STROLL: ST rolls that work in GURPS/DFRPG

Yay, new content! And look, it’s… Oh. More nonsense about ST.

Wait, don’t go. This is a useful tool that I’ve meant to post for a long time. It patches one of the few problems with ST that GURPS 4e left standing: getting rolls against ST (and Contests of ST, and even ST-based skills) to work correctly. The below fixes these rolls for any and all jotuns, teeny faerie folk, super-beings, or normal humans involved.

Seriously, don’t run! This upgrade calls for no cost revisions and no new mechanisms, comparisons, or calculations, inside or outside of play. No wholesale reworking of ST into a logarithmic attribute, no changes to ST-related stuff like lifting ability or damage, no “scaling” of this or that – really, no meaningful change to anything. It’s dead simple – in fact, so simple and obvious that I expect it’s already in use out there, maybe even long-published on a blog or an online forum thread or an old Pyramid article. (If I’m rehashing someone else’s work, please tell me so I can give credit.) It’s simple enough to drop instantly into the most rules-averse Dungeon Fantasy Roleplaying Game (DFRPG) session.

Still here? Good. Prepare yourself for a tool that lets all roll-against-ST-related stuff finally play nicely in the game, even as it underwhelms you with the less-than-genius insight required to do so. I shall call this work… STROLL. (It’s not an acronym; it’s just “ST roll” looking like a name. See? The underwhelming has already begun.)


Introducing ST Roll

Roll this way

For any ST score, the ST Roll Table (PDF here) shows a score called ST Roll.

When it’s time to use ST in a Contest, roll against a hypothetical ST-based skill, or perform some other roll that tests ST, use ST Roll in place of ST.

Examples:

If your ST is 12, use ST Roll 12 when making a roll against ST.

If your ST is 8, use ST Roll 6 in a Contest of ST.

If your ST is 35, use ST Roll 28 as the base for ST-based skills.

That’s it. That’s the thing. Take it to your GURPS or DFRPG table.

A few notes to appease anyone who’s naturally suspicious of rules proposals that short:

The concept behind STROLL

STROLL equates any multiple of physical power to a fixed difference in ST Roll (give or take a point, what with rounding). This lets Contests and other rolls against ST properly properly reflect relative differences in strength, anywhere along the ST continuum.

Example: The jumps from ST 1 to ST 2, from ST 10 to ST 20, and from ST 62 to ST 124 all yield the same +10 boost to rolls.

Where to use it

As noted above, replace ST with ST Roll in any Quick or Regular Contests of ST, rolls against ST-based skills, or other rolls against ST.

Handling Lifting ST

If a character has Lifting ST, get ST Roll from combined ST + Lifting ST.

Handling negative ST Roll

Rolling against a negative number may seem all wrong for most traits, but it’s perfectly normal and needed where ST is concerned. Just as any GURPS roll against ST 2 or less will necessarily fail, any roll against ST Roll of 2 or less will of course fail. However, actual tasks will likely offset low strength with bonuses appropriate to the level of the challenge, or will call on margin of failure. A negative ST Roll doesn’t change anything about these; handle resolution normally.

Example: With ST Roll 2, a roll of 11 means a margin of failure of 9. With ST Roll -14, a roll of 11 means a margin of failure of 25. But in a typical roll that tests strength, either of these outcomes could yield success if the bonus for the task is high enough. And in a Quick Contest, either of these margins of failure could figure into a margin of victory if the opposed margin of failure is even worse.

Handling Regular Contests

As described under Extreme Scores on p. B349, Regular Contests involving scores too low to roll under or too high to roll over need to be brought into a rollable range. As described there, increase or reduce the lower ST Roll score to 10, then increase or reduce the higher ST Roll by the same amount.

The sole change: Using STROLL, do this for any ST Roll scores, whether high, middling, low, or even negative. Don’t use the multiplication and division that Basic Set prescribes for a Contest of high ST scores.

Examples: To make a Regular Contest out of ST Roll -8 and ST Roll -4, add 18 to each. The Contest is now ST Roll 10 vs ST Roll 14.

To make a Regular Contest out of ST Roll 32 and ST Roll 38, subtract 22 from each. The Contest is now ST Roll 10 vs ST Roll 16.

Write it down!

For most PCs, ST Roll is wonderfully the same as ST; there’s nothing to take note of.

But if your ST is below 10 or over 20, or if you have any Lifting ST, look up your ST Roll and write it down. (Actually, even if you ignore STROLL entirely, jotting down combined ST + Lifting ST somewhere is a good idea for characters with the latter trait.)

GURPS sadly didn’t prophesy decades ahead to this article to set aside a field for ST Roll on its character forms. So I recommend a do-it-yourself circled number to the left of the ST score:

In the absence of a dedicated space on a bespoke character form, ST Roll sits nicely to the left of ST. (Better ideas are welcome!)

If that one-time (and only-sometimes) lookup and jot-down still feels like a hassle… well, bear in mind that looking up or calculating stuff like damage and Basic Lift and encumbrance levels is already the main use for your ST score.

You can stop reading now

Rest assured that STROLL changes nothing else about ST (damage, Basic Lift, HP, muscle-powered missile ranges, etc.). It addresses problems with rolls involving ST, and that’s it.

That said, a number of rich and interesting (?) considerations surround the topic of ST and rolls. Delve into discussion below if you like – and further into the Appendices if you’re really foolhardy.

None of it’s essential reading. You’ll have more fun by skipping it all and heading straight to the gaming table.

Q&A!

This is the part where we pretend you ask “why?” and stuff so I can add commentary. (Even more side topics appear in the Appendices, hidden away there to preserve reader patience and sanity.)

“I’m new to these parts. What’s wrong with just rolling against ST?”

In a nutshell:

One problem is rolls that pit extreme-level ST (i.e., ST above or below the human range) against an inappropriate difficulty level. This includes Contests that pit ST against other attributes (or skills based on them), rolls against skills based on ST, and even straight rolls versus ST. Examples include choking a foe (ST vs the higher the foe’s ST or HT), a pull-up (roll vs ST-based Climbing), or a leg up (roll vs ST). (See Action 2: Exploits for those latter feats.) Witness the hapless trials of a ST 2 pixie PC who’s barred by rules from strangling even a tiny mouse-sized foe, pulling his own tiny weight up onto a ledge, or providing a leg up to even a pixie-weight pal. “Nope, can’t do those things”, the rules insist.

The other problem is odd interaction between ST and the dice at extreme-level ST. In a Quick Contest of ST 2 vs ST 1, one contestant boasts quadruple the lifting power of the other, while in a Quick Contest of ST 102 vs ST 101, the relative difference in physical power is negligible. Yet the Quick Contest mechanism looks only at the absolute difference in ST, and deems both Contests essentially identical, with the same likelihoods of outcomes. (For Regular Contests, GURPS offers a fix that does properly preserve relative differences in strength, though it’s suggested only for unusually high strength, and it calls on multiplication and division during play.)

“What does STROLL do to fix anything?”

The problem of rolls against inappropriate difficulty levels (e.g., prescribing the same unmodified roll vs ST to offer a leg up whether you’re boosting a pocket-sized pixie or an SUV-sized ogre) is only solved by setting appropriate difficulty levels. That’s its own topic and isn’t directly addressed by STROLL – though it’s not an unrelated matter, and so gets some attention below.

STROLL tackles the other issue: ensuring that all manner of ST-related rolls properly handle relative differences in physical power. Specifically, STROLL is set up so that, anywhere along the strength continuum, a 2-fold difference in ST (meaning a 4-fold difference in Basic Lift) yields a difference of 10 in ST Roll. Likewise, a difference of 3 in ST Roll equates to about a 1.25-fold difference in ST and about a 1.5-fold difference in Basic Lift. A difference of 5 in ST Roll equates to about a 1.4- to 1.5-fold difference in ST and about a 2-fold difference in Basic Lift. And so on. (ST Roll is rounded to neat integers, so multiples aren’t always exact.)

That lets rolls against ST, Contests of ST, and related exploits work for any beings, whether we’re talking dinosaurs with ST Roll scores of 30+ or wee critters with ST Roll scores down in the negative range.

“Ack! Negative ST Roll scores?”

Yep. Rolling against a negative score seems – and is – a weird idea for most traits you’d roll against. But it’s perfectly kosher and even necessary where ST is concerned. There’s no getting around it: as long as the game’s going to offer rolls against ST as a thing, and as long as it sets some wee level of ST that equates to a roll against 1, then it has to allow rolls against 0 and lower as creature ST dips below that level.

And as long as proper target difficulties are used, it works fine! A creature with ST Roll -4 is decidedly weak, but it’ll normally be pitting its power against targets that offer huge bonuses: say, bending the bars of a birdcage, not an Alcatraz cell door, for a +10 or higher bonus.

The same applies to Quick Contests. In some head-to-head Contest of ST, the wee creature’s ST Roll of -4 will likely fail by a whopping 10 or 15 or more, but its similarly-small opponent’s ST Roll of (let’s say) 0 will also likely fail by 10 or so. Per normal rules, the one that fails by less has the margin of victory and wins the Contest. It works, and it works anywhere along the ST continuum.

“But what about a Regular Contest? That would require actually rolling under negative ST Roll scores for anything to happen.”

The Regular Contest mechanism already requires the Extreme Scores fix to handle low ST scores that can’t be rolled under and high ST scores that can’t be rolled over. So just raise or lower extreme ST Roll scores to make them rollable. STROLL preserves the relative differences in power with no multiplication or division.

“Does anything change for plain old rolls against ST? Or ST-based skills?”

Rolls against ST are a fun way to resolve some tasks. Rolls against a ST-based skill are simply the same thing, modified for skill.

STROLL turns these into rolls against ST Roll and rolls against ST Roll-based skill, respectively. This ties outcomes to relative differences in power: in a roll or in skill level, STROLL means ST 2 enjoys the same advantage over ST 1 that ST 20 enjoys over ST 10.

Beyond that, making rolls behave well is a separate matter of setting proper target difficulties. Which means, again, awarding a nice bonus for a leg up offered to a lightweight halfling, and a really big bonus to ST Roll-based Climbing for a pull-up that hefts a pixie’s weight.

(And just what might be proper bonuses for these? That’s a subject all its own, but maybe we can touch on it in an Appendix.)

“But wait – when ST Roll is negative, a ST Roll-based skill means…”

Yes, when the rules call for a ST-based Artillery roll to load a heavy weapon (p. B178), using ST Roll means that a ST 2 cannon-loading pixie is going to approach the task with a skill of negative 10 or 15 or so.

This is correct. This is the way. When manhandling massive human-scale shells, the wee PC should fail by big, double-digit points. But, when switching to a mini-cannon with firecracker shells just heavy enough to strain a pixie, he’ll enjoy a bonus of +20 or so, and things will make sense.

“How about Contests of ST versus something that’s not ST?”

As noted already, a low-ST PC can never strangle a foe, no matter how much smaller and weaker, because the rules pit his tiny ST against “universal-scale” HT.

Again, this is a fundamental mismatch that STROLL doesn’t fix. You need a proper target difficulty, which for feats involving strength typically means ST versus opposing ST, or versus appropriate weight, or versus other appropriate resistance to ST. Reworking all such feats in GURPS to take this approach is too big a job for this article (though maybe we can touch on a few points below). Use GM sense in cleaning up problem areas on the fly.

“How about modifiers to ST in tasks? Do they add to ST or to ST Roll?”

Good question. Generally speaking, mods in the game affect what you roll against, and here that means ST Roll.

GURPS usually presents absolute, not relative, ST-related mods, i.e. “+5” instead of “+ ST/2”. This runs into the problem of absolute versus relative differences: something that modifies ST by +5 does very little for a ST 100 giant, while multiplying ST six-fold (and lifting power thirty-six-fold!) for a ST 1 fae.

That weirdness is good if it’s intended: a magic ring that “adds the strength of a bookish halfling to the wearer’s own power” is modeled perfectly by slapping +5 directly onto ST. But most mods to ST aren’t intended as such; they’re “+3 ST” instead of “+30% ST” for ease of play, not by intentional effect.

STROLL keeps the simplicity while delivering relative effects. When strangling a foe, modifiers to ST Roll of -5 for one hand, 0 for two hands, and +2 for three hands each yields a certain relative change to strength, at any power level. This holds for a wide variety of mods, including those from skill. When a pull-up calls for a roll against ST Roll-based Climbing, the +3 from the PC’s Climbing at DX+3 is equivalent to about a 1.5-fold advantage in lifting ability, no matter where the PC lies along the strength continuum. This is good.

In short: If a flat mod is intended to change strength by some absolute amount, add it to ST. Otherwise – and this will be most cases – add it to ST Roll for a nice relative modification to power.

“How about modifications to power for extra effort or Lifting skill?”

Whoa, those are some deep cuts into ST miscellanea. You’re right, those two power-boosters also need consideration.

The short answer is simple: extra effort and Lifting already involve relative boosts to strength that are valid at any power level; moreover, lifting is normally a static “you can or you can’t” task determined by Basic Lift alone, with no roll involved. At a glance, there’s nothing here for STROLL to do.

That said, a few questions and thoughts do crop up. Interested souls are directed to the Appendices.

“Besides all this rolling stuff, do you promise that STROLL changes nothing else about the ST attribute?”

STROLL doesn’t change any other workings of ST: muscle-powered damage and missile weapon ranges, Basic Lift and its uses, HP and its handling, and so on. Honest.

This website offers a lot of other toys for playing with such things, but STROLL aims to be a tool a GM can drop into any game to make ST rolls work, with no other changes.

“Not even Striking ST and Lifting ST?”

Correct. First, any roll that tests ST is almost certain to be a task involving lifting or other “steady pressure” power, so Striking ST is irrelevant.

Lifting ST is relevant to such rolls, and works normally under STROLL. Add Lifting ST directly to ST (not to ST Roll!) as always, then figure characteristics like Basic Lift and ST Roll.

Example: With ST 21 and Lifting ST 3, you have effective ST 24 for lifting, carrying, and similar feats of ST. From that ST 24, your Basic Lift is 24 x 24 / 5 = 115. From the ST Roll Table, ST 24 means your ST Roll is 22. Done. (Taking a peek inside the box to confirm that things are working right: ST 24 means twice the ST (for lifting purposes) and thus four times the Basic Lift of ST 12. So the ST Roll score for ST 24 should be 10 higher than the ST Roll score for ST 12… and it is.)

“Does STROLL make any difference to ST for the purpose of wielding weapons?”

No, nothing changes. But since you’re asking: STROLL could do some interesting things here! It’s a tangent, so I’ll toss it to an Appendix.

“While we’re brainstorming here… It seems to me you could turn ST Roll into a modifier for other uses.”

Wow, we really think alike. Yes, just subtract 10 from ST Roll, and you’ve got a nice modifier that’s ready to spice up some other roll with a brawn factor. An example: For ST 1, ST 10, and ST 80, the ST Roll scores are -24, 10, and 40. Subtract 10, and you get -34, 0, and 30, respectively, as mods.

Ah, what the heck. There’s no need to add this simply-derived stat to a table, but it takes just seconds to do it, so here’s the ST Roll Table enhanced with this modifier. (See the full-size, vibrant green PDF download at the end of the article.)

I’ll call this new score “ST Mod”. (Clever!) What good is it? Say you’ve got a Contest or other roll that calls on a DX-based skill, but you want ST to play a key part as well. Add ST Mod to the skill, and you’ve got a skill that’s based equally on agility, technique, and strength. (Wrestling and similar skills come to mind as candidates for this treatment.)

A deeper dive is a matter for some other time. For now, consider slapping that ST Mod onto whatever looks interesting.

“ST Roll, ST Mod… With these tools for dealing with ST, why not also create some mods for the weight handled in a ST-related roll?”

You can do that, and you’d then have quite the toolbox for finessing a bunch of stuff, particularly that matter of setting proper target difficulty for many feats of strength. It’s a rich subject that probably calls for its own detailed article, though it at least deserves a quick look. Still, it’s a tangent to the main topic of ST Roll itself, so… again, Appendix.

“Hey, here’s a wacky idea: How about applying ST Roll-like scores to other attributes like DX and IQ?”

You mean like… DX 7 paired to a DX Roll of 4? IQ 30 paired to an IQ Roll of 25?

That’s crazy… or is it? Appendix!

“Yikes, it’s past dinner time. How about you put up and show some quick examples of STROLL in action?”

Let’s take a quick look at an area where is ST always important: wrasslin’! Grappling with that topic from p. B370 onward:

“Gimme that!”

Wresting a grappled weapon away from a foe, or forcing a grappled arm to drop a weapon, is a straight-up Regular Contest of ST. The effect of STROLL here is simply to properly reflect relative power differences in the Contest, so (for example) twice the ST will always mean an advantage of 10 in the rolls.

If the ST Roll scores are outside rollable range, raise or lower them equally. Done.

Takedowns

Here we have a Quick Contest, with each contestant using the highest of ST, DX, or a grappling skill. Unfortunately, this is one of those situations in which small combatants are barred from taking down anyone, even smaller combatants. Powerful combatants, meanwhile, end up in a pure ST-vs-ST match, with DX and skill meaning nothing.

What we really want is for both strength and DX or skill to matter. The Universal Solution for cases like this is a topic for elsewhere, but for now there are plenty of approaches you can play with. See the note a bit above about ST Roll as a modifier: that approach would yield workable takedown Contests that are based on DX or a grappling skill and take strength into account, at any level of power.

Pinning foes

A pin is a Regular Contest of Strength. This one’s easy: use ST Roll, adjust the scores to a rollable range, and go from there. (A nice feature of STROLL is that the flat pinning bonuses awarded for larger SM and greater number of hands, as well as bonuses for Wrestling skill, all act as effective multipliers to the power represented by ST Roll.)

Breaking free

This is a simple Quick Contest of Strength. STROLL lets the Contest, and its flat mods for number of hands and so on, work nicely at any power level.

Choking

As already noted, the flat modifiers to this feat work nicely under STROLL, but the basic Quick Contest of ST vs the higher of the foe’s ST or HT suffers the same problem as that of takedowns. Fortunately, a fix is easy: just make it a Contest of ST Roll vs ST Roll.

This cleanly fixes the earlier-noted problem of a small strangler being unable to choke anything (so smaller prey had best be wary). And as noted, it’s fine that the strangler “fail” his roll by a lot; as long as the victim fails by even more, the aggressor still has a margin of victory.

Unfortunately, the part of the rules that sets damage equal to margin of victory won’t work here. A fix may be as easy as letting success in the Contest deliver damage based on a normal damage roll, such as thrust dam. That delivers reasonable results across the strength continuum (if overly grainy results at the low end, but that’s a fundamental issue with the Damage Table). It also brings the mechanics of choking into line with Neck Snap, which uses a normal damage roll following a Quick Contest of ST-4 vs the higher of the foe’s ST or HT. (That should of course be ST Roll-4 vs the foe’s ST Roll in order to work right at any level of power).

More

There are more wrestling actions to look at (I haven’t even touched the offerings of Martial Arts: Technical Grappling here!), along with many other feats of strength. Let’s save them for a later article or talk about them in comments below.

The wrap

Discursions aside, using STROLL is a simple thing: in ST-related rolls, replace ST with ST Roll to get results that respect relative differences in strength regardless of the level of power. Separate from that, set ST-related rolls against proper target difficulty wherever GURPS doesn’t quite do so.

Do both of these things, and issues related to ST rolls – among the last vestiges of problems with this prickly attribute in 4e – will weaken and tap out.


Appendix 1: More stuff to do with STROLL

Extra effort, Lifting skill, and ST Roll

To expand on the short bit noted earlier:

Extra effort and Lifting skill are interesting in that GURPS already has these deliver relative boosts to power. The workings: to boost strength with extra effort, roll against Will at -1 per desired 5% boost to Basic Lift (for lifting or digging) or to ST for other uses. A roll against HT-based Lifting skill, meanwhile, boosts Basic Lift for appropriate tasks by 5% per point of success.

In either case, the boost is relative to ST, so the concept is valid at any power level. And if the task at hand is a lift, that’s usually gamed as a static “you can or you can’t do it” task determined by Basic Lift alone; GURPS doesn’t prescribe a roll to begin with. At a glance, there’s nothing here for STROLL to do.

That said, a couple of questions come to mind:

  1. Say you did want to game a lift by using a roll against ST Roll. How would Lifting’s direct boost to Basic Lift convert to a bonus to ST Roll?
  2. For any task involving a roll against ST, now that you’ve used extra effort to, say, boost ST 2 by 20% to get ST 2.4… what do you do with ST 2.4? How does that connect to ST Roll?
  3. Could you instead use extra effort to directly boost ST Roll, not ST?

Let’s see…

1. A +1 to ST Roll hews closely to x1.15 Basic Lift. A 15% boost to Basic Lift normally requires success by 3 on a Lifting roll. So, if you game a lift as a roll against ST Roll, let a roll against HT-based Lifting boost ST Roll by 1 per every full 3 points of success.

Actually, I recommend this: Let Lifting boost ST Roll in a lift by 1 for every full or partial 3 points of success (including success by 0). That’s clearly more generous, but I suggest it in the spirit of “any success should yield something” and in the spirit of getting more fun out of this rather unexciting skill.

2. Okay, say you use extra effort to boost ST 2 by 20% to ST 2.4. You can easily calculate a new and improved Basic Lift for that, but otherwise, where’s the playable benefit from ST 2.4? You certainly can’t make a standard GURPS roll against it. There’s no extra damage. Even the ST Roll Table doesn’t seem to help, as it doesn’t cover fractional ST scores.

So… Should you create an expanded ST Roll Table that pairs little fractional ST scores to ST Roll scores? You could do that, but you don’t need to. Just look at how a 20% boost in ST affects ST Roll elsewhere on the Table – say, from ST 10 to ST 12, or ST 20 to ST 24. In either case, the boost raises ST Roll by 2, which means the boost from ST 2 to 2.4 does the same. Your ST Roll of -14 increases by 2 to -12.

3. It’s easier to let extra effort boost ST Roll by a flat amount than have it boost ST by a percentage, then convert that to ST Roll… Extrapolating from the GURPS rules (as done for Lifting skill above), roll Will at -3 for every +1 to ST Roll for the purpose of lifting or digging, or roll at only -2 for every +1 to ST Roll for other purposes.

DX Roll, IQ Roll…

ST Roll makes sense for ST… but how about other attributes? Should there be a DX Roll? IQ Roll? Others?

Quick Contests and other rolls treat the difference between DX 11 and 12 the same as the difference between DX 31 and 32 and between DX 1 and 2. In each of these pairings, the difference can be defined as… well, just enough difference to give the higher score an advantage of 1 in the roll.

Is that good or bad? Arguably, it’s no problem; if the jump from DX 1 to 2 represents the same thing to you as the jump from DX 31 to 32, then so be it. DX is abstract; it’s tied to no measurable quantities that make this identical treatment of the two Contests a wonky thing.

But if you want to apply the ST Roll idea to DX-related rolls, it’s a thing you can do. Use the ST Roll Table to grab your DX score’s “DX Roll”, and make all rolls against that. Things will work quite differently at the extremes: DX 2 will have a 10-point advantage in a Contest vs DX 1, because it’s twice as high. DX 32 will have no advantage in a Contest vs DX 31, because the relative difference isn’t big enough to matter.

The same goes for other attributes: if this better fits your image of how extreme levels should work, then there you go. IQ Roll it is! And HT Roll! Will Roll! Anything you like!

Sound good? Great. Except… what about skills? And general attribute rolls? Do you want athletic skills at DX 7 to be based on DX Roll 4? Do you want most animals to have IQ Roll (and skills based on it) of 0 or lower? I don’t know about that…

Attribute caps

Let’s set aside those super-low DX Roll and IQ Roll scores for now. The other end of the scale is more appealing.

The Rule of 20 says to cap an attribute at 20 for the purpose of skills defaulting from it. There’s nothing wrong with that. But if you instead use the ST Roll Table to find the base for defaults from a high-level attribute, you get a more interesting base that’s less than the full attribute yet not chopped off at an intractable 20. For example, IQ 24 would let skills default from IQ Roll of 22; IQ 30 would let skills default from IQ Roll of 25.

Some GMs have even experimented with setting 20 as the attribute cap for skill purchases (not just defaults). Using the above idea instead, a crazy-high IQ of 27 would base both skill purchases and skill defaults on IQ Roll 24.

It’s an interesting idea for the few GMs wanting to finesse the workings of sky-high attributes.

Even weirder rolls

Could a game use rolls against even odder scores, like HP Roll? Move Roll?

What you’d use those for, I don’t know. In rules that use HP as an abstract stand-in for mass, rolls and comparisons involving HP Roll could be put to some use. In mapless, abstract combat, a Move Roll could be used to answer the question “did you get far enough from the danger?”

I leave these things to tinkerers. I only note that by pressing the ST Roll Table into service here, you get the effect by which HP 6 yields a roll that’s 10 higher than HP 3, Move 2 yields a roll that’s 10 higher than Move 1, and so on. Cool, if that’s what you need for some rules idea.

(A tangent: There’s already a tool for creating mods based on relative difference in Move scores: the Size and Speed/Range Table. That table readily yields a mod of +2 for every (rough) doubling of Move, a number you can use as a mod or use as a roll by adding 10. It’s the same deal as using the ST Roll Table, with a much coarser grain.)

Feats of weight

As briefly mentioned way above, how about weight-based mods to go with ST-related rolls? Just for fun, here’s what such a thing might look like:

The scaling is set to mesh with the ST Roll Table: just as that table raises ST Roll by 10 for every quadrupling of lifting power, this table raises Weight Mod by 10 for every quadrupling of weight.

The zero point for Weight Mod could be set anywhere, depending on how you plan to use the table. Here I’ve paired Weight Mod of 0 with “average” human weight, for ease of use with tasks like a pull-up or leg up. Use ST Roll for the power of the character performing the exploit, add Weight Mod for the weight of said character (pull-up) or the weight of the friend she’s boosting upward (leg up), and you’ve got a modified roll that’ll work reasonably for characters of any power level.

If that’s what you’re looking for, of course. I get that most players aren’t interested in gaming explicit “power vs weight” factors for characters, and I appreciate GURPS‘ stance of assuming that this factor is already built into DX and Move and so on. That’s all fine and good – except that the game’s nicely simple assumption doesn’t keep things from breaking when ST-related rolls enter the picture. With or without STROLL, feats like a leg up simply won’t work for your ST 2 pixie if you don’t make appropriate adjustments for the weight or whatever else it is that’s opposing the strength in question.

ST Roll + Weight Mod may not be the solution for you in every situation, but it does offer a solution, at least to play around with.

What else can you do with that Weight Mod Table? Lots of stupid weight tricks come to mind.

Skill mods

Like, hey, how about a mod to Stealth? Weight Mod sounds like a realistic penalty to the skill (which means a bonus if it’s negative), but think first: how exactly should that work? Take an example:

  • A 10-lb. animal has a Weight Mod of -20. Do we want to give every 10-lb. animal an automatic +20 (!!) bonus to Stealth?
  • Should we instead consider stealthiness in terms of weight and the power available to gracefully move that weight? Let’s see… If our 10-lb. animal has ST 4, that’s -14 to skill for ST Mod, but +20 for Weight Mod, so a solid +6 bonus to Stealth. That seems much better…
  • Should we do the above but with a divisor to the net mod to moderate its effect? Say we modify Stealth by half of net (ST Mod – Weight Mod)… Our 10-lb. animal nets a modest but still nice +3 bonus to Stealth for its power-to-weight ratio. Seems reasonable…
  • Or should we just assume that Stealth’s DX base already accounts for these factors, with the only added modifier coming from encumbrance (per normal rules)?

And so on. There are plenty of Big New Ideas you can wring from tools like ST Mod and Weight Mod, but do some testing before springing them onto a gaming group!

Taking Basic Lift, etc. from ST Roll

Imagine a version of the Weight Mod Table that adds 25 to all Weight Mod scores. 20 lbs., for example, would be paired with a Weight Mod of 10.

Hey, 20 lbs. is also Basic Lift for a ST Roll of 10! Hm, let’s rename the “Weight Mod” columns to “ST Roll” for this new table. We’ve just created a Feats of Strength Table that directly pairs Basic Lift to ST Roll. (Resulting Basic Lift values may differ a bit from normally calculated values due to rounding.)

The same table could yield a number of weight milestones. For a (ST Roll + modifier) value below, the paired weight can represent:

ST Roll + 0: Basic Lift, or Encumbrance level of None
ST Roll + 5: Two-handed lift (one second), or Encumbrance level of Light
ST Roll + 8: Encumbrance level of Medium
ST Roll + 10: Two-handed Lift (two seconds)
ST Roll + 13: Encumbrance level of Heavy
ST Roll + 15: Two-handed lift (four seconds)
ST Roll + 17: Encumbrance level of Extra-heavy
ST Roll + 20: Maximum press
… and so on.

All quite unnecessary, of course, but there it is as a toy for tinkering. (In essence, this takes a feature of “log ST” schemes, that of tying a given lifting feat to some “ST + x“, and brings it to GURPS.)

Weight Roll?

If we can have a table offering Weight Mod scores, we could of course have a Weight Roll Table, for when you want to… roll against Weight, I guess! Hm, maybe a roll to see whether a given weight breaks through ice?

Say you set up a table that used the above Weight Mod numbers, but augmented by 10, as Weight Roll. Weight between 140 and 160 lbs. gets a Weight Roll of 10, and so becomes the weight with a 50/50 chance of breaking through the ice. The ST Roll of the ice would then offer a mod affecting this. All of which… uh, is fine, but isn’t meaningfully different from the more intuitive scheme of setting and rolling against the ice’s ST Roll, with the traversing character’s weight as a mod.

I don’t see a big demand out there for “roll against Weight”, but hey, if you’ve got some use for it, tinker away.

Other

I may add more stupid weight tricks if people want to see them. (I assume this means there will be no more.)

STROLL and weapon ST

The ST of weapons – commonly called “minimum ST” or “min ST” by players – is typically in the range of 5 to 15 or so, with weapons for weaker or stronger fighters left to special cases and rules. But especially in the high and low ranges, absolute comparisons of min ST to wielder ST yield some weirdness. A ST 2 wielder of a min ST 4 weapon suffers a mere -2 to skill, despite having but a quarter the required physical power (as measured by Basic Lift). Meanwhile, a ST 22 wielder of a min ST 24 weapon suffers the same -2 to skill, despite a far more modest shortfall in physical power.

Imagine that we instead use ST Roll in the comparison, and, to make things match up, that we convert min ST itself to its ST Roll equivalent: min ST Roll 6 (instead of min ST 8) for a short sword, min ST Roll 0 (instead of min ST 5) for a dagger, etc. Good things happen from there.

One, there’s a lot more room for fine-grained min ST Roll scores at the low end: plenty of open min ST Roll scores between broadsword and shortsword, between shortsword and dagger, and even further below that, with weapons taking on min ST Roll -1, -2, and lower, as low as you want to go for teeny PCs’ weapons.

Two, the business of “-1 to weapon skill per point of ST you lack” works properly now, tying skill penalty to relative shortfall at any power level. A leprechaun with half the power needed to wield a human shillelagh and a superhero with half the power needed to swing a telephone pole will each face the same -5 skill penalty.

Three, the above holds for other rules that specify absolute, not relative, differences between character ST and min ST, such as the rules for crossbow loading. To needlessly belabor what’s wrong in this case, the ST 2 wielder of a ST 4 crossbow is hugely lacking in the power needed to cock that bow, while the ST 22 user of a ST 24 crossbow is only slightly short of needed power, yet the game slaps each with the same readying time penalty. Using STROLL, comparisons like “if crossbow ST Roll is three or four greater than wielder ST Roll, cocking takes 18 turns” make sense at any power level.

Four, when rules instead specify multiples of min ST (e.g., 1.5 times min ST to use a two-handed weapon one-handed or 2/3 min ST to use certain guns with a tripod), STROLL can replace these with additions and subtractions that are easier to use. For example, “at least 1.5 times the listed ST” and “at least twice the listed ST” become “ST Roll of 5 higher than min ST Roll” and “ST Roll of 10 higher than min ST Roll”. Again, this works properly anywhere along the ST continuum.

Wielding weapons with enhanced ST

STROLL specifies Lifting ST as the relevant enhancement to ST that figures into ST Roll. But GURPS specifies Striking ST as the enhancement that boosts ST for purposes of meeting weapons’ min ST. So, which is it?

Sticking to the published rules, you’ll want to make an exception to STROLL’s general procedure, and figure ST Roll from (ST + Striking ST) for comparison with weapon min ST.

However, I take friendly umbrage with GURPS on this point. While Striking ST is your friend for boosting damage, I see Lifting ST, not Striking ST, as the enhancement that’s appropriate for wielding heavy weapons and guns, pulling bowstrings, cocking crossbows, and so on. I spell out the reasons here; if you agree with that, you can consistently figure ST Roll from (ST + Lifting ST) for all purposes, including comparison with weapon min ST.

Appendix 2: Building the ST Roll Table

Basics

The ST Roll Table is set up so that a 2-fold difference in ST (a 4-fold difference in Basic Lift) equates to a difference of 10 in ST Roll. Why? Because that’s the existing relationship set in 4e for ST 10 and ST 20, two ST scores that (more or less) bookend the typical ST range of PCs in most settings. STROLL arbitrarily takes that relationship as its “benchmark” and extends it everywhere, with the goal of changing little or nothing for PCs in that typical range.

The ST Roll score for all other ST scores gets calculated from there. That naturally yields non-integer ST Rolls for most ST scores, and in turn these questions: How should ST Roll be rounded? Are any other tweaks called for?

Here’s how I answered those:

  1. I rounded all ST Roll numbers down: a calculated ST Roll of 13.79 became 13; -7.37 became -8.
  2. I made one arbitrary tweak purely for aesthetics. The calculated ST Roll for ST 21 should actually round down to 20, meaning ST 20 and 21 get ST Roll 20 and ST 22 alone gets ST Roll 21. There’s nothing bad about that, but it’s ugly on the Table. So I fudged it: ST 20 alone gets ST Roll 20, while ST 21 and ST 22 share ST Roll 21, creating a neater-looking table. That’s my sole cheat. (If your response to that is “Dagnabbit, I want everything as precise as possible!”, read on.)

Why round fractions down, instead of to the nearest integer? While the latter yields more “precise” results, rounding down yields one wonderful bit of neatness: between ST 10 and ST 20, ST Roll is the same as ST. That’s not a kludge for convenience or aesthetics; it’s how the numbers work out!

A different pattern emerges from ST 9 down to ST 5, but it’s a neat one: a nice -2 ST Roll for every -1 ST. (ST Roll for ST 1 to ST 4 doesn’t follow a special pattern, but the few values down there are easy to remember.) Meanwhile, from ST 21 to 36 the pattern is simple: ST Roll is 20 + (half of ST over 20, rounded up).

In the end, over half of the table is simple to memorize, with calculated ST Roll scores blissfully identical to ST scores in the range most common to PCs and a whole lot of NPCs. (It’s interesting that, in the process of declaring “ST rolls are all wrong and must be fixed!”, STROLL finds that GURPS‘ by-the-book ST-related rolls in the common range of ST 10 to ST 20 really aren’t broken after all. That’s GURPS for you: getting a bunch of stuff right even when it does stuff wrong. : )

Figuring the numbers

Feeling like hitting the spreadsheets yourself? The following will give you ST Roll for any ST score:

ST Roll = LOG(ST÷10,2)×10+10

From there, round as you prefer.

And how about that Weight Mod Table? To attach a weight value to a Weight Mod score, try this:

weight = 4^(ST Roll÷10)×X

where every ±10 to Weight Mod equates to a four-fold change in weight, and X sets the weight that occurs at Weight Mod 0. Four times that weight will pair with Weight Mod 10, and so on.

My table above uses X = 160. Modify that for your intended use. For example, X = 40 creates a table on which 160 lbs. corresponds to Weight Mod 10, should you have a use for such.

Expanding the ST Roll Table

Need to expand the table to massive ST scores? The shortcut should be clear: take ST Roll for half the target ST and add 10. Or take ST Roll for one-fourth that ST and add 20. Or take ST roll for one-eighth that ST and add 30. (Another shortcut of note: Every 10-fold increase in ST equates to +33 or +34 to ST Roll.)

Example: You want ST Roll for ST 1000. Take one-eighth the ST (ST 125), get its ST Roll of 46, and add 30 to yield ST Roll 76.

Add another 30 to that, and you’ve got ST Roll for ST 8000. And so on, for numbers as large as you could possibly need. (Just what sort of game do you have going on?)

Going the other way, you can do the same to get ST Roll for low, fractional ST scores, should you ever want to use such. Say your ST 1 character gets a big boost to (ooh!) ST 1.5. Computing Basic Lift for ST 1.5 works normally. Damage will have to be the same as that for ST 1 and 2, barring any custom mechanisms you work up. And ST Roll? In this case, it’s as easy as looking at ST 3, a score handily twice as high. Grab ST Roll -8 from ST 3, and subtract 10 to get ST Roll -18 for ST 1.5.

How low can you go in an expanded table of microscopic power levels? As low as you like. The only thing out of bounds is ST Roll for the actual ST 0 of a ghost: that’s ST Roll negative infinity. (Go ahead, Ghost, and total up whatever bonuses you can talk out of the GM; you still won’t get far in a roll against negative infinity. Props for trying, though!)

A more precise ST Roll Table

An alternative table for the discerning die-roller.

Instead of rounding all calculated ST Roll scores down, wouldn’t rounding to the nearest integer make things more precise?

Yes. Here’s a purple-hued “precise version” of the ST Roll Table that rounds scores to the nearest integer. (There’s no consideration of aesthetics here; all numbers fall where they fall.)

What’s the difference?

The overall difference from the “standard version” is, of course, an increase of 1 in ST Roll for many ST scores. The most noteworthy ranges where ST Roll increases by 1 are:

  • The “strong human PCs” range of ST 12 to 17
  • The “halfling PCs” range of ST 6 to 8
  • The “pixies and other wee PCs that exist mainly to illustrate examples of low ST, not to actually raid dungeons” range of ST 1 to 4

Play around with this Table to see how well differences in ST Roll map to multiples of physical power. You’ll find that its rounding yields results a bit more consistent than those of the standard version way up above. That’s a good thing, so run with it if you like!

Which to use?

As much as I appreciate precise stuff, I’m using the standard version, purely for its neatness and ease of adoption. I like the neat appearance of its ST Rolls below ST 10 and its cleaner aesthetics at the higher end of the human ST range.

Most of all, for the all-important PC range of ST 10 to 20, I love the standard version’s siren call of “just use ST”. A bit less precise, I know, but it’s too sweet to pass up.

So, unless stated otherwise, any future entries on this site that mention the ST Roll Table will refer to the green-hued standard version. (Go ahead, call me a form-over-function sell-out.)

Appendix 3: “Log ST”?

STROLL and Knowing Your Own Strength (KYOS)

Isn’t there already a “logarithmic strength” option for GURPS that handles Contests and other ST-related rolls correctly?

Pyramid 3/83 offers “Knowing Your Own Strength” (KYOS), which does indeed re-envision ST so that every multiple of lifting power equates to a flat difference in the stat (x4 lifting power = +6 ST, to be exact). But KYOS and STROLL aim for very different things.

KYOS gives ST a full working over: logarithmic underpinnings, a new damage table, new costs for components like HP and Lifting ST, and much more. It’s a complete rethink for the daring GM.

STROLL is far less ambitious! It wants to keep everything about ST just as it is, with the sole change of retrofitting logarithmic ST Roll scores onto an otherwise unchanged ST attribute. (Accordingly, it chooses x4 lifting power = +10 ST as the scaling that makes the least change for most PCs.) STROLL is a modest tweak for the less-than-daring GM.

If you’re up to overhauling ST, by all means check out KYOS. But should you decide that the only change you really want in ST is rolls that work, STROLL is here for you.

Other “log ST” systems?

Sure, I’ve played with my own take on “log ST” systems. For home-brew stuff outside of GURPS (and going back a lot of years), I’ve mostly played with a scheme having these features:

  • The scaling is “x2 lifting power = +6 ST”. With slight rounding, x10 lifting power = +20 ST, which is easy to work with. (I know, using “x2 lifting power = +3 ST”, like KYOS, yields a niftier “x10 lifting power = +10 ST”. Unfortunately, that’s a coarser scale than what I want.)
  • The ST stat is “zero-centered” – that is, ST 0 is the human norm. ST -1 and below are weaker than this norm: ST 1 and higher are stronger than this norm. (Other stats work that way too, so it’s all consistent.)
  • Damage is… well, too much to describe here, because it’s an equally “logarithmic” stat. (“It’s a wound system, not a hit points system” is the sort of description tinkerers might use; if that makes vague sense to you, then you’ve got it.)
  • Needless to say, there’s no need for a separate ST Roll score, as ST itself works as a mod or roll.

Could this be adopted into GURPS? I’m sure it could, given the game’s robust underpinnings. Should I do more GURPS testing and write things up, my own take on KYOS would look something like this:

  • Staying conservative, the scaling would be “x4 lifting power = +10 ST” to preserve current workings in the “ST 10 to ST 20” range where most PCs reside.
  • Getting all “tear down the system!” radical, the ST stat would be “zero-centered” – that is, ST 0 would be the human norm. ST barely acts like other 10-centered attributes to begin with, and any proper logarithmic ST scheme must allow for scores below 0. So what the heck, let’s just put that 0 front and center.
  • Retreating back to conservative, damage would stick to the existing GURPS (and KYOS) concepts of damage points and hit points. Basic hits would scale with the square root of lifting power. HP would also have to scale in a similar way (setting it equal to ST won’t work any more).
  • There’d be no need for a separate ST Roll score, as ST itself would work as a mod or roll.
  • I’d name it with a goofy acronym. Like “Strength Incorporating New Exponential Workings” (SINEW). Works for me.

Well. Maybe some day. Until then, if you care to read more about “log ST” schemes, I suggest these hoary old things:

Beyond that, this link will take you to all the posts on this site with a focus on some aspect of ST.

And there may be more to come. I actually lightened the above Appendices by a bunch of ST-related content that strays just a bit too far from STROLL: commentary on what rolls against ST represent, when to use Quick vs Regular Contests with ST, the differences between ST and other attributes, etc. You’ll find pulse-pounding prose on those thrilling topics here.

(Yeesh. Let’s end the typing and post this silly STROLL thing already.)


Downloads

Want the above tables in PDF form? Of course you do.


Header image: Toad wrestling? Down at the ST 1 level? Not a problem with robust rules!

Sumo-wrestling toads; Ohara Koson (1877-1945)

10 Comments

  • Keith Collins

    This is simply awesome,

    I have been looking for ways to have characters roll vs ST to use their basic lift and derivatives and have body weight and encumbrance factor into the equation.

    This is a simple and elegant solution!

    From the charts. explanation, formulas, to the Sumo Toads (look out Ninja Turtles) top notch work that has saved me time.

    Hats off to you sir!

    • tbone

      Thank you for the kind words! If you do anything particularly interesting with ST Roll and weight mods or whatever else is useful up there, please drop a comment here. I imagine there are many more uses for the tools than I’ve thought of…

  • Maximilian D Wilson

    Whew! I’m excited by the header, and I took a look at the STROLL table and mentally worked through some examples like a DF Knight pinned by a jelly or a giant ape, but there’s a lot to digest here. I’m excited by also intimidated and now mentally “full” for a bit.

    This is an important topic and I am glad it is getting attention. ST isn’t like the other stats. I will have more to say after I examine the solution and its derivation.

    Thanks T-bone!
    Max

  • Maximilian D Wilson

    I love the concept–it’s very elegant–and I’ve been tinkering around with Regular Contests to represent grappling/pinning. I like the idea of converting all grappling regular contests to exponential contests scaling the lowest value to 10. However, it turns out that even the more-precise purple table has at least one rounding artifact:

    Specifically, ST 10 (STRoll 10) vs. ST 15 (STRoll 16) gives a +6 margin, but ST 12 (STRoll 13) vs. ST 18 (STRoll 18) gives only +5.

    The non-rounded table for convenience:

    ST 8 STRoll 7 (6.78)
    ST 9 STRoll 8 (8.48)
    ST 10 STRoll 10 (10.00)
    ST 11 STRoll 11 (11.38)
    ST 12 STRoll 13 (12.63)
    ST 13 STRoll 14 (13.79)
    ST 14 STRoll 15 (14.85)
    ST 15 STRoll 16 (15.85)
    ST 16 STRoll 17 (16.78)
    ST 17 STRoll 18 (17.66)
    ST 18 STRoll 18 (18.48)
    ST 19 STRoll 19 (19.26)
    ST 20 STRoll 20 (20.00)
    ST 21 STRoll 21 (20.70)
    ST 22 STRoll 21 (21.38)
    ST 23 STRoll 22 (22.02)
    ST 24 STRoll 23 (22.63)
    ST 25 STRoll 23 (23.22)

    We can see from this that ST 12 vs. ST 18 ought to have a margin of 18.48-12.63 = 5.85, which rounds to 6 (just like all the other cases do, like ST 10 vs. ST 15 (15.85 – 10)).

    I think what I’ll probably do is make the unrounded table the canonical table, but use the purple table in practice with a mental note that contests of ST 12 vs. 18 are a special case due to rounding, and to ignore the purple table in that case and treat the margin as +6.

    I love it. Thanks, T-bone!

    • Maximilian D Wilson

      One more followup–a complete list of all rounding artifacts in contests between ST 1-25. Some of them are pretty significant to gameplay, e.g. ST 11 vs 12 should be +1, not +2. That’s the difference between a 62% success rate and a 74% success rate!

      I think this persuades me to use the unrounded table instead of the green or purple table, even in practice.

      ST 1 vs. 9: Rounded margin +31. Should be +32 (+31.70)
      ST 1 vs. 11: Rounded margin +34. Should be +35 (+34.59)
      ST 1 vs. 18: Rounded margin +41. Should be +42 (+41.70)
      ST 1 vs. 22: Rounded margin +44. Should be +45 (+44.59)
      ST 2 vs. 9: Rounded margin +21. Should be +22 (+21.70)
      ST 2 vs. 11: Rounded margin +24. Should be +25 (+24.59)
      ST 2 vs. 18: Rounded margin +31. Should be +32 (+31.70)
      ST 2 vs. 22: Rounded margin +34. Should be +35 (+34.59)
      ST 3 vs. 9: Rounded margin +15. Should be +16 (+15.85)
      ST 3 vs. 11: Rounded margin +18. Should be +19 (+18.74)
      ST 3 vs. 18: Rounded margin +25. Should be +26 (+25.85)
      ST 3 vs. 19: Rounded margin +26. Should be +27 (+26.63)
      ST 3 vs. 22: Rounded margin +28. Should be +29 (+28.74)
      ST 3 vs. 25: Rounded margin +30. Should be +31 (+30.59)
      ST 4 vs. 9: Rounded margin +11. Should be +12 (+11.70)
      ST 4 vs. 11: Rounded margin +14. Should be +15 (+14.59)
      ST 4 vs. 18: Rounded margin +21. Should be +22 (+21.70)
      ST 4 vs. 22: Rounded margin +24. Should be +25 (+24.59)
      ST 6 vs. 9: Rounded margin +5. Should be +6 (+5.85)
      ST 6 vs. 11: Rounded margin +8. Should be +9 (+8.74)
      ST 6 vs. 18: Rounded margin +15. Should be +16 (+15.85)
      ST 6 vs. 19: Rounded margin +16. Should be +17 (+16.63)
      ST 6 vs. 22: Rounded margin +18. Should be +19 (+18.74)
      ST 6 vs. 25: Rounded margin +20. Should be +21 (+20.59)
      ST 7 vs. 9: Rounded margin +3. Should be +4 (+3.63)
      ST 7 vs. 11: Rounded margin +6. Should be +7 (+6.52)
      ST 7 vs. 18: Rounded margin +13. Should be +14 (+13.63)
      ST 7 vs. 22: Rounded margin +16. Should be +17 (+16.52)
      ST 8 vs. 9: Rounded margin +1. Should be +2 (+1.70)
      ST 8 vs. 11: Rounded margin +4. Should be +5 (+4.59)
      ST 8 vs. 18: Rounded margin +11. Should be +12 (+11.70)
      ST 8 vs. 22: Rounded margin +14. Should be +15 (+14.59)
      ST 9 vs. 12: Rounded margin +5. Should be +4 (+4.15)
      ST 9 vs. 13: Rounded margin +6. Should be +5 (+5.31)
      ST 9 vs. 14: Rounded margin +7. Should be +6 (+6.37)
      ST 9 vs. 15: Rounded margin +8. Should be +7 (+7.37)
      ST 9 vs. 16: Rounded margin +9. Should be +8 (+8.30)
      ST 9 vs. 17: Rounded margin +10. Should be +9 (+9.18)
      ST 9 vs. 21: Rounded margin +13. Should be +12 (+12.22)
      ST 9 vs. 24: Rounded margin +15. Should be +14 (+14.15)
      ST 11 vs. 12: Rounded margin +2. Should be +1 (+1.26)
      ST 11 vs. 13: Rounded margin +3. Should be +2 (+2.41)
      ST 11 vs. 14: Rounded margin +4. Should be +3 (+3.48)
      ST 11 vs. 15: Rounded margin +5. Should be +4 (+4.47)
      ST 11 vs. 16: Rounded margin +6. Should be +5 (+5.41)
      ST 11 vs. 17: Rounded margin +7. Should be +6 (+6.28)
      ST 11 vs. 21: Rounded margin +10. Should be +9 (+9.33)
      ST 11 vs. 24: Rounded margin +12. Should be +11 (+11.26)
      ST 12 vs. 18: Rounded margin +5. Should be +6 (+5.85)
      ST 12 vs. 19: Rounded margin +6. Should be +7 (+6.63)
      ST 12 vs. 22: Rounded margin +8. Should be +9 (+8.74)
      ST 12 vs. 25: Rounded margin +10. Should be +11 (+10.59)
      ST 13 vs. 18: Rounded margin +4. Should be +5 (+4.69)
      ST 13 vs. 22: Rounded margin +7. Should be +8 (+7.59)
      ST 14 vs. 18: Rounded margin +3. Should be +4 (+3.63)
      ST 14 vs. 22: Rounded margin +6. Should be +7 (+6.52)
      ST 15 vs. 18: Rounded margin +2. Should be +3 (+2.63)
      ST 15 vs. 22: Rounded margin +5. Should be +6 (+5.53)
      ST 16 vs. 18: Rounded margin +1. Should be +2 (+1.70)
      ST 16 vs. 22: Rounded margin +4. Should be +5 (+4.59)
      ST 17 vs. 18: Rounded margin +0. Should be +1 (+0.82)
      ST 17 vs. 19: Rounded margin +1. Should be +2 (+1.60)
      ST 17 vs. 22: Rounded margin +3. Should be +4 (+3.72)
      ST 17 vs. 25: Rounded margin +5. Should be +6 (+5.56)
      ST 18 vs. 21: Rounded margin +3. Should be +2 (+2.22)
      ST 18 vs. 24: Rounded margin +5. Should be +4 (+4.15)
      ST 19 vs. 21: Rounded margin +2. Should be +1 (+1.44)
      ST 19 vs. 24: Rounded margin +4. Should be +3 (+3.37)
      ST 21 vs. 22: Rounded margin +0. Should be +1 (+0.67)
      ST 21 vs. 25: Rounded margin +2. Should be +3 (+2.52)
      ST 22 vs. 24: Rounded margin +2. Should be +1 (+1.26)
      ST 24 vs. 25: Rounded margin +0. Should be +1 (+0.59)

      Code: https://gist.github.com/MaxWilson/fa57042f7a21cb5844ccc61acc4b9860

    • tbone

      Thanks for the great checking of numbers. I have some travel coming up so won’t be able to look at them in detail for a few days. But to be sure, I would expect that even the precise table is imperfect, in that a given ST multiple won’t yield the same margin everywhere you look. Such is rounding.

      What’s key, though, is that these “off by 1” comparisons will appear less often with the precise table than with the standard table. And more importantly, unless I’m missing something, such a discrepancy in margins should never be 2 or greater, only 1. (If you find a discrepancy of 2 or greater, let me know; I think that’d mean a mistake in the table!)

      • Maximilian D Wilson

        The error is never greater than 1.0, but as a matter of taste I would rather be sure that a given strength ratio always yields the same odds in a Regular Contest, so I will use the formula instead of the table.

        • tbone

          Fair enough! I want to emphasize ease of picking up and introducing the rule for potentially interested GMs, so the friendly-looking green Table gets the attention in the article. But I happily tip a salute to your solidly worked out variant numbers that aim for best precision.

          In the end, what’s key to me is that even the green Table’s somewhat roughly-rounded numbers are a big improvement over “ST 1 vs ST 2? Oh, that’s just a difference of 1, so it’s a nearly even Contest”.

          • Maximilian D Wilson

            As a matter of pedagogy I think the decision to start with the green table is a wise choice. : ) You provided the formula so it’s easy for nitpicky GMs like me to adjust the precision. Precomputing the logarithms is a key insight, and scaling those logarithms to roughly match normal ST ranges is also great. Thank you for this work!

            P.S. The sumo frog picture is great too!

            • tbone

              Maybe the master plan is to get ’em hooked on the easy Table; then tell ’em that what they really want is the precise Table. Bait and switch! (Then I’ll hit ’em for the extended warranty and dealer undercoating, too. HA HA HA)

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