 23.5% 33.3%
1 19.8% 14.8%
2 12.3% 14.8%
3 4.9% 0.0%
4 1.2% 3.7%

But they’re close enough, I think, for the situations where you’re likely to use it. Also, the ranges of -4 to -2, -1 to 1, and 2-4 all add up to the same totals (so you’ll get a result of -1, 0, or 1 just as often, it will just be distributed differently).

Group Random D&D Chargen

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A bit of a simple idea this week as I recover from GenCon and gear up for PAX.

As a GM, I tend to favor point buy over randomly rolled D&D/Pathfinder character creation primarily because it leads to imbalance among the PCs. Inevitably, someone’s going to roll a character with stats much lower than someone else’s (and even lower than he could have gotten in point buy) and resent either his character or the player with the best rolls. Since I don’t run games with much lethality, getting stuck with a subpar character has enduring ramifications over the course of a whole campaign.

This system is designed to allow players the thrill of random rolls, but to distribute those rolls among the party so everyone comes out at a similar point buy total. However, rather than rolling them and distributing them totally equitably, there’s an element of strategy involved that may result in players putting higher or lower scores in different abilities than they would have if they got all six rolls up front…

The process is:

  1. Have each of your players roll two sets of 4d6 (drop lowest) and put the results in the middle of the table (either just leave the dice there, or write down the result if you don’t have enough sets of d6s). If you have four players, there should be eight ability scores on the table.
  2. Randomly decide an order among the players for the first turn.
  3. The players each pick one number from the table in their sorted order (which will leave a number of sets on the table equal to the number of players once they’ve all taken one).
  4. Each player goes ahead and assigns the chosen number to an ability score (this is where the strategy comes in; if you grabbed a 16, do you go ahead and assign it to your prime requisite, or do you put it somewhere else and hope that a 17 or 18 comes around for you on a later turn?).
  5. Once everyone has picked and assigned a score, have each player roll another 4d6 (drop lowest) and place it in the middle of the table (returning the number of sets back to where it started).
  6. Have each player total up what their current set of ability scores would be worth in point buy (e.g., someone that currently has an 18 and a 13 has 20 points).
  7. Change the player sort order from lowest point buy total to highest (this is another point of strategy; a player might deliberately take a low number rather than the highest one available hoping to get first pick on a later round with better rolls).
    1. Break ties based on who has the smallest big number (e.g., an 18 + 13 goes after a 16 + 16, even though they both have 20 points).
    2. If that’s still tied, break based on who has the smallest low number (e.g., 13 + 15 + 16 goes after 10 + 16 + 16).
    3. If they’re still tied, just go in the original sort order for the first round.
  8. Repeat steps 3-7 until everyone has five scores and there is only one set per player left on the table.
  9. For the last round, simply repeat steps 3 and 4 (i.e., don’t roll another set; on the last round, the players have to fill in their last score from the leavings of the whole process).
  10. Continue with the normal process of making a character.

For example:

Turn Pool Amy Brad Cora Dan
1 8, 9, 12, 12,
12, 13, 13, 16
STR –
DEX –
CON –
INT –
WIS –
CHA 16
(Point Buy 10)
STR –
DEX –
CON 13
INT –
WIS –
CHA –
(Point Buy 3)
STR –
DEX –
CON –
INT –
WIS 9
CHA –
(Point Buy -1)
STR –
DEX –
CON –
INT 13
WIS –
CHA –
(Point Buy 3)
2 8, 9, 10, 12,
12, 12, 15, 17
STR –
DEX 15
CON –
INT –
WIS –
CHA 16
(Point Buy 17)
STR –
DEX 10
CON 13
INT –
WIS –
CHA –
(Point Buy 3)
STR –
DEX 17
CON –
INT –
WIS 9
CHA –
(Point Buy 12)
STR –
DEX –
CON –
INT 13
WIS –
CHA 9
(Point Buy 2)
3 6, 8, 11, 12,
12, 12, 14, 14
STR –
DEX 15
CON 12
INT –
WIS –
CHA 16
(Point Buy 19)
STR –
DEX 10
CON 13
INT –
WIS –
CHA 14
(Point Buy 8)
STR –
DEX 17
CON –
INT –
WIS 9
CHA 12
(Point Buy 14)
STR 14
DEX –
CON –
INT 13
WIS –
CHA 9
(Point Buy 7)
4 6, 7, 8, 10,
11, 12, 12, 15
STR –
DEX 15
CON 12
INT 11
WIS –
CHA 16
(Point Buy 20)
STR 12
DEX 10
CON 13
INT –
WIS –
CHA 14
(Point Buy 10)
STR –
DEX 17
CON –
INT 12
WIS 9
CHA 12
(Point Buy 16)
STR 14
DEX –
CON 15
INT 13
WIS –
CHA 9
(Point Buy 14)
5 6, 7, 8, 9,
10, 12, 14, 15
STR –
DEX 15
CON 12
INT 11
WIS 10
CHA 16
(Point Buy 20)
STR 12
DEX 10
CON 13
INT –
WIS 15
CHA 14
(Point Buy 17)
STR 12
DEX 17
CON –
INT 12
WIS 9
CHA 12
(Point Buy 18)
STR 14
DEX 14
CON 15
INT 13
WIS –
CHA 9
(Point Buy 19)
6 6, 7, 8, 9 STR 6
DEX 15
CON 12
INT 11
WIS 10
CHA 16
(Point Buy 14)
STR 12
DEX 10
CON 13
INT 9
WIS 15
CHA 14
(Point Buy 16)
STR 12
DEX 17
CON 8
INT 12
WIS 9
CHA 12
(Point Buy 16)
STR 14
DEX 14
CON 15
INT 13
WIS 7
CHA 9
(Point Buy 15)

Amy wants to play a Sorcerer, Brad wants a Cleric, Cora wants a Rogue, and Dan wants a Fighter. For the example, their initial sorting winds up in alphabetical order.

In turn:

  1. Amy goes ahead and assumes 16 is good enough to put in her Charisma. Brad grabs a 13 and puts it in Constitution, hoping for higher scores later. Cora doesn’t like what’s left, so goes ahead and puts a 9 into Wisdom, assuming that will give her first choice once some better options show up. Dan goes ahead and grabs the last 13 and puts it into Intelligence, knowing that at least he’s covered for the Combat Expertise feats.
  2. Cora’s choice last round immediately pays off, and she puts the new 17 into Dexterity. Dan and Brad are tied, so Brad goes first according to the initial order and takes Cora’s strategy; he grabs the 10 and dumps it into Dex, hoping for better rolls later where he gets first pick. Not to be outdone, Dan grabs the 9; now he gets to go first next turn. Amy shrugs at the guys leaving her a nice 15 and puts it into Dex.
  3. Halfway through, suddenly it’s starting to look like it might be dangerous to count on some more 17s and 18s showing up, and nobody wants to be the one stuck with that 6. Dan goes ahead and grudgingly puts a 14 into Strength, starting to plan for being a generalist Fighter rather than a big pile of Strength. Brad goes ahead and grabs the 14 for his Cha, but is still holding out hope for something better to put into Wisdom. Cora grabs the 12 to put into Cha. Amy puts another 12 into Con.
  4. This is starting to be a pretty bad set of rolls; the whole group starts to wonder whether they should have insisted on point buy as a 7 comes up to add to the 6 and the 8. Dan goes ahead and grabs the 15 for his Con. Brad grabs the 12 for his Str. Cora takes the other 12 for her Int. Finally, Amy’s left with an 11 and also throws it into Int.
  5. The last round of rolls comes up and the best results are a 14 and 15; at least the lowest was only a 9 this time. Brad very grudgingly puts the 15 into his Wisdom. Dan puts the 14 into Dex and starts thinking seriously about a two weapon fighting Rogue multiclass or Whirlwind build. Cora drops the 12 into Strength. Amy agonizes about Strength vs. Wisdom, and finally decides to be weak rather than blind, putting the 10 into Wis.
  6. With only the sub-10 stats left, the table completely agrees that next time they need to totally roll better, but at least they’re in this mess together. Brad gets the 9 for his Int. Cora gets the 8 for her Con. Dan gets the 7 for his Wis. And Amy is, indeed, stuck with the 6 for her Str.

Overall, the whole group wound up within 2 point buy points of one another. Given that the same set of rolls reserved to individual players could have had one player with a character worth well over 20 while another was worth zero or less, at least everyone’s in the sub-standard boat together. And the uncertain placement of scores resulted in some interesting choices that the players might not have made if they’d known in advance exactly what their numbers were.

Fatenoir: Dresden Files with Technoir Dice

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If you haven’t read Technoir, some of this might make more sense after this week’s review.

While I’m a big fan of Fate in general, sometimes I want a dice system that doesn’t owe so much to FUDGE. Particularly for the Dresden Files, I’d potentially like something without as much swing on the low granularity traits (i.e., having a 1 higher skill is meant to indicate a huge difference in competence). Further, perhaps something that makes spending Fate good but not as overwhelming as it is normally, something that’s not so much work on the GM to remember to compel, and something that makes more use out of situational tags. Fortunately, the Technoir dice system suggests the following mods that should affect all of these nitpicks. This is completely untested, and might result in some wonkiness at low and high skills.

For this system, you will need a lot of d6s. These are preferably in three distinguishable colors (and will be passing around the table a lot).

At the beginning of each story/scenario, each player has Fate dice equal to his or her character’s adjusted Refresh (even if the total was higher at the end of the last scenario). The GM does not get any Fate dice to start with: the total Refresh of all the PCs is the total available Fate dice. All Fate dice begin “charged.”

Players can “discharge” Fate dice to use them in rolls.

  • Do this at any point in the roll: they can be rolled one at a time after seeing the total.
  • They can be used for active or reactive/defensive rolls.
  • See the system below for how they are interpreted.
  • Discharged dice return in two ways:
    • All available dice recharge at the beginning of a session.
    • One Fate die recharges for every Consequence die a player voluntarily adds to a roll as a self-compel (e.g., “Because I’m a Drunk, I think this roll would be harder for me, I’m adding 1 Consequence die”). As usual with self-compels, the GM can deny the addition/refresh (typically because the roll isn’t particularly important).

Players can “spend” Fate dice (giving them to the GM) to make Consequences, Maneuvers, or other generated tags sticky.

  • Fate dice can only be spent in this way if the player used them in the roll that generated the Consequence (e.g., you can’t succeed with no Fate dice used and then spend a Fate die when that resulted in a Consequence).
  • The stickiness increases by the following factors (these replace the normal Consequence recovery rules):
    • A normal Maneuvered aspect  lasts for the number of shifts on the roll to apply it, or until the target makes a roll to remove it. A sticky Maneuver lasts until the end of the scene.
    • A normal Minor Consequence lasts until the end of the scene. A sticky Minor Consequence lasts until the end of the session.
    • A normal Moderate Consequence lasts until the end of the session. A sticky Moderate Consequence lasts until the end of the current scenario.
    • A normal Severe Consequence lasts until the end of the current scenario. A sticky Severe Consequence is permanent (like a normal Extreme Consequence).
    • A normal Extreme Consequence is permanent as per the basic rules. A sticky Extreme Consequence allows the target to be immediately taken out in the manner defined by the attacker (and remains permanent if this is non-fatal).
  • Any result of “Taken Out” for a named character (PC or NPC) must generally be backed by a spent Fate die to make it stick.
    • If an NPC is taken out but the active PC does not elect to spend Fate, the result is narrated in a way that removes the target from the scene but allows a return shortly thereafter (with any Consequences persisting but Stress emptied).
    • At the GM’s option (but it should be used sparingly), a NPC that has not taken all possible Consequences may choose to turn a player’s decision to make Taken Out sticky into sticky Consequences that remove the incoming Stress and a Concession (i.e., the NPC leaves the scene but with sticky Consequences instead of a fatal wound).
  • Players gain back Fate dice at the beginning of a scenario (up to Refresh), when the GM spends dice to make a Consequence sticky on a player (the die goes to the player with the Consequence), or when the GM suggests a non-roll-related Compel (giving the player the die if the Compel is accepted).

When performing an action:

  1. The active character’s player rolls 1 skill die.
  2. The player must roll 1 to 4 Consequence dice (take the worst Consequence currently suffered: 1 die for Minor, 2 for Moderate, 3 for Severe, and 4 for Extreme) to the roll.
  3. The player may discharge and roll up to 1 Fate die for every applicable Aspect (advantages possessed by the character, disadvantages and maneuvers on the target, and applicable aspects on the scene).
  4. The result (explained below) is compared to the target’s defensive skill (or the difficulty, if there is no target).
  5. The target does not roll a skill die, but must roll all Consequence dice.
  6. The target may discharge and roll Fate dice for defense-applicable aspects (personal, attacker, or scene).
  7. The final result of the active character’s roll is compared to the target’s final roll (or static difficulty) to generate Shifts. As usual with Fate, a tie is a 0-Shift success for the active character.

To interpret a roll:

  1. Find the base skill total.
  2. Read the skill die first. Treat it as a modifying skill (i.e., if it is higher than the base skill, add 1, and if it is lower, subtract 1). This is the new skill total.
  3. Arrange the Consequence dice from highest to lowest.
  4. For each Consequence die that is higher than the skill total, reduce the total by 1. Recalculate the skill total before each subsequent die (i.e., Consequence dice can penalize a roll even if they weren’t higher than the original total).
  5. Arrange the Fate dice from lowest to highest (and rearrange them as additional Fate dice are added).
  6. For each Fate die that is higher than the Consequence-adjusted skill total, increase the total by +1.

Thus, without additional flat bonuses and penalties, the highest possible roll is 6, and the lowest possible roll is -4. If you’d like higher possible totals, allow Fate dice that roll 6 to count as infinitely high (i.e., every 6 adds +1, even if the total is already 6).

An example roll: The base skill is Fair (+2), the skill die is 5 (new total +3), the Consequence dice are 4, 3 (reducing by -2 to +1), and the Fate dice are 2, 4, 6 (increasing to +4). If the 4 on the consequence dice had been lower, neither die would have been higher than the total, and the final result would have been a +5.

GMs use this system much like the players:

  • The GM does not have any Fate dice at the start of an adventure. He or she only gets them when players make enemy Consequences sticky.
  • Fate dice the GM acquires begin discharged.
  • The GM’s Fate dice recharge at the beginning of each scene.
  • The GM spends Fate dice used in an antagonist’s roll to make the player’s Consequences sticky.
  • The GM may spend Fate out of conflict to Compel a PC’s Aspect.

2d20 for Fading Suns

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Based on a suggestion from another Fading Suns GM, my preferred method of using the Victory Point system was with two d20s instead of one. The gist of the system (apart from accenting and wyrd mechanics explained at the link) was:

  • Roll 2d20, keep the highest die that’s still a success.
  • The roll is only a critical success if one die roll the target number and the other is also successful.
  • The roll is only a critical fumble if one die rolls a 20 and the other is also a failure.

Doing this changes the success rate pretty drastically:

Target 1d20 Success 2d20 Success
1 5.0% 9.8%
2 10.0% 19.0%
3 15.0% 27.8%
4 20.0% 36.0%
5 25.0% 43.8%
6 30.0% 51.0%
7 35.0% 57.8%
8 40.0% 64.0%
9 45.0% 69.8%
10 50.0% 75.0%
11 55.0% 79.8%
12 60.0% 84.0%
13 65.0% 87.8%
14 70.0% 91.0%
15 75.0% 93.8%
16 80.0% 96.0%
17 85.0% 97.8%
18 90.0% 99.0%

Just looking at the chance of success, it’s interesting how much it suddenly curves to look much more like a White Wolf-style dice pool mechanic than a percentile mechanic. Importantly, in my mind, this means that it’s not as drastically necessary for players to try to absolutely max out their skills to regularly succeed: in practice, a trait total of 10 is supposed to be pretty good for a starting character, and now that character has better than a 50/50 shot on rolls. It’s immersion-breaking in the extreme for the system to pretend that you have a good trait and then fail on it half the times it’s important, at least in my opinion.

Additionally, this method puts a curve on fumbles and criticals. In 1d20, you have a 5% chance of a crit and a 5% chance of a fumble, no matter what. In 2d20, the chance of crit goes from 0.3% at TN 1 to 9.3% at TN 19, while the chance of fumble does exactly the opposite. Effectively, the higher your TN, the bigger your chance to crit and the smaller your chance to fumble, which seems more logical.

The other interesting thing is what it does to expected success totals:

Target 1d20 Avg. VP 2d20 Avg. VP
1 0.0 0.0
2 0.0 0.0
3 0.3 0.4
4 0.5 0.5
5 0.6 0.6
6 0.8 0.9
7 1.0 1.1
8 1.1 1.2
9 1.3 1.5
10 1.5 1.7
11 1.6 1.9
12 1.8 2.1
13 2.0 2.4
14 2.1 2.6
15 2.3 2.8
16 2.5 3.1
17 2.6 3.3
18 2.8 3.7

The chart above is the average number of victory points for a successful roll (not counting criticals). The numbers don’t look terribly different, save that the 2d20 is slightly higher. In practice, this is because, with 1d20, success VPs are completely flat: if you succeed on 1-10, you a successful roll has a 10% chance for each result. In other words, any time you succeed, you will roll less than half your best result half the time. Conversely, with 2d20, you have at least a 75% chance of rolling over the halfway mark (because if both dice are under the target number, you choose the larger result).

Old school game design looks at the 1d20 and declares it adequate: the higher your score, the higher the chance of success and the result of success. But looking at the raw numbers doesn’t cover the feel at the table, where excessive swinginess results in player disappointment. Over multiple rolls, a flat die result evens out, giving an advantage to the better character, but how often do characters make multiple rolls on the same skill outside of combat? In practice, a player may get once chance to shine with a given non-combat skill per session, and, with a flat die, the result of the roll can feel almost completely disconnected from the score. Using 2d20 to curve the result creates a situation where, even on a single roll, a higher score feels meaningful.

D&D/Pathfinder: How much is +1 worth?

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A friend of mine is looking to play a dual wield fighter (I did try to talk him out of it), and was curious about the tradeoff between attack and damage: i.e., which feats should he take, when should he power attack, etc. So I started thinking about the math.

Basic Premise: In d20, unless you can only miss on a 1, each +1 is an additional 5% of your base effectiveness, per roll.

This is pretty easy to calculate:

  • Each roll has a chance of success based on the number you need to roll on the die to succeed. If you succeed on an 11 or better, that’s half the possible rolls on the die, so you have a 50% chance of success. If you only succeed on a 16 or better, you have a 25% chance of success. And so on.
  • Because there are 20 possible results, each represents 5% (100%/20).
  • Each +1 to your roll makes you 5% more likely to succeed (e.g., you go from needing a 11+ to a 10+ to hit, going from 50% chance to 55% chance to succeed).
  • Thus, over time, you can add 5% of base effectiveness (e.g., 50% hits at your normal value vs. 55% hits at your normal value). If you do an average of 10 damage, a +1 is going to give you half a point of damage per attack.

Attack bonus is, thus, more effective over time the more damage you do, base.

 

Basic Premise: In d20, each +1 damage is an additional X damage, per roll, where X is equal to 1 times your chance of success.

This is a similar calculation:

  • As above, over time you can base your expected damage on the chance to hit: if you hit 50% of the time, you will do 50% of your base damage over time.
  • At 50%, each point of damage is, therefore, actually worth half a point of damage per attack.
  • Meanwhile, if you have a higher or lower chance to hit, the worth of the point of damage scales accordingly.

Damage bonus is, therefore, more effective over time the greater your chance to hit.

 

Obviously, these two premises stack very nicely: if you have a higher attack, you’ll deliver your base damage more often, and if you have a higher damage, it will benefit more from having a high attack.

But what if you have to choose? Greater Weapon Focus or Weapon Specialization? Activate Power Attack or stick with regular hit bonus?

In these situations, attack bonus becomes more valuable the higher your damage already is, and damage bonus becomes more valuable the higher your chance to hit already is. Obvious based on the premises above, right? But where is the breakpoint?

Base Damage 2 4 6 8 10 12 14 16 18 20
Value of +1 Attack 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Necessary Roll to Hit 2 4 6 8 10 12 14 16 18 20
Value of +1 Damage 0.95 0.85 0.75 0.65 0.55 0.45 0.35 0.25 0.15 0.05

Effectively, at around 10-11 points of damage and having to roll 10-11 to hit, a point of damage and a point of attack are roughly equivalent. Lower base damage is equivalent to a higher chance to hit when trading off.

What about 2 damage? Power Attack in Pathfinder gives you +2 damage for each -1 attack (with one-handed weapons).

Roll Needed to Hit
Damage 2 4 6 8 10 12 14 16 18 20
2 19 17 15 13 11 9 7 5 3 1
4 9.5 8.5 7.5 6.5 5.5 4.5 3.5 2.5 1.5 0.5
6 6.3 5.7 5 4.3 3.7 3 2.3 1.7 1 0.3
8 4.8 4.3 3.8 3.3 2.8 2.3 1.8 1.3 0.8 0.3
10 3.8 3.4 3 2.6 2.2 1.8 1.4 1 0.6 0.2
12 3.2 2.8 2.5 2.2 1.8 1.5 1.2 0.8 0.5 0.2
14 2.7 2.4 2.1 1.9 1.6 1.3 1 0.7 0.4 0.1
16 2.4 2.1 1.9 1.6 1.4 1.1 0.9 0.6 0.4 0.1
18 2.1 1.9 1.7 1.4 1.2 1 0.8 0.6 0.3 0.1
20 1.9 1.7 1.5 1.3 1.1 0.9 0.7 0.5 0.3 0.1

The chart above shows the ratio of the value of 2 Points of Damage to 1 Point of Attack. So if you’re doing 2 points of damage and hit on a 2+, 2 points of damage is 19 times as good as +1 attack. Meanwhile, if you already do 20 damage and need a 20 to hit, 2 points of damage is less than 10% as good as +1 attack. The breakpoints are in red: past that number, you shouldn’t Power Attack (for example). If your chance to hit is decent, though, you need huge amounts of base damage to make Power Attacking a bad idea.

The more you know!

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