Duel of Wits Simulation

Burning Wheel Subsystem Advice and Guidance
21

I think the question to ask about varying FoRKs and Help is this: can you predict when they will occur? (For both sides?) If you can’t, then it won’t affect your scripting much - a random +1D here or there isn’t a lot. (I assert.)

Variable Skills

Variable skills could be very important, you’re right. The main area of interest here is skills that can’t be used for Point: Extortion, Falsehood, Ugly Truth, Command, Intimidation, Religious Diatribe, Seduction, Soothing Platitudes and Suasion.

Extortion and Suasion can be used to Rebut. Do this if your Extortion/Suasion exponent is high enough to give you a 4D advantage over your enemy’s main duelling skill.

Ugly Truth, Command, Intimidation and Religious Diatribe can be used to Dismiss (but can’t Point). The time to Dismiss is when your additional dice are worth more to you than your entire next action. For example, if you have B1 Oratory, then +2D now is worth as much as your next two volleys combined, so Dismiss is always better than Point for you, hesitation be damned. In general, Dismiss if:

Diss Skill + 2D - Point Skill >= Point Skill

(or)

Diss Skill >= (Point Skill x 2 ) - 2D

For a given Point skill, Dismiss looks attractive when your Dismiss-but-not-Point skill is:

B3 -> B4+
B4 -> B6+
B5 -> B8+

As for the other skills, Falsehood, Seduction and Soothing Platitudes, I suspect they need to be sky-high before they’re worth using. Since Rebuttal is only worth it for contenders with a huge advantage, Feint is for underdogs. But you had better be really, really effing sure your opponent is going to Rebut, or you’re going to get pasted outright. But since Rebut is only marginally better for your opponent Point, why would they risk the exposure? IMO, Feint is a long shot for outmatched gamblers who don’t mind losing badly most of the time.

Incite doesn’t make sense to me at all. First of all, it’s really hard. Ob=Will is pretty punishing, and that’s the case against the better actions (Dismiss, Point, Rebuttal). Meanwhile, all those same actions are Ob 0 standard tests against Incite. Incite seems to translate to: I’ll skip my current action for a modest chance of having my opponent miss his next action. Where’s the upside?

AdBu talks about the Incite-Point combo, but this isn’t very good. Assuming a sensible opponent who is trying to reduce your dispo, you’re letting in a free shot (Point is Std. against Incite).

Obfuscate is more interesting. I haven’t looked at this carefully enough yet. It strikes me as an underdog action, since it’s best against Rebuttal-heavy scripters (and Rebuttal is for people with an overwhelming advantage) because of the double penalty thing. Definitely for use early on because of the vulnerability to Dismiss.

22

Point has very few downsides. Too few, IMO. There are some good reasons to not script Point, but not enough.

  1. Point is vulnerable to Avoid, while Dismiss isn’t. Hardly a problem since the Avoider makes zero progress either.
  2. Point has fewer dice than Dismiss. A slight problem, but it doesn’t come up enough, since the gain is usually not worth the entire lost action except as your last action in a DoW.
  3. Point can’t use Falsehood, Ugly Truth, Soothing Platitudes, etc. Definitely a reason to script some non-Points, if only for the tests.
  4. Point doesn’t defend. Of course, the only things that defend while still giving some benefit are Rebuttal and Obfuscate. Rebuttal is only good if you have more dice, and has a large weakness if predictable. Obfuscate, if you can pull it off fairly reliably, is quite good against a similarly powerful opponent if followed by a maneuver that actually does something.

This is very fixed in Fight!, since many weapons can’t continually Strike, since Reflexes 4 can Strike on second actions and defend on first, since Block now actually does something good ;), since armor means Push and Lock are often way better, since disadvantage now means defense until next exchange is good. DoW lacks this nuance.

Of course, DoW PvP has these issues, but DoW versus GM is a different story. The GM can fix a flawed game by playing to the fiction rather than the mechanics, just like he does in Fight!. It’s still unfortunate that the GM doesn’t have a script that straight up punishes Point Point Point - a better Duelist will do very well by Obfuscate Rebuttal Obfuscate, but it punishes soooo slowly.

23

I was hoping you’d post, you were the one that got me started down this path.

To be clear, I’m really just looking at how to achieve the best compromise possible (or yield as little of one as you can). Many of the actions are very colorful, and have a place in duels for that reason alone.

One of the things I learned from my genetic trials is that there is a profound safety in scripting similarly to your opponent. If your opponent is mixing it up and using plenty of non-optimal actions like Avoid, Rebuttal, and Feint, then using those becomes safer for you too and you can enjoy the fun interactions. If your opponent is going for the throat, however, doing everything possible to win with as little compromise as possible, don’t touch them.

  1. As you say, this isn’t really a weakness of Point - Avoid is terrible. At best, nothing happens. Hardly worth the risk, since more likely you’ll take a bit of damage, or just as bad, waste any extra successes you roll. If Avoid was particularly good against Dismiss, it would be interesting - stop your opponent cold and then kick him while he’s down. But Avoid isn’t good against Dismiss.

  2. I’m not convinced about Obfuscate. +1 Ob is a pretty modest effect, and you need a commanding advantage to achieve it reliably. But enough angels on pinheads, I’ll plug in your Obfuscate/Rebuttal/Obfuscate point and see how it does.

Ah… I’ve just realized one thing about Rebuttal, though - Rebuttal doesn’t have to declare the dice split until the opponent’s action is revealed. This makes it slightly more adaptable than it appears in the simulations currently. It can go full defense (well, save for 1D) against Obfuscate, but full offense against Avoid.

24

I wonder if restricting point to every second volley might fix some of this. In that case, Avoid becomes the script you use to fill the gaps between points, protecting yourself against disposition loss while you can’t attack.

25

That’s a fascinating idea.

26

As Matt pointed out above, people have different dueling skills at different exponents. As a GM, it is my role (not the player’s) to determine which skill is appropriate to roll based on the action chosen and the content of the roleplay. Players can and will attempt to play to their strengths, but that does create limitations for them both in terms of actions available and the content they can bring to bear.

I also invoke obstacle penalties for repetitive content. Players must continue to bring in fresh content.

Also, in my games at least, NPCs and other players react to the tactics that you use in a Duel of Wits. If you hammer on them relentlessly and don’t allow them a word in edgewise, they will remember. If you are gracious and discuss ideas politely, they’ll remember that too. This sort of ephemera is an emergent property that is very important but also difficult to capture in a simulation. You can win a duel of wits and create an enemy or win (or lose) a duel of wits and make a friend.

For instance, I have one NPC in one of my games who is an interrogator and torturer for an inquisitorial holy order. A few of the PCs have been under his tender mercies on a few occasions. But the players actually like it when he comes on stage. He is urbane, polite and mild mannered. They enjoy talking to him and sparring with him in the duel of wits. Not only does he get them to engage in duels when he wishes, he usually comes out ahead, even though Rebuttals, Feints, Obfuscates and Avoids are large parts of his repertoire.

There’s a player character who is a savage, blood-spattered hayseed that constantly tries to hammer home his message in a duel of wits. He likes points, dismisses and incites a lot. He’ll occasionally throw in an Avoid to gun for a big Will test. The only problem is that no one in power wants to listen to him. They have no need to accept a duel with a brute and so they don’t–more often than not they have him thrown in the oubliette instead for bothering them (I think he’s made at least 4 trips at this point).

When he does actually get into a duel, his straightforward method serves him pretty well, unless he runs into a very savvy and skilled opponent. On several occasions he’s lost with no compromise or only a minor compromise. Someone skilled with a rebuttal can usually draw a duel out to the point where a person with a pointx3 strategy starts running out of fresh points to make.

27

Wicked! With a 2D+ skill advantage, Obfuscate/Rebuttal(50/50)/Obfuscate is more effective against Point/Point/Point than any other script. But it is very dependent on that advantage - even a 1D advantage means a probable loss, and if you’ve got the same skill as your P/P/P opponent and you try O/R/O, you will be eaten alive. The O/R/O is particularly good at lower exponents. 6D vs. 4D will win by a much bigger margin than 8D vs. 6D, I assume because the +1 Ob penalty from the Obfuscations is not nearly so pronounced.

I’m delighted!

28

:slight_smile: And I assume you’ve got it doing O/R/O, R/O/R, etc.? The idea is to maximally punish low-dice Points by negating one, then Rebutting with enough defense to bring your opposition to essentially 0 successes (but not too far below, or you give up offense), then negating, rebutting, etc. My guess is that 6d versus 4d works better than 8d versus 6d because a) Obfuscate will work more often with the lower variance, and b) when it does work your opponent must overcome 1+1.5ish successes with 4d which is much harder than 1+2ish successes with 6d.

29

Awesome, Thor. The fact that you can walk away from a Duel in a way that you just can’t walk away from a fight is very important to this discussion! And just to add to that: someone pointed out above that there’s the issue of earning tests. That’s an enormous consideration, IME. Especially when most DoW’s are against NPCs, whose skills are generally static. You want to get to the point where you have +2D against them? Better advance!

One of my proudest BW moments: a DoW between my Art Mage and a professor at the Magic Academy. We had both boosted ourselves before the fight, me to a Rhetoric of 7D, and him to a Will of 9. He scripted an Avoid the Topic against my Point. Knowing that I wasn’t likely to get anywhere, and having already earned my Rhetoric test for this Duel, I dropped to my knees and begged the professor to help me, sobbing that [whatever I wanted] was only for the good of the entire school. Unskilled Persuasion against his 5 or 6 Avoid Successes = Will test!

Matt

30

My “simple” script for DoW NPCs with decent social skills is Obfuscate, Rebuttal, Point (or Dismiss if starting dispo is low). I’ve found it to work well.

As Thor notes, Rebuttals work great to “wear down” a Pointer if you penalize for repeating yourself (which I thought was an actual rule in BWG now?). I’ve done this a couple of times against our resident DoW monster (high exponent Stentorious Debate).

31

What I mean is that if I’m not confident of a victory, then I want to aim for as big a compromise as possible (so I’m gonna point-point-dismiss probably for maximum damage). But if I am confident of victory, I want to grant as small a compromise as possible (and that’s when things get squirrelly – I care less about doing big damage than I do about avoiding any damage).

This all assumes the GM and players are competent in submitting suitably tough compromises, and that the other side actually does care. This situation may be rare-ish at actual tables in actual play, truth be told. Several of my players, for example, are pretty sly when it comes to expressing outrage at compromises while really not caring that much about them.

Luckily there’s still lots of player-reading and experience and instinct to all this. Just ask Mark Delsing about getting crushed in a DOW at the convention. :cool:

32

These are good points. Just to be completely clear, this isn’t an attempt to validate DoW or anything, this is purely a look at the actions that lead to low compromises.

Cool, I’ll try this one.

33

When you’re done noodling with this, can you write one for Mouse Guard?

34

Gotcha. So, the insight that GreedyAlgorithm helped me to was that you can accomplish both of these things at the same time - they’re not mutually exclusive. All you need to do is script to produce the highest possible ratio of damage done to damage received.

This ratio implies that Avoid is usually a waste of time - you may avoid a lot of damage, but you never inflict any. Your ratio is always zero.

Amusingly, one of the best ways to avoid losing dispo is for your opponent to be defeated! Accordingly, the purely offensive actions like Point and Dismiss do very well, as these reliably produce high ratios of damage done to damage taken.

What’s interesting is that having a massive dispo (or facing one) doesn’t seem to affect scripting strategy from the perspective of scoring a good compromise. It’s a bit like two sprinters, one of whom has to run along a track that’s 50m longer than the other. If you’re being scored on the distance you win or lose by, the best strategy is still to run as fast as possible.

If you have a big skill advantage, however, then opponent-delaying strategies (Obfuscate & Rebuttal) start to become practical. If you don’t, then the best way to have a high ratio seems to be to do damage as fast as possible. (One of the surest ways to avoid taking more damage is for your opponent to be defeated and no longer attacking you.)

Hmm, looking at it from the point of view of ratios, Obfuscate is pretty clearly a skill-advantage action: a failed Obfuscate is like Avoid - you may reduce the incoming damage, but your ratio is zero (and there’s that +1D you’ve given away). If you can guarantee success, you can use it to set up something better next action.

Rebuttal I wasn’t so sure about. What’s the ratio for rebuttal? Turns out it’s complicated:

Against an enemy Point (p), the damage is a function of how many dice you put on offense (ra) vs. defense (rd). I do ‘ra’ damage, and the opponent does ‘p - rd’ damage. As a function of rd:

f(rd) = ra / p - rd

And since…

f(rd) = r - rd / p - rd

I had no effing idea what this would look like until I plotted it. This graph shows the ratio (y-axis) as a function of the number of dice allocated to defense of a 5D rebuttal against a 4D point:

5d rebut vs 4d point.png

Basically, if you toss 3D onto defense, you’ll have the highest possible ratio. This explains the weird results I was getting when I worked out the optimal rebuttal dice by simulation.

The next graph shows rebuttal’s ratio against a higher-skill point - 5d rebuttal vs. 6d point. Here you can see that defensive dice are a losing proposition - the more you allocate, the worse off you are.

5d rebut vs 6d point.png

I still haven’t gotten around to Incite, but it doesn’t look good to me from a ratio perspective. But I was wrong about Obfuscate, so I could be wrong about Incite!

35

Sure, no problem. The Mouse Guard actions are much cleaner, so that won’t take long. But I expect I will need more help from the community for good scripting strategies. In my experience, Conflict often comes down to a nailbiting rock-paper-scissors game as the dispos get low, since a high-skill player can use a judicious Defend to dig himself out of a tight spot, making the temptation to Feint much higher!

If people contribute scripts in rough pseudo code, I can implement them. Arithmetic, random choices, consulting either side’s disposition or skill are the starting points.

36

To me it seems that the best strategy is to go into the DoW asking far more as stakes than you really want, then when the inevitable compromise happens, win or loose, you can try to angle for what you were really after all along.

This seems much like politics to me, and seems a viable tactic.

37

Comedy gold is when your opponent agrees to the stakes and you win them without compromise. It’s definitely a teachable moment!

38

This is the heart of the feedback I was giving via chat before Christmas took me offline. The only thing I hadn’t thought of was the GM getting to set the skill—this needs to be far, far more explicit in the DoW section as it is huge.

The reality of bringing your A-game skill to every action is you’ll be seen as that sort of person—someone constantly making up for a lack of persuasive ability with Seduction Incites and Ugly Truth Dismisses is going to be seen very differently than someone stumbling along to try using Persuasion with convincing Points. And the advancement system plus Trait / Reputation voting is going to reinforce that even more than just NPC reactions. I don’t think that it is punitive or cruel to turn to those things, but it is definitely something that should be made clear to players—especially as critical DoWs are generally Artha sinks (no one wants to let all those sixes on a Dismiss go to waste).

39

Some new and interesting findings!

So, Rebuttal is good when you have a big lead, since you can sop up damage while still dishing it out. On the other hand, the more your opponent rebuts, the more it pays to Feint. But… how much of the time, exactly?

  1. Let’s say we have two opponents, A and B. A has a skill advantage, enough that Rebutting some of the time is worthwhile, which gives B reason to Feint some of the time.

  2. I’ve got the optimal # of dice to rebut with, for a given pair of skill levels. (It’s crazily chaotic, you’ll just have to trust me; we can take it up in another post. I have ignored skill levels of 1 and 2.)

Pointer Skill
1 2 3 4 5 6 7
Rebut Skill 1
2
3 2 2 2 2 2
4 3 3 3 3 3
5 3 3 4 4 4
6 2 2 4 5 5
7 2 3 3 4 5
8 2 2 3 4 4
  1. I also have a chart of the expected amount of damage that will be done for a given number of offensive dice vs. defensive dice.
Attack
Defense 0 1 2 3 4 5 6 7 8 9
0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50
1 0.00 0.25 0.62 1.06 1.53 2.02 2.51 3.00 3.50 4.00
2 0.00 0.12 0.38 0.72 1.12 1.57 2.04 2.52 3.01 3.51
3 0.00 0.06 0.22 0.47 0.80 1.18 1.61 2.07 2.54 3.02
4 0.00 0.03 0.12 0.30 0.55 0.87 1.24 1.65 2.10 2.56
5 0.00 0.02 0.07 0.18 0.37 0.62 0.93 1.29 1.69 2.13
6 0.00 0.01 0.04 0.11 0.24 0.43 0.68 0.98 1.34 1.73
7 0.00 0.00 0.02 0.07 0.15 0.29 0.48 0.73 1.04 1.38
8 0.00 0.00 0.01 0.04 0.10 0.19 0.34 0.54 0.79 1.08
9 0.00 0.00 0.01 0.02 0.06 0.13 0.23 0.38 0.58 0.83
  1. Using these as ingredients, I’m able to work out the given/taken damage ratios for various combinations of A using Point or Rebut, and B using Point or Feint. For example, if A has B6 and B has a B4, A’s expected damage to B looks like this:
A’s Damage
A Rebut
B Point 1
B Feint 0
0.5
B’s Damage
A Rebut
B Point 0.55
B Feint 2
  1. Now - what if B knows that A will rebut 60% of the time, what’s the ideal mix of Feints and Points? I started investigating by working out a weighted average of the outcomes. For example, here’s the chart of how much damage A will do:
A Rebut %
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
B Feint % 0 3.00 2.80 2.60 2.40 2.20 2.00 1.80 1.60 1.40 1.20
0.1 3.00 2.79 2.58 2.37 2.16 1.95 1.74 1.53 1.32 1.11
0.2 3.00 2.78 2.56 2.34 2.12 1.90 1.68 1.46 1.24 1.02
0.3 3.00 2.77 2.54 2.31 2.08 1.85 1.62 1.39 1.16 0.93
0.4 3.00 2.76 2.52 2.28 2.04 1.80 1.56 1.32 1.08 0.84
0.5 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 0.75
0.6 3.00 2.74 2.48 2.22 1.96 1.70 1.44 1.18 0.92 0.66
0.7 3.00 2.73 2.46 2.19 1.92 1.65 1.38 1.11 0.84 0.57
0.8 3.00 2.72 2.44 2.16 1.88 1.60 1.32 1.04 0.76 0.48
0.9 3.00 2.71 2.42 2.13 1.84 1.55 1.26 0.97 0.68 0.39
1 3.00 2.70 2.40 2.10 1.80 1.50 1.20 0.90 0.60 0.30

If B feints 40% of the time, and A Rebuts 60% of the time, A can expect to do 1.56 disposition damage each action (assuming A is using the optimal attack/defend allocation).

40
  1. But, as GreedyAlgorithm pointed out, the key thing is having a high damage given/taken ratio, not doing absolutely more damage. Here’s A’s damage ratio chart:
A Rebut %
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
B Feint % 0 1.50 1.51 1.52 1.53 1.55 1.56 1.59 1.62 1.66 1.72
0.1 1.66 1.65 1.63 1.61 1.59 1.56 1.53 1.49 1.44 1.37
0.2 1.87 1.82 1.76 1.70 1.63 1.55 1.46 1.36 1.25 1.11
0.3 2.13 2.03 1.92 1.80 1.68 1.55 1.40 1.25 1.09 0.91
0.4 2.49 2.30 2.12 1.93 1.73 1.54 1.34 1.15 0.94 0.74
0.5 2.98 2.66 2.36 2.07 1.79 1.53 1.29 1.05 0.82 0.60
0.6 3.72 3.15 2.67 2.24 1.86 1.53 1.23 0.96 0.71 0.49
0.7 4.93 3.88 3.08 2.45 1.94 1.52 1.17 0.87 0.62 0.39
0.8 7.34 5.05 3.65 2.70 2.02 1.51 1.11 0.79 0.53 0.31
0.9 14.33 7.24 4.49 3.03 2.12 1.50 1.06 0.72 0.45 0.24
1 (div/0) 12.90 5.88 3.46 2.23 1.50 1.00 0.65 0.38 0.17

If A rebuts 60% of the time and B Feints 40% of the time, as before, we can see that A will have a damage ratio of 1.34.

Most crucially, what this chart shows is that A has an incentive to rebut less. By rebutting 50% rather than 60%, A’s ratio goes up to 1.54. The best option against someone who feints 40% of the time is to Rebut 0% of the time.

In fact, rebutting seems to be a bad idea against someone who feints at all. According to my charts, for various skills, even a 10% chance of a feint makes rebutting a bad idea.

  1. However, there is a really interesting cycle. Here’s a chart showing the pressures on both combatants to either raise or lower their percentages. An up arrow ^ means that B should Feint less, and a down arrow means that B should feint more. A left arrow means that A should rebut less, and a right arrow means that A should rebut more. Once more this is a chart for 6D vs. 4D:
A Rebut %
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
B Feint % 0 > > > > > >V >V >V >V >V
0.1 ^ <^ <^ <^ <^ <V <V <V <V <V
0.2 ^ <^ <^ <^ <^ <V <V <V <V <V
0.3 ^ <^ <^ <^ <^ <V <V <V <V <V
0.4 ^ <^ <^ <^ <^ <V <V <V <V <V
0.5 ^ <^ <^ <^ <^ <V <V <V <V <V
0.6 ^ <^ <^ <^ <^ <V <V <V <V <V
0.7 ^ <^ <^ <^ <^ <V <V <V <V <V
0.8 ^ <^ <^ <^ <^ <V <V <V <V <V
0.9 ^ <^ <^ <^ <^ <V <V <V <V <V
1 ^ <^ <^ <^ <^ < < < < <

If I haven’t lost you so far, you can see a cycle here - when both are using point/point (0%/0%), A has an incentive to increase his rebuttal %. But as soon as he reaches 50%, B has an incentive to Feint. As soon as the Feint % reaches 10%, however, A has an incentive to quit rebutting altogether. This appears to suggest that the gains for using rebuttals at all are so slight that even one feint ever three exchanges means rebuttal isn’t worth the risk.

However, if B knows that A will never, ever rebut, he has no incentive to Feint. This brings us back to the starting point - A now has an incentive to make 50% of his actions Rebuttals, which means that B should scare him off with a blast of Feints.