Challenge Systems: Quantitative Analysis

A core element of many games (both board games and RPGs) is the binary challenge resolved by a dice roll. This might represent an attempt to hit a target with an artillery piece, an attempt to jump over a chasm, or an attempt to persuade a guard to let you past a security door. Previously I discussed the four possible ways to implement the roll itself: rolling over a target versus under it, and modifying roll results versus modifying targets. For example, a roll-high and modify-result system would involve something like "If your 1d20+3 roll is greater than or equal to 15, then you succeed".

This is mostly an aesthetic issue. From a gameplay perspective, a more important question is how the probability of success changes as modifiers are added. This depends on whether how many dice are rolled (a multi-dice bell curve generates diminishing returns in both wings), what modifiers are applied, and how targets are set. There are an infinite number of different possible systems, but I'd like to focus on four distinct approaches in existing RPG games. The systems are:

1. Moldvay's B/X edition of D&D, which used a simple "roll a 1d20, with result at or under the attribute to succeed"
2. The system proposed by Wesley Ives in Dragon #1 (June, 1976), for use with original 70s-era D&D. This system is rather baroque in presentation, even by the standards of that era, involving rolling lots of dice both to set the target and then to test it.
3. The modern convention of a "skill system", with small modifiers based on attributes. Here I've chosen the SEIGE engine (from Castles & Crusades) as a representative example, using a non-prime target of 12, although most other post-3.0 systems in the OGL d20 line work in a similar way.
4. The use of multiple dice against a single target. In this case, I've elected to use the D6 engine from 80s-era West End Games products (like Star Wars), also using a target of 12. (d20 attribute points have been converted one-for-one into "pips" for the calculations below.)

One comment on the "skill system" approach. In practice, this system has substantial modifiers based on custom design, which shift the chance of success up linearly as "skill points" are invested in a category. In practice, however, this kind of system involves illusory improvement, in that the targets (DC's) are simply adjusted higher at the same rate! (In fact, I think the 3.5 DMG explicitly instructs the DM to do precisely this.) So the skill system, rather than producing real improvement, just places characters on a leveling treadmill where they start to fall behind in any category where they fail to pay the appropriate "skill tax".

Here are the results of a computer simulation of 100,000 dice rolls using each method, to show the qualitatively different effects that this choice has on the game system.

The Moldvay approach creates a linear success rate, and the skill-based approach flattens the chance out substantially without altering linearity. (Of course the DM can rather easily shift the entire line upward or downward, by the use of DC-setting fiat powers!) Attributes matter much less in a modern game, apparently.

The Ives system, despite apparent complexity, has a simple effect. It takes the Moldvay system and forces it to saturate at high skill levels, bending it down into sublinearity. This means that even when using his optional bonuses (including level), the chance of success improves very slowly beyond a certain point. This is an excellent example of the design principle of diminishing returns! I rather like this feature, despite the obscurantist feel of the convoluted mechanics.

The multidice system involves a true bell curve of results, which shows up here as an S-curve in the binary check. Note that below a certain point, success is basically impossible, but even at the top end there's a small chance of failure. An alternative system is to replace the roll-high system with a roll-low system (as used in, say, Ninja Burger or Kobolds Ate My Baby), which reverse the curve ends to always provides a small chance of success at the low end, with guaranteed success at the high end. This friendly option works well for beer-and-pretzels games, where you never want a check to be impossible.

Overall, it's hard to beat the Moldvay roll-under-attribute system for simplicity, but I think I prefer the Ives system on philosophical grounds. I wish I could find a way to implement it with less complexity, though!

WiF Optional Rules

With ambitions for a summer WW2 campaign using the World in Flames Deluxe set, I've been pondering the use of a few optional rules beyond the ones included in the RAW. In particular, I'd like to make production less random; currently it just involves drawing counters blindly from the available force pool, which can result in oddities like the British accidentally building an Australian infantry just as the Germans are massing an invasion fleet! It's also difficult to draw units randomly when using magnetized counters, which make it impossible to use the old "shake 'em all up in your hands and draw" method.

The first rule is from our old days at the Calvin Historical Simulations Club:

What's in this stack?!?

• Fog of War: The units in each stack of the board are normally concealed, except during combat by any units that cover them. Any other player may request to see only the top land unit, the top naval unit, the top air unit, and any stationary assets like fortifications or factories.

The advantage of this rule is that is prevents excessively time-consuming calculation of pre-combat odds, and represents a realistic level of operational intelligence.

The second rule, which I'm proposing for the first time, is intended to reduce production randomness:

• Production Specialization: Sort units into force pools (and sub-pools) as usual. Any pool that contains only units that have no year-dates on the reverse side must build randomly, as usual. For any other pool, do the following.
• If the pool contains units from only one year, the unit(s) to be built may be selected non-randomly by the builder.
• If the pool contains units from more than one year, and a single unit from the pool is built, it may be selected non-randomly by the builder, but may not be from the most recent year.
• If the pool contains units from more than one year, and multiple units from the pool are being built, then the first unit must be selected non-randomly from the earliest year available, but all subsequent units may be selected non-randomly from any year.

That's a little more complicated to explain than the current rule, but it should be faster to apply it in practice. It avoids the horrendous ordeal of constantly having to sort out force pools at the end of each turn, or else buying a stack of extra game trays to keep them sorted. The logic behind this is that, if you are building just one bomber wing a turn, your Ministry of War Production isn't going to be nearly as proficient at designing good planes as it would be if it were cranking out a dozen bomber wings.

There are a few weird side effects from this rule, like the fact that small powers like the Chinese will have to wait an extra year to build most of their top-end units. On the other hand, they'll get to avoid the indignity of having to build some completely obsolete junk, which helps to balance it out.

Building A Magnetic Game Surface

Pretty much any game with a high counter density is in constant danger of being instantly destroyed by an errant elbow brush, table-leg kick, or gust of wind. And never mind the curious 18 month-old child I currently have roaming the house. So I'm currently trying to build my own portable gaming panel with a magnetic surface, so I can do something like this:

OK, I'm a long way from having anything that works this well, but I did put together a rudimentary approximation to the basic concept. Currently I have three 22-gauge metal plates, side by side, backed with a sheet of 11/32' plywood. That's not very sturdy, but it does have the merit of being something I can move by myself if necessary. That's the right size for both World in Flames maps at their usual scale, or for a single map if it's been double-sized as in the image above. I really need to buy a set of self-driving wood-screws to connect the plates more firmly to the wood. Currently they're just held on with duct tape and carpet tacks. (I tested this with two tiny screws I found around the house, and they work great.) I definitely should have bought a sturdier wood board, too, even at the cost of needing a second person to transport the game.

Alas, the set of  400+ game counter magnets I own seems to have been stored improperly (too much heat? not aligned correctly during transport?) and the magnets no longer grip the metal as well as they should. The idea of turning the board vertically and mounting it on the wall seems to be out of the question. At the same time, they do snap together into useful stacks, and they don't slide around nearly as much as they would if they were free, so I still consider it an improvement over non-magnetic counters. At least I should be able to move it into a back room less accessible to toddler fingers and pedestrian traffic, in between sessions.

If anyone has the slightest idea of where to buy the (apparently discontinued) 1/2" game counter tiles that used to be sold in a box that looks like this one, let me know. I see only a single instance of them being sold on Ebay within the last year, so the existing stockpile must be either dwindling or subject to hoarding. Looks like an economic opportunity for a magnetic-sheet manufacturer to exploit. Or maybe that's just wishful thinking, in an age where hex-and-counter games are virtual dinosaurs.

MEK-OP Game Night: Final Exam Week!

Everyone was busy with the wrap-up of the semester (I'm giving an exam on Monday, Tuesday, and Wednesday), so we just spent a few hours playing through the first half of a Runebound game (1st edition). With six people the pace of the game is significantly slower, but I think everyone still had fun. We had to quit just as I had assembled a perfect combo of melee maces!

A few thoughts about the game:

• Although the biggest changes from 1st to 2nd edition was the norming of the dice distribution (2d10 vs 1d20) and necessary tweaks to keep the game challenging, playing with this many players makes it absolutely essential to use regenerating encounters. That's a rule that should import pretty easily from 2nd edition without needing to use the 2e Adventure Card set.
• The combat system is apparently more confusing to other people that I expected. I needed to explain it a few times before it made sense. It's very counterintuitive that "attacking" and "defending" use the same mechanic and can both cause damage to you after a failed check.
• The movement system is still wonky to me, since it doesn't really reflect any simulationist attitude toward terrain difficulty. Walking along a road, for example, requires "road face" results -- which means that it's almost impossible to be allowed to walk along four consecutive roads instead of taking a mandatory detour through the nearby mountains! Whether this sort of thing bothers you or not is probably a signature of where you reside on the vertical GNS axis.

For my own purposes in designing an "exploration game" that involves some similar pseudo-RPGish elements, the aspect of this game that I'd most like to modify is the "downtime" issue. I don't want to completely eliminate downtime; it's actually an advantage in slow, strategic games that are left up over multiple sessions so that, for example, my wife can put my daughter to bed while the rest of us keep playing. But I do want to make it more optional, and create a role for players who are not active in the turn cycle.

Some ideas for how to keep off-turn players engaged in a multiplayer adventure board game:

1. Group players into teams. I always prefer this approach to a free-for-fall once the number of players goes past three. In some games, even three players makes for too many sides to be stable in game-theoretic terms. (It's easy but rare for a two-player game to create an asymmetric equilibrium, but trivially easy to accomplish in an n-player game.) With good coordination, a team of players can complete certain portions of the game (like movement) simultaneously, speeding up the sequence of play.
2. Give players an intervention mechanism that activates during other players' turns. In a free-for-all, this needs to be something that involves hostile interference: playing a "wandering monster" in Munchkin, say, or anything in the Dungeonlord phase of Dungeoneer. But in a team-based game, this could be a form of material support. I prefer the latter mechanism since it has simulationist precedent (Lend-Lease during WW2, for example), which avoids the question of "Why am I suddenly playing the bad guys now?" In some games, it might make thematic sense that the enemies could be influenced by agents of the other team.
3. Segregate starting points. Instead of having all six players begin at the same location (which forces them to go one at a time in a race to valuable objectives/resources, etc), the players can then spend the early development portion of the game doing simultaneous movement. This works pretty well in 4x strategy games that involve exploration.

I'd recommend the first and the third ideas, but also apply the second idea sparingly. I can see some merit in having the game start with (3), and then transition toward emergent or preset alliances (1) and occasional cooperative interventions (2). But I appreciate a very small component of hostile intervention (2) to function as a wildcard, as long as it doesn't preclude effective strategic planning. Everyone deserves a healthy backstab now and then, right?

Strategy RPG History

Just a few days ago, I commented on the fact that I had seen very few examples of strategic level board games that involved a neutral arbiter (umpire, judge, etc), to allow for hidden information and general player-neutral aspects of gameplay. I only lived through the 80s and 90s, and even then had only limited experience with a range of game activities during those periods (mostly Avalon Hill games on the board-game side, and West End systems on the RPG side). History goes back quite a bit farther than that, and so I've been reading through Peterson's Playing at the World to get more of the backstory.

One area of activity of which I had little awareness was the innovative play-by-mail community during the 1960s. Peterson spends a great deal of time delving into the publications of various groups involved in PBM campaigns for Avalon Hill's Diplomacy. Although I had played this a few times back in college (as a single-night "one-off" when we weren't running something larger), I hadn't really appreciated its popularity during the wargame era. In fact, if someone had told me that such a simple game had been able to generate extensive activity of the sort that we'd today classify as "fan-fic", "LARP", and "cosplay", as a sort of abstracted counterpart to the SCA, I would have found it hard to believe.

A multi-player game, when played by mail, can only be manageable when information is centralized through a single player who functions as the hub, and a neutral referee is probably the only fair way to accomplish this. What's more interesting is that, almost as soon as the player-referee structure is established, players seem to have begun speaking in the voice of a dramatic persona (what we'd today call "in-character", or IC) to create a fictional narrative. Once someone else takes responsibility for running the mechanical side of the game, the players are freed to concentrate on immersion and story-telling. This is despite the fact that Diplomacy is nearly as abstract a game as chess!


Oh, a fascinating bit of trivia I learned: The now-standardized trope of dragons (and other similar mythical creatures) being distinguished by a set of vivid primary colors is actually something that traces to this era. The original publication of the various canonical chromatic dragon types (black, white, red, green, blue, and the so-called "purple worm") was actually in a Diplomacy fanzine written to support a Lord of the Rings variant game being played by mail. The author, "Professor S.K. Eltolereth" (an apparent Gygax pseudonym) was really intended to support the narrative of one of these postal campaigns.

Let me say that again. The purple worm was invented to play this game. I just can't get over how strange and wonderful that is. Don't ever change, obsessive fantasy fans. Don't ever change.

Curious Feature Of Naval Thunder

There are three basic dice mechanics in this game system:

1. A "to-hit" check, using "roll high, modify target".
2. A "penetration" check, using "roll high, modify result". Just to make things extra confusing, for this one it's necessary to beat the target and not just match it.
3. A damage control (or command) check, using "roll low, modify result".

Oh, and critical hits use a hash-table with a bell curve, placing less damaging criticals (guns, engines) in the center of the distribution, and more dramatic results (bridge, magazine) out in the tails.

Three different systems, three totally different implementations. That's pretty unusual in games today. The only mechanic missing from the list is the rarely-encountered "roll low, modify target" method, which is the one I actually like best!

I'm kind of curious why the designer used such a piecemeal approach, but I think I have my own idea. For the to-hit roll, it's often necessary to roll identical guns from the same ship against two different targets. For the penetration roll, it's necessary to roll different guns against the same target. This is something I encountered during the design of a morale system for the fast-combat system I wrote over the summer. All of a sudden, I wanted to apply a single roll against a variety of different targets, and suddenly a "modify target" system made perfect sense. And so I can respect the decision.

I think that so many games today use result modification instead of target modification that even when a target-mod system makes logical sense, designers still try to shoehorn everything into the industry standard. I chalk it all up to lingering trauma over the complicated "THAC0" experiment, which tried to mix negative bonuses to the target with positive bonuses to the result, all at once. That was probably a bridge too far, even by my standards.

MEK-OP Game Night: Naval Thunder

Tonight I was all prepared for an all-out brawl, fighting the surface engagement of 1st Guadalcanal on a set of four tables. But apparently we were too close to final exams, and so attendance was greatly truncated. Instead, we played out a quick daylight engagement between a few forces from the official order of battle.

IJN Hiei's historical fate: crippled and hunted down

The Imperial Japanese Navy (me!) ended up with

• Battlecruiser Hiei
• Two destroyers

The US Navy took

• Two heavy cruisers (Portland and San Francisco)
• Two light cruisers (Atlanta and Juneau)

 It was probably a good thing we scaled things back, since the fight still took most of the evening. By sheer luck, I think, it was a remarkably balanced scenario.

Both destroyers went down quickly as they attempted to close to torpedo range. In hindsight, I think it actually makes more sense to hold the destroyers behind the battlecruiser and use them to engage anything that tries to close range, rather than detaching them. Using the larger ship to block line-of-sight doesn't "feel right" historically, but on the other hand, it might have been the correct lesson to learn from 2nd Guadalcanal!


The Japanese battlecruiser took a long time to kill. It knocked off two cruisers before it started taking fire control criticals, but still had plenty of hull integrity left. At that point the battle slowed to a grind, with the lighter American cruisers mostly unable to penetrate heavy armor, but the Hiei's main battery effectively blinded.


Superstructure criticals eventually took their toll. By the end of the battle, the Hiei was reduced to about 20 hull points (two good hits away from death), and was suffering from serious fire damage. A lucky bridge critical finally drove it from the battle, leaving the Portland as the sole survivor... with less than a quarter of its hull strength remaining, and half its guns silenced.


In a few situations, the battle could have swung in a radically different direction. The Juneau missed with both its port and starboard torpedo volleys, which could have ended the engagement quickly. But the Hiei suffered from poor long-range gunnery that allowed the battle to even last long enough for the range to close. Still, we present the victor of the battle, whether by tenacity or luck: the Enterprise's faithful handmaiden, USS Portland.

• Two destroyers

The US Navy took

• Two heavy cruisers (Portland and San Francisco)
• Two light cruisers (Atlanta and Juneau)

 It was probably a good thing we scaled things back, since the fight still took most of the evening. By sheer luck, I think, it was a remarkably balanced scenario.

Both destroyers went down quickly as they attempted to close to torpedo range. In hindsight, I think it actually makes more sense to hold the destroyers behind the battlecruiser and use them to engage anything that tries to close range, rather than detaching them. Using the larger ship to block line-of-sight doesn't "feel right" historically, but on the other hand, it might have been the correct lesson to learn from 2nd Guadalcanal!

The Japanese battlecruiser took a long time to kill. It knocked off two cruisers before it started taking fire control criticals, but still had plenty of hull integrity left. At that point the battle slowed to a grind, with the lighter American cruisers mostly unable to penetrate heavy armor, but the Hiei's main battery effectively blinded.

Superstructure criticals eventually took their toll. By the end of the battle, the Hiei was reduced to about 20 hull points (two good hits away from death), and was suffering from serious fire damage. A lucky bridge critical finally drove it from the battle, leaving the Portland as the sole survivor... with less than a quarter of its hull strength remaining, and half its guns silenced.

Image Source: http://grzegorz-nawrocki.com/

In a few situations, the battle could have swung in a radically different direction. The Juneau missed with both its port and starboard torpedo volleys, which could have ended the engagement quickly. But the Hiei suffered from poor long-range gunnery that allowed the battle to even last long enough for the range to close. Still, we present the victor of the battle, whether by tenacity or luck: the Enterprise's faithful handmaiden, USS Portland.