As the title says, is there a rules-lite game out there that has a formula for attackers?
What I'm looking for, in short is Barbarians of Lemuria with something to tell me how many mooks, or sergeants, or saber tooth cats, or villians three beginning PCs (for example) can handle.
Slightly longer: I'm mostly looking for a rules-lite game. And I don't generally like class systems. I love how BoL gives character 4 starting careers and does combat stats separately. I want to be able to run my friends through some existing adventures using such a system, but want something to tell me how much the characters can handle. I'm not looking for advice on the BoL issue exactly--I'm looking for a game that includes rues for building appropriate opponents.
As it is, I'm creating my own system, and getting my wife (who is working on her PhD in cancer genetics) to do a statistical analysis of all combinations of 1-on-1 and 1-on-2 and 1-on-3 attack combinations, to see if she can give me a ranking formula. I'm a software developer and I'm generating the data--the 1-on-1 file is 152,473,105 lines long and takes about 2 days to generate (each case is tested 1000 times).
Hard question, often rules-lite games don't seem to go in much for CR-estimation. The only thing I can really think of offhand is 3:16. It may be be exactly what you're looking for but it has some system for the GM to spread out alien "threat tokens" per mission.
CR estimation seems popular in 3E-derivative games (3E itself, 4E, FantasyCraft) but they're generally not that light. JAGS' designer Marco was doing something similar to your software approach with their game on their blog too, but its not light either (more GURPSesque).
I also wouldn't be surprised if there's some boardgame or other that would have something like what you're after. Maybe.
Thanks for the reply.
3:16 sounded a bit interesting at first. I wish the previews would give something useful instead of 5 pages of useless fluff. But I read a few reviews and it sounds a bit on the narrative side (players get narrative control by calling for Flashbacks and narrative [that's a new RPG verb from me] their strengths/weaknesses). Combat is "balanced" by making the enemy statless--you attack by rolling against your skill and your weapon damage decides how many enemy there were based on how many your weapon kills.
I've looked at JAGS before and just looked at it again. The crunch--it hurts! :eek: *joke* I don't mind crunch during character creation, but if you're going to have 15+ pages of grappling moves and still not let me simulate Aikido... :p If PowerFrame, for example, had lighter in-game rules, I wouldn't mind that level of building complexity. (Especially since I'd just write a program to help if needed.)
My second test file of 1-on-2 and 1-on-3 combat finished last night. Only 14,224,897 lines, since the opponents only have their modifiers go up to 3--but it looks like I'll have to redo it with the numbers going higher, since a maxed out attack easily wins against three opponents at half strength 100% of the time.
On 3:16 - Yes it does have flashbacks and such, which is not my bag either (I think I picked up the .pdf in one of the big disaster relief downloads).
rpg.net had a review of it with some more explanation of how the system worked
http://www.rpg.net/reviews/archive/14/14870.phtml (http://www.rpg.net/reviews/archive/14/14870.phtml)
Oh also - there's, oddly, still a free older version sitting around on the author's webpage.
http://gregorhutton.com/roleplaying/ (http://gregorhutton.com/roleplaying/)
On JAGS - heh, yep I feel your pain. Just mentioning for interests' sake.
Good luck.
Quote from: Bloody Stupid Johnson;860246...CR estimation seems popular in 3E-derivative games (3E itself, 4E, FantasyCraft)...
Microlite20 (PDF here (http://donjon.bin.sh/m20/Microlite20.pdf)) is about as lite and stripped down as you can get, but it still allows you to draw upon the d20 SRD (http://www.d20srd.org/) when you need to, which has the encounter calculator (http://www.d20srd.org/extras/d20encountercalculator/) all ready to go.
Tunnels & Trolls defines monsters by a single characteristic "Monster Rating" or MR. MR determines how many dice and adds the monsters get in combat. This can be easily compared to the number of dice plus adds the PCs do. In combat the losing side suffers the difference in hits between the total dice score plus adds of the high scoring side and the low scoring side.
Not quite a Challenge Rating formula, and spells and special abilities will affect it, but it gives a good baseline.
BOL is straight 2d6 to hit, then some toss or other for damage, right?
Just figure the average damage per round, then you can work out how far down the winner is on average after felling the others.
If damage per hit is not much different, then eyeballing chances to hit should be close enough. Seriously, you should have a damn good ratio if you're thinking about taking on more than one guy in the first place.
Hit on 4+ vs. hit on 10+ is 33:6, or 5.5:1.
Is JAGS2 lighter enough in the relevant 'crunch' areas?
Averages don't necessarily tell enough of the story--some games are going to have a fairly high variance in damage per round, which would militate in favor of building a good margin of safety into your "CR".
That said, if a game's combat system doesn't offer much in terms of options, I have to wonder why have CR. If there are interesting options in combat, then you might want CR in order to keep combats balanced enough that the players can exercise those options in a meaningful way.
For a simple game, frankly, the bulk of interest with the combat is exploring and learning what you can handle and what you can't, and deciding what's worth risking. A CR system deprives players of that experience by guaranteeing that they can run into every combat without thinking.
Maybe replacing BoL's 2d6 with a single d10 or d12 roll would make the odds easier to figure out?
No, the difference is trivial mathematically and computationally.
The problem (and the reason you need a monte carlo simulation which I assume is what the OP is doing) is that there are so many intermediate results possible in the iterative process (i.e., round-by-round).
If instead you had a game where each attack would result only in no damage or defender incapacitated, it'd be a lot easier to write a complete flowchart of possible events and then calculate the probability of each final outcome.
Quote from: Bloody Stupid Johnson;860467Maybe replacing BoL's 2d6 with a single d10 or d12 roll would make the odds easier to figure out?
Sure, but it's only slightly obfuscated with straight 2d. BoL figures typically have separate attack and defense factors.
I typed in a table, but I guess it needed HTML to format it. Not too hard to figure if you know the 2d pyramid:
02 03 04 05 06 07 08 09 10 11 12
01 02 03 04 05 06 05 04 03 02 01
36 35 33 30 26 21 15 10 06 03 01
Quote from: Arminius;860471No, the difference is trivial mathematically and computationally.
The problem (and the reason you need a monte carlo simulation which I assume is what the OP is doing) is that there are so many intermediate results possible in the iterative process (i.e., round-by-round).
If instead you had a game where each attack would result only in no damage or defender incapacitated, it'd be a lot easier to write a complete flowchart of possible events and then calculate the probability of each final outcome.
Arminius, is very correct about average damage being meaningless. I did some testing on that early. If character A has 6 HP and does an average of 3 damage per round, and character B has 36 HP and does an average of 1 damage per round, what happens? Switch the damage, but add in armor with one having 1 and 3? Then reverse the armor. Also, average damage is going to depend on the opponent's defense (at least the way I do combat, and the way anyone else who uses the opponents skill or armor, etc as a target number or modifier). If you hit less often, you do less damage. But you don't want to have to calculate everything the way I did when designing monsters/encounters. Although, that's my fall-back position if necessary. :o
I actually did an exhaustive simulation--all possible combinations. According to my wife, this makes the ranking calculations easier. Hopefully, she'll have time to explain the analysis steps tonight or tomorrow. She is working on her PhD, so she's pretty busy.
I used something similar to but different from BoL combat. It "feels" better to me and has some features I like.
There are five traits--I'm uncertain whether these are stand alone or based on other traits as yet, but they are:
To Hit Modifier (0-6) modifies chance to hit
Damage Dice (1-6) number of dice of damage possible
Defense Modifier (0-6) modifies chance to be hit
Armor Dice (0-6) modifies the damage they receive
Hit Points (1-6x6) this is a number from 1-6 multiplied by 6 and is the amount of damage they can take
In tests, initiative made less than 10% (usually much less) difference in results for several different versions of combat, so this version got rid of it.
To determine if a hit is made you roll 2d6 and add the attacker's To Hit Modifier and subtract the defender's Defense Modifier. If the result is greater than or equal to 7, then you hit. (This gives a base chance of ~58%.)
To Hit: 2d6 + Attacker Hit - Defender Defense >= 7
If a hit is made, damage is based on the number found by rolling the attacker's damage dice and subtracting the number found by rolling the defender's armor dice. Any value above 0 is subtracted from the defenders hit points.
Damage: (Attacker Damage Dice)d6 - (Defender Armor Dice)d6
The damage method means, a tank with 6d6 armor is not going to be hurt by a 1d6 sword or pistol or even a 5d6 elephant gun. (Those numbers aren't meaningful, just illustrative of the conditions.) This is one of the things I like about this method. It gives some flavor of armor being proof against some weapons, but doesn't require a lot of paperwork keeping track of what is proof against what.
I ran with A attacking first. After A attacks, if B still has any hit points, they get to attack. That makes a turn.
Each set of characteristics was tested against each other 1000 times. (In testing this gave stable results.) Tests proceeded until either A or B's hit points were reduced to 0 or less or 21 rounds had been tried. At that point, whoever had taken less damage was declared "the winner" and if damage taken was equal, then a tie was declared. The average number of turns is recorded.
When designing battles, I'd like turns to stay under 5. So I'm hoping to be able to reflect that in the rating if possible.
I have a second file, testing one against 2 or 3 opponents, with opponent characteristics going up to 3. (I'm going to need to redo that one and cover all the way up to 5 or 6, since a maxed out character A always beats 3 character B with all 3 characteristics.)
I went with d6 "just because" and because it limits the stat variances to a lower calculable number of permutations. Part of what I plan is, similar to Barebones Fantasy, "extra" skill levels allow you extra attacks at -2 (or something) per extra attack. So your first attack is as described earlier, your second attack at -2, third at -4 and so forth. I haven't checked the statistics on that yet. My earlier tests were one attack attempt each.
I also haven't decided how to do active defenses--probably some version of rolling to create a higher defense modifier.
You'll recognize stuff in here from a variety of games, particularly BoL, BareBones Fantasy, and EABA. I'm thinking of calculating the To Hit and Damage Dice similar to how Ryuutama does, off of a variety of characteristics. So, you can have a dexterous and intelligent character who does better with bows and firearms than a strong character, who is better with swords.
To add one, since I'm doing a simulation, the number and size of dice are also pretty irrelevant, except to max stat/skill levels and target numbers. Once I've figured out how or if we can get a useful ranking, I can share Java or C++ code for doing the calculations, or just run them for people. The stats part might be in R.
I'm worrying there is going to be a ranking calculation, but it is going to either be too complicated to be useful or end up dependent on the opponent.
Quote from: Phillip;860417Is JAGS2 lighter enough in the relevant 'crunch' areas?
Still too crunchy. In my case, "crunchy" often means "too many things to remember". Just figuring out the numbers to try for in JAGS2 requires a half page of explanation. I'm not going to remember that. That's my fault, and not the game's. :o
Quote from: Arminius;860452Averages don't necessarily tell enough of the story--some games are going to have a fairly high variance in damage per round, which would militate in favor of building a good margin of safety into your "CR".
That said, if a game's combat system doesn't offer much in terms of options, I have to wonder why have CR. If there are interesting options in combat, then you might want CR in order to keep combats balanced enough that the players can exercise those options in a meaningful way.
For a simple game, frankly, the bulk of interest with the combat is exploring and learning what you can handle and what you can't, and deciding what's worth risking. A CR system deprives players of that experience by guaranteeing that they can run into every combat without thinking.
I'm looking for numbers/ranking so I can know if I've created an easy or a tough encounter. By easy, I mean you can reliably expect the characters to win. By tough, I mean you can reliably expect the characters to win. Or something in between--with something in between or tough you can give the players enough hints via description of the opponent, or their sheer numbers, that they need to do something other than a head on attack.
I took BoL's intro adventure and ran the three beginning characters against the guards and a trio of three animals whose name escapes me. The animals are described in the book as apex predators (or words to that effect) and even without Hero Points, the characters tended to wipe the floor with the animals in simulation. But it is described as a really tough battle in the book.
Unless I'm running a "gritty" campaign, I don't really want to accidentally let loose a monster or villain that can one-hit kill my player's characters. (On purpose is another matter.)
What's your standard of 'reliably'?
If you're doing a D&D type thing where you've got, say, 5 figures getting into an average of 4 fights per session for 50 sessions, that's 1000 chances to get killed. If the odds of surviving a fight are 'only' 99:1, that's an average of 10 characters -- two parties' worth of adventurers -- killed.
A figure killed doesn't necessarily mean the party loses the fight, or vice versa. This is just a start on figuring out what you really do mean. It's easier to hit a target when we know what to aim for in the first place!
If you had a single combat factor and switched to a roll-off of 2d6+bonus for each side, lower takes a hit, then the difference in bonuses would yield a ratio that goes up pretty quickly. For the most part that's close to what you'd get with 3d6 'reflexive' (from 11+ each to 12+/10+, then 13+/9+, etc.).
Note that this way, it's just the difference that matters; +10 vs. +3 is the same as +8 vs +1 (about 84 to 1).
Tod13,
Well, your simulation approach is the right one, I guess, for what you're trying to do. I assume there isn't much in terms of positional maneuver, and also that you aren't too troubled by targeting issues.
In military simulation there's something called the Lanchester Equations or Lanchester's Laws, which you might want to look up.
Basically, the more freedom each "unit" has in terms of which enemy it can target, the greater the effect of outnumbering. If combat is restricted to a series of 1:1 battles, with each new "duel" only forming after both units become unengaged, then outnumbering doesn't matter so much. On the other hand if maneuver or ranged firepower can allow the creation of local situations where multiple combatants on one side are only facing a single opponent (even if you ignore the tactical effect of outflanking), then things aren't so simple, and outnumbering also matters more.
So just how simple is your overall combat model? Is there any range, movement, and positioning involved?
Quote from: Phillip;860500What's your standard of 'reliably'?
If you're doing a D&D type thing where you've got, say, 5 figures getting into an average of 4 fights per session for 50 sessions, that's 1000 chances to get killed. If the odds of surviving a fight are 'only' 99:1, that's an average of 10 characters -- two parties' worth of adventurers -- killed.
A figure killed doesn't necessarily mean the party loses the fight, or vice versa. This is just a start on figuring out what you really do mean. It's easier to hit a target when we know what to aim for in the first place!
For my testing, mostly one on one, I figure 70% is "reliably" at this point. Given multiple players, in my case three, I
assume (to be tested later) that means that one of the other two people can help the player who falls into that 30% category.
Quote from: Phillip;860505If you had a single combat factor and switched to a roll-off of 2d6+bonus for each side, lower takes a hit, then the difference in bonuses would yield a ratio that goes up pretty quickly. For the most part that's close to what you'd get with 3d6 'reflexive' (from 11+ each to 12+/10+, then 13+/9+, etc.).
Note that this way, it's just the difference that matters; +10 vs. +3 is the same as +8 vs +1 (about 84 to 1).
This is me thinking through this...
It makes sense when you say it, I'd have to simulate it too see what "really" happens. For certain values of "really". :D
One thing I though of while doing this was: one thing is that I'm looking for outcome results, not to hit/damage results. Which party wins the encounter?
That's just for hitting--that is, you've confounded to hit and defense.
But then you've got damage and armor.
Maybe use the difference for damage and similarly combine damage/armor into the to hit and defense?
That is, a combat turn between two opponents would be:
2d6 + A's bonus versus 2d6 plus B's bonus
Highest score wins.
Difference between scores becomes the damage.
Hmmm. I kind of like this as simple and somewhat elegant.
I kind of want to keep the idea of armor of a certain level being proof against attacks below a certain level, which adds complications in determining outcome.
What does it do to the ranking if you have two rolls per turn? That is, first you have the A's attack versus B's defense, and then B's attack versus A's defense. The attack and defense values are the same for a particular person, but only the attacker can do damage. (This allows you to handle defending against someone you don't want to kill, while your friend gets the sleep spell running.) That should still work.
I say the values are the same, I think what I might do is add add the appropriate stats, skills, or whatever that go into armor, to hit, and defense, and make that the "combat value". It sort of even makes sense, with better armor, you're defending less and can attacker better.
How would this handle "touch" type attacks? That is, whatever happens isn't a damage type roll but an effect? I guess it still works, with the level of difference being meaningless.
What if you use the bonus or "combat value" as a dice pool instead?
Hmmm (These numbers may be wrong. Anydice is down and I'm not as familiar with Troll.)
2d6 average 7
3d6 average 10.4
4d6 average 14
5d6 average 17
I'll have to run some simulations and see what the results are.
Quote from: Arminius;860506So just how simple is your overall combat model? Is there any range, movement, and positioning involved?
As simple as makes sense for the situation? :D
Movement and positioning is mostly abstract. You can use cover or concealment. There are bonuses/minuses for ranges and for surprise or unaware. I'm not going to try to track facing directions but if someone invisible/stealth-cloaked hits you from behind, they get a good plus.
I haven't gotten far into the details, as I wanted to get the basics down first. Basics being the basic dice mechanics and ranking system.
For Lanchester's Laws a la outnumbering, I'll look into that, but I'd probably handle that more with either GMing/roleplaying the tactics.
Not saying you should incorporate Lanchester's Laws into your mechanics, but that the theoretical underpinning and general considerations of the Laws can enlighten your analysis.
Although, if you wanted to abstract to high degree, you certainly could add general modifiers for situational advantages--such as terrain, speed/agility, or "tactical coordination" allowing one side to concentrate their attacks and minimize exposure to the enemy. Personally, I think that would be more difficult to do right than just using a map, but it would be an interesting angle.
Quote from: Tod13;860514One thing I though of while doing this was: one thing is that I'm looking for outcome results, not to hit/damage results. Which party wins the encounter?
You can multiply an advantage by requiring more wins of rounds to win the contest. For instance, if I have a 1/3 chance of winning one then I have only 1/27 of winning 3 in a row.
With just that one toss to consider, the odds are trivially clear. Complications mount as you add things such as "first to win 3", "first to add up so many points from a die tossed each won round", etc.
One thing's pretty clear, though: if your spread of decisiveness (e.g., "damage points" dealt relative to what's sustainable) is big, then you've got a big spread in how many rounds there will be.
More rounds gives more chances for swings of luck to cancel out, so you get a bulge of frequencies around your average outcome and the extremes become more rare.
using difference between scores in a roll-off for damage jacks up advantage in a big way. Adding more dice adds only very slowly to the usual spread, the sums adding more tiny tail probabilities.
Even with 4d6 per side you're typically looking at just 4 points or so with no advantage. It makes even a single pip a very big deal.
This gets very weird for various reasons in Tunnels & Trolls, but in a way that means a straight melee is usually close enough to deterministic. Missiles and magic and stunts done with saving rolls shake things up.
Zenobia uses difference in 2d6 roll-off, with armor deducting from damage. You can save your points scored IF you keep winning rounds, and then deliver especially nasty "critical hits". That's groovy for a gladiator who has things well in hand, and maybe a worthwhile gamble for someone who is just looking anyway at close enough to certain death.
Phillip, combining the numbers does make the combat value for 1:1, 1:2, 1:3 a useful comparator, but there is a narrow band of chance.
2d6 + bonus versus 2d6 + bonus
HP = bonus * 6
One on One
If the bonus values are equal, this is 50/50 with an edge to the first to go.
At 1 point difference, the lower bonus has a 5% chance of winning.
At 2 points difference, the lower bonus has less than 1% chance of winning.
At 3 points or greater difference, the lower bonus never wins.
One versus Two
If the single is lower, the pair always wins.
If the bonuses are equal, the one has a 1-2% chance of winning.
If the single is 1 point greater than the pair, the single has a ~50% chance of winning.
If the single is 2 points greater than the pair, the single has a ~95% chance of winning.
If the single is 3 points or greater than the pair, the single always wins.
One versus Three
If the single is equal or lower, the triple always wins.
If the single is 1 point greater than the triple, the single has a ~15% chance of winning.
If the single is 2 points greater than the triple, the single always wins.
(bonus)d6 versus (bonus)d6
HP = bonus * 6
One on One
If the bonus values are equal, this is 50/50 with an edge to the first to go.
At 1 point difference, the lower bonus has ~1% chance of winning.
At 2 point or greater difference, the lower bonus never wins.
One versus Two
If the single is lower, the pair always wins.
If the bonuses are equal, the one has a 1-2% chance of winning.
If the single is 1 point greater than the pair, the single has a ~75-90% chance of winning.
If the single is 2 points or greater than the pair, the single always wins.
One versus Three
If the single is equal or lower, the triple always wins.
If the single is 1 point greater than the triple, the single has a ~25-30% chance of winning.
If the single is 2 points greater than the triple, the single wins 99% of the time.
If the single is 3 points or greater than the triple, the single always wins.
"Edge to the first to go" is not part of what I was talking about. I was talking simultaneous, as in Fighting Fantasy: either you tie (no hit), or one of you scores a hit.
Your two-on-one, etc., are I presume upping that swing in decisiveness: a single round can mean getting whacked so many times as much. A heavy loss in a round tends to mean fewer further rounds, a synergy compounding effects of any further oddities in the same favor.
Quote from: Phillip;860653"Edge to the first to go" is not part of what I was talking about. I was talking simultaneous, as in Fighting Fantasy: either you tie (no hit), or one of you scores a hit.
Yea--I mentioned I changed that in my long meandering initial response, to allow for defense only. So, the one person will have three "attacks"? Let me run those numbers too.
You could give him three chances to hit, or you could say he gets just one and can at best fend off the two other attackers. (This could be a matter of expertise.)
Again, three rolls on the outnumbered guy's part will yield less swing than a single toss against the opponents' three, and less still than the three likewise getting just one throw for all.
Some different, but not that noticeable.
Simultaneous 2d6 + bonus versus 2d6 + bonus
HP = bonus * 6
One on One
If the value is the same, roughly 50%.
If 1 point difference, higher wins ~90%.
If 2 point difference, higher wins ~99%.
If 3+ point difference, higher wins 100%.
One versus Two
If the pair is 2 points or greater, pair always wins.
If the pair is 1 point greater, pair wins ~98%.
If the pair is the same, the pair wins ~50-60%.
If the single is 1 point greater, pair wins ~8-10%.
If the single is 2 points greater than the pair , the pair never wins.
One versus Three
If the triple is larger, triple always wins.
If the triple is the same, the triple wins ~98%.
If the single is 1 point greater, the triple wins ~50-60%.
If the single is 2 points greater than the triple, the triple never wins.
Quote from: Phillip;860671You could give him three chances to hit, or you could say he gets just one and can at best fend off the two other attackers. (This could be a matter of expertise.)
Again, three rolls on the outnumbered guy's part will yield less swing than a single toss against the opponents' three, and less still than the three likewise getting just one throw for all.
I ran my newest numbers as three separate attack/attack events.
The previous numbers were also run separately. The main difference being there was an attacker and a defender in those. You could defend as often as needed but could only attack once. That is, three opponents each get their own separate attack.
The computer my wife was trying to load the data onto this weekend did not have enough memory. She'll try one with more memory this week.