Gambling for Checks

Earlier I've written about using alternate mechanics for skill checks:
http://vedronspotionshop.blogspot.com/2009/12/gambling-for-skill-checks.html
http://vedronspotionshop.blogspot.com/2009/12/more-on-gambling-and-auctions.html
http://vedronspotionshop.blogspot.com/2009/04/hack-overview-of-classes.html

Upon a little more thought, I was thinking that it might be appropriate to use this mechanic as a class or archetype specific one. That's one neat thing about AD&D: each class has its own mechanics, which makes them feel unique. Clerics have the turn undead table, magic-users vancian magic, and fighters use the THAC0 D20 roll more than anyone else. Thieves have their percentile charts, but I've never been a big fan of those.

What if you used a Klondike poker style mechanic for a trickster/rogue type archetype? That seems like it would perfectly reinforce the desired feel of the class. The trickster is a classic archetype that goes back through the earliest literature.

The scenes in Heinlein's "The Moon is a Harsh Mistress," where Loonies casually roll for almost every transaction, are really flavorful in a book and I think it could be equally flavorful for an RPG.

One issue is that manipulating the odds in Klondike is obscure. The easiest way is to deal with ties: If ties are a tie (resulting in a reroll), then the chance of the player winning at 50/50. If ties go to the house/DM, then the DM has an edge of 5%. If ties go to the player, then they have an edge of 5%. I am not sure how rerolling dice or rolling larger pools would manipulate the odds (although I can tell in which direction they'd move). Another method might be to manipulate information if betting is involved. For example, a skilled character might have the privelege of last action (like being the big blind in Texas Hold 'Em). This lets them see what their adversary roles before they place a bet. If unskilled, then they might have to place their bets with no such advantage.

Alternatively, you could just keep the odds pretty much 50/50. This encourages roguish types to only use their special skills against very hard tasks. For example, if the normal chance to succeed is much less than 50%, then the rogue's gamble is a big improvement in the odds. If the chance to succeed is much greater than 50%, then its a foolish gamble. That could also be interesting as a mechanical way to reward (and permit) the trickster archetype to bite off more than he can chew!

However the details are worked out, I think its an intriguing idea for a class-specific mechanic. Double or nothing!

Scales

Delta has been blogging about this topic lately too.

Why I Don't Game Much These Days

Recently DW and I had a discussion about why we aren't gaming much right now. Here's the list of factors we came up with, in no particular order:

• Not socially acceptable among our circles of friends from work.
• Tired of maintaining two separate circles of friends -- it requires lots of energy.
  
• Takes up too much time: In college, we could easily throw together an impromptu session. Everyone lived within 20 mins of each other, so it was easy to say, "Hey, you free? Yeah? Me too. Let's meet up in 15 mins and play for an hour." Now, it requires scheduling ahead of time. We were playing in a real time game via skype with our old college group which was fun, but it required wiping out a whole day every weekend. The beauty of gaming locally is that you can utilize time you would have wasted anyways watching TV or something.
  
• Worried about the character of people we game with. We had a bad experience with a group in Texas where one of the members turned out to be a felon or something. Associating with such types is bad juju for both of our jobs. Unfortunately, it seems like our hobby tends to attract a fair number of skeezy sketchy dirtbags.
• Elitism -- we won't accept a shoddy DM. I will DM but it gets tiring.
• Online play by post games often move too slowly and require a much higher effort to entertainment ratio than tabletop games do -- especially to run.
• Constantly moving. Since 2007, I've lived in three states. Since 2008, I've spent less than 9 months at home due to travel for work. Its just too hard to build a cohesive group much less a decent campaign in that time.

So, for now, I am playing in a single 4E arena game online (its actually quite enjoyable). That's about it. We've thought about running some games between just the two of us but that seems weird. It'd be nice to have another two gamer couples that lived nearby, so you could whip up a three person + DM group anytime.

Moving between scales

Recently I've been discussing a more fleshed out set of rules for "Hexploration." Hit the tag at the bottom to see the post series.

Previously, I discussed the "rule of three's" ability to help you move between different scales. Keeping a consistent ratio between the levels of scale certainly helps with this!

Now that I have come up with a relatively stable set of time/distance relationships, let's flesh out how you can move between one scale and another. For now, I'll just cover movement. We can extrapolate to other issues later.

PRINCIPLE #1: A character moves 4+/-MOD hexes every time unit at a normal walking pace. So, in one segment, 4+/-MOD hexes are covered. The MOD could include bonuses and penalties for factors such as ability scores, terrain, burden carried, armor worn, race, etc.

PRINCIPLE #2: The ratio between the distance covered on the initial scale and the distance covered on the next higher scale is, on average, 4:10 (reduced to 2:5, or 1:2.5). Even though one chain is about 10 paces, remember, the average character covers 4 paces in a segment, not one.

PRINCIPLE #3: The ratio between the first order of magnitude and the second order of magnitude is 1:10. There are about 10 chains in a furlong. For now we'll also assume a perfect 1:10 ratio between each scale level even though we know our customary units don't quite match up perfectly.

Here's some data points:

• MARATHONS: A world-record athlete can run a marathon (about 8 leagues -- about 2/3 of a hex on the weekly scale) in about two hours (one "chunk"). The "average" time in the US is about 4:30 for men (~2 chunks) and 6:00 for women (3 chunks). Just walking would take around 4 chunks (1.5 miles x 4 hexes = 6 miles per chunk).
  
• 10K (2 leagues -- the hex size on the daily scale): A world record time is about 30 minutes (3 turns). An average time for a novice runner might be around 60 minutes (6 tuns). Just walking we'd expect it to take about 12 turns.
• 5K (1 league): A world record time is about 12 minutes (1 turn). An average time might be about 3 turns. A walking pace would be about 6 turns.
  
• SPRINTERS: A world-record athlete in the 200 meter sprint covers 1 furlong (10 chains or 132 -- we will assume 100 -- paces... Normally, 4+/-MOD are covered in a ~10 minute turn) in about 20 seconds (3 segments). An average time for a decent athlete might be around 25 seconds (~4 segments). I don't have a good time for an "average" person, but 5-6 segments might be accurate. I should go run one... Just walking, we'd expect it to take 26 segments.
  
• HORSE RACES: The record for a horse running a two-mile race (normally the size of a hex for a "chunk") is just over three minutes (3 rounds). I don't have a time for an average horse trotting. Walking, we'd expect a horse covering 6 chain-sized hexes per round to take 26 rounds.
  
• HORSE SPRINTING: The record for a one furlong horse race would be around 10 seconds; I'm extrapolating from records for two furlong races here. So, we're going from a furlong (normally measured in turns), skipping a round, and ending up with ~1-2 segments. Walking, we'd expect a horse to cover a furlong in about 22 segments.
  

What do I extrapolate from these admittedly limited data points?

• There is a noticeable difference between expert and average performance. The difference becomes most marked in the middling distances, and less pronounced when sprinting.
  
• The ratio between an expert's performance, an average performance, and a performance requiring no extra expenditure of energy is about: 1:2.5:7. That is, the expect can accomplish in about 1/2 the time what the average to above average person can do. The average person can exerting effort can cover a distance in about 1/3 the time expected.
  (If you reduce the ratios above you get, with a bit of rounding: 1:2:4... 1:2:4... 1:3:6... 1:3:6... 1:2:9... Horses -- 1:X:9... 1:X:11...)
• "If you are operating on Time Scale X, an expert can cover one distance unit of Scale X+2 with great effort using approximately 3 Time Scale X units. An average individual also exerting effort requires approximately 7 Time Scale X units. Just walking would require an average individual to expend 27.5 Time Scale X."
  Example: "If you are operating in Combat Segments/Paces, an expert can skip chains and cover one Furlong in around three segments. An average individual exerting great effort requires about seven segments. Just walking would require about 28 segments."
  
  Exceptions: Exceptions are required when you start dealing with the transition to weeks/12 leagues; a different ratio is needed for the strategic scales as they are based on a 1:4 ratio rather than a 1:10 ratio.

Let's talk recovery time. Recovery time after a marathon takes 1-4 weeks. Sports medicine has found that it takes about 2 days for a fit runner to recover from a 10K. It takes 10-30 minutes or so to recover from being winded after a 200 meter sprint. Less well trained athletes take longer to recover. Interestingly, that's the amount of time that corresponds to the distance scale! So, let's add another point:

• "Expending significant effort means that, you expend a resource that is recovered on the Time Scale of X+2. One way of implementing this would be to require you to expend a resource each and every Time Scale X that elapses, with an approx 50% to avoid expending it."
  

Let's put this into game rules terms.

ACCELERATED MOVEMENT AT HIGHER DISTANCE SCALES (FORCE MARCH AND RUNNING):
1) Make an appropriate check, for example, "Athletics," "CON + Athletics," etc (system dependent; if no skills are utilized, the DM shall utilize a 2/3 chance of success for expert characters and a 1/3 chance of success for amateurs).
2) You take a wound appropriate to a scale equal to your current one + 2. For example, tactical combat (Segment) wounds are often measured in individual HP; a wound taken in combat measured over turns would be about 25 times as intense, or would take several turns to recover. For example, the DM may rule that you expend healing surges or temporarily gain negative levels. You may make a saving throw (system dependent, but should have approx 50% odds of success) to avoid this damage.
3) Move the normal distance allowed at your scale.
4) Once you have accumulated two successes, you automatically move one hex of the distance two scales greater. Special: If your move is 8 or greater, then you accumulate two successes with one good check. If your move is 2, then you accumulate 0.5 successes with every good check. If your move is reduced to 1, then accumulate only 0.25 successes with every good check!

Example of Play: Running a Marathon
The players need to cover 12 leagues in a hurry to deliver a critical message. This is 36 miles -- longer than a traditional marathon -- but in the same ballpark.

One character, a dwarf in heavy armor trained in running has a 66% of success every check he makes. However, because his modified speed is two, he will need to accumulate four successes, not just two. On average, this will take him six checks (six chunks). He will finish the race in about 12 hours, and is likely to expend about three healing surges as wounds.

Another character, a human who is untrained in running, has but a 33% of success. It will also take them about six checks to accumulate the required successes. On average, this character will finish with the dwarf!

Another character is a human athlete with a 66% of success. This athlete will, on average, run the course in three checks (six hours). This is a pace of 6 miles per hour. If fortunate, he could finish in two chunks for a pace of 9 MPH. These are a bit slower than real world marathon paces but not far off. He will probably incur one or two healing surges as damage.

A final character is mounted on an exceptionally swift courser with speed 8! He could finish in as short as one chunk (two hours), but it will probably take 2-3 chunks depending on his horsemanship and the courser's training.

Example of Play: Running a Marathon
A character seeks to disengage from a melee occuring at the segments/paces scale. He is trained in athletics and has a move of 4.

The first segment, he moves his normal speed and must make a saving throw to avoid taking some sort of significant damage that will take turns to recover from. He makes his check and succeeds! One success. He is still in the melee however and can certainly be chased or targeted.

The second segment he fails his check -- no success accumulated -- but must still check for fatigue damage. He still gets to move his speed, however, and is still part of the melee.

The third segment, he succeeds. He checks for final fatigue and moves a whole furlong away. He's probably removed from the melee, although missile fire may be a factor. Unless pursued, the character can be assumed to have disengaged.

Another hack at appropriate scales

I wanted to take another hack at the scales to try and come up with a system that preserves a consistent ratio between each scale.

This is the original system:

• 1 month: 48 leagues (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
  
• 1 week: 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day: 2 leagues -- 36 x 54 miles (duchy?)
  
• 2 hour "chunks:" 2 miles (if you require 2 chunks/day for downtime)...or 0.5 leagues (if downtime is abstracted -- 12 x 18 miles or 9 x 13.5 miles (barony?)
  
• 1 turn (~10 mins): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1 min): 4 rods (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~10 seconds): 2 paces (10' or ~3 yards) -- 20 x 30 yards (1/2 rood; about 1/8 acre)
  
• 1 segment (~6 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)

Here's a hack at a system that attempts to maintain a 1:10 ratio as best as possible. In keeping with my love for "7," we'll start with a segment as 7 seconds long!

• 1 year (12 months, 6 x 2 month periods, or 4 quarters): 576 leagues -- Could represent the entire world's circumference with 14 hexes!
  
• 1 quarter or season (12 weeks): 144 leagues -- Larger continents
  
• 2 months (8 weeks): 96 leagues
• 1 month (4 weeks): 48 leagues -- (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
• 1 week (7 days): 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day (24 hours or 10 chunks + mandatory downtime or 12 chunks): 2 leagues -- 36 x 54 miles (duchy?)
  
• 1 chunk (2 hours or 10 turns): 0.5 leagues -- 9 x 13.5 miles (barony?)
• 1 turn (~12 mins or 10 rounds): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1.166 min or 10 segments): 4 rods or 1 chain (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~7 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)

This maintains a strict 1:10 ratio all the way up to "chunks." You have to fudge a bit for Chunks:Days. Days:Weeks also poses a problem, unless you create 10 day weeks.

Another way you could deal with the week issue would be to rejigger the system so as to use 1 hour chunks. Then you can have half-days instead of days, and then use 10 half days for a week (plus a weekend where activity is discouraged).

You could also use odd units; for example, 10 day weeks, like in the ancient Egyptian calendar, or seasons of two months length like the Bangledeshi calendar. Straying from well known units however can cause confusion.

The downside to this system is that rounds and turns are no longer nice even numbers of 1 minute and 10 minutes respectively. The upside is that its very easy to shift between the tactical and early operational scales. Everything is a factor of 10, which allows for easy transitions for the most part.

CONSEQUENCES OF DIFFERING SCALES

Let's think about consequences of differing scales. Say you can expend 1 Mana Point to cast a spell that has a duration of 1 segment. Since all of our scales are linked, you could say that it costs 10 MPs to affect something for a round, 100 MPs to affect a turn, and 1000 MPs to affect a chunk. Everything scales neatly by 10s. This is also great for things like map paper. You can print up a bunch of sheets of hex paper that have large hexes subdivided into 10 x smaller hexes in width. Then you can use them for comparisons between any two scales in the game. It also holds true for consumption of resources: If someone consumes X resources in a one period of time, then they consume 10X resources in the next scale up. A token representing 1 soldier in one scale represents 10 soldiers in another.

However, if the ratio between time units is >10 and the cost continues to increase by 10, then you basically get something for free. For example, let's scale up from a chunk to a day. The cost is now 10,000 MPs, but the player basically got four hours for free when casting the spell! This creates increasing returns: its more efficient to cast the spell to last all day than it is to cast it again every two hours. Alternatively, if you have to drink 1 unit of water every chunk, or 10 units of water each day, its better to just pay by the day.

If the ratio between time units is <10, then it introduces entropy. For example, going from a day (10,000 MPs) to a week (100,000 MPs) costs 10 times as much but you only get 7 times the duration. This creates diminishing returns. Its actually more efficient to play out casting the spell every day than it is to opt for the longer duration of a week. The same would go for, say, food consumption. You're better off ticking off one unit of food every day than ticking off 10 for the week.

One work around is to have a table that let's people know when the ratio is not exactly 1:10. For example, your rule could say, "In general, to go up a scale, multiply by 10. However, if going from days to weeks, you only have to multiply the cost by 7." This obviously increases complexity however.

Another work around would be to somehow compensate for either consistently diminished or augmented returns with a random variable. For example, say you get consistently augmented returns and wish to discourage people from exploiting them by casting all their spells for a day instead of two hours. You could rule that any spell with a duration of 1 day has some percentage chance of backfiring or otherwise failing. If dealing with consumables (say, water) then maybe there's a small chance that extra is expended. If you want to compensate for diminished returns (say, going from 1 day to 1 week) then do the opposite: there's some chance that a random boonful event occurs.

CONSISTENTLY AUGMENTING RETURNS (Ratios >=10):

• 1 Day --> 1 Fortnight (1:14) --> 1 Semester of Six Months (1:12) --> 1 Lustrum of Five Years (1:10)

CONSISTENTLY DIMINISHING RETURNS (Ratios <=10):

• 1 Day --> 1 Week (1:7) --> 1 Month (1:4) --> 1 Season or Quarter of Three Months (1:3) --> 1 Year (1:4) -- 1 Olympiad of Four Years (1:4)
• 1 Day --> 1 Week (1:7) --> 1 Month (1:4) --> 1 Trimester of Four Months (1:4) --> 1 Year (1:3) -- 1 Olympiad of Four Years (1:4)

This system suggests using two scales; Perhaps a 1:10 cost explosion all the way up to weeks (perhaps with a random bonus/penalty system to deal with the awkward 1:12 ratios for chunks to days and 1:7 for days to weeks), then switch to a 1:4 cost ratio for the "strategic" scales. So, if it costs you X units of resources to do something in a week, it only costs 4X units to do it for a month, season, year, or olympiad. Again you might need a random bonus to deal with the season (or trimester-->year) discontinuities.

This is why the world went to metric!

Scales: Factor of 10 or something else?

Originally when I started thinking about scales, I had a vague idea to keep as close to a 1:10 ratio as possible. That is, each level being approximately 10 times larger or smaller than the previous. The advantage of this is easy multiplication in all cases. For example, you could take 10 hexes across and put them inside one single larger hex of the next scale up.

My musings on previous posts in the shower today made me reconsider that. A factor of 10 is convenient for some things (say, multiplying salaries: 1 GP for a "chunk," 10 GPs for a day, etc). However, its not so good for other things. For example, say you're mapping. I can't remember 10 hexes across. However, I might be able to remember 7. The 7+/-2 rule strikes again!

I'm not convinced that moving away from base 10 is worthwhile but its something worth thinking about.

Levels of Conflict and Scale

I had a long post on refining Hexploration drafted, but I don't like where it was going so I'm going to scrap it for now. I do want to tie in Hexploration with a series of posts at Delta's blog and a thread over at the OD&D boards however. This one will be short.

To remember, these are my rough scales:

• 1 month: 48 leagues (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
  
• 1 week: 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day: 2 leagues -- 36 x 54 miles (duchy?)
  
• 2 hour "chunks:" 2 miles (if you require 2 chunks/day for downtime)...or 0.5 leagues (if downtime is abstracted -- 12 x 18 miles or 9 x 13.5 miles (barony?)
  
• 1 turn (~10 mins): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1 min): 4 rods (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~10 seconds): 2 paces (10' or ~3 yards) -- 20 x 30 yards (1/2 rood; about 1/8 acre)
  
• 1 segment (~6 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)

You can break them into categories of Tactical, Operational, and Strategic levels of warfare/conflict/scale. The tactical ones are easy to identify: Segments, rounds, and possibly turns. So are the strategic scales: months and possibly (probably?) weeks. Its the stuff in the middle that's hard to define.

There is no good definition of operational level scale. This is the (cumbersome) DOD definition:

The level of war at which campaigns and major operations are planned, conducted, and sustained to accomplish strategic objectives within theaters or areas of operations. Activities at this level link tactics and strategy by establishing operational objectives needed to accomplish the strategic objectives, sequencing events to achieve the operational objectives, initiating actions, and applying resources to bring about and sustain these events. These activities imply a broader dimension of time or space than do tactics; they ensure the logistic and administrative support of tactical forces, and provide the means by which tactical successes are exploited to achieve strategic objectives.

The best, simplest definition I've heard is from Norm Koger, a game designer.
The Operational Scale: A view of the battlefield on a scale just exceeding that at which differing ranges of various direct fire weapons are significant. So, as we can see, the scale of "chunks" is operational, as a longbow's range compared to a crossbow isn't really relevant when hexes are a mile or three across.

But, it does highlight the difficulty associated with this scale. Where exactly does it begin? What should the time/distance units used be? There is gray area on both the tactical and strategic sides.

Its interesting all the grief that Chainmail has caused, as its basically still at the tactical level of conflict. It isn't even necessarily a viable "end game" for D&D. In my opinion, it'd almost be better and easier to have an operational level engine rather than a limits-testing tactical one like the 1:20 scale suggested in Chainmail features.

Hexploration

A DF thread brought up the idea of overland travel to me again.

I've discussed movement rates, scales, etc here before, and I think that a hex-based exploration minigame would be a great addition to any version of D&D. All too often, the magic of overland exploration is lost in an orgy of mathematics, calculating movement rates, terrain modifiers, etc. That just sucks the life out of what should be a really exciting part of the game. Additionally, due to the ass-painery, all too often considerations such as encumbrance or food carried become glossed over, which means that they are not as important as maybe they should be as balancing factors. What I'd really like is a minigame similar to Barbarian Prince, perhaps, that actually is fun and exciting to play.

I think one of the first decisions that one would need to make in a "Hexploration" type game is deciding on the hex sizes and time scales. I'd imagine that for time scales, we need:

Turn (~10 minutes)
Hour/Quarterday (Somewhere between 5-10 turns?) -- I'm not sure exactly what this time scale should be... But I think you maybe need something to bridge the gap between turns and days.
Day exploration (Somewhere between 5-10 hour chunks)
Week or fortnight (7-14 days)

Now we need to think about movement rates. I like to go back to imperial units in this case, so let's say that a typical unarmored movement rate for foot travel is 1 league per hour -- ~3 miles/hour. So, a day's march is about 8 leagues, or 24 (round to 25?) miles.

This will drive the size of each hex. I want characters to move either 3 or 7+/-2 hexes each "turn," typically. Moving 3 hexes makes each move feel very special. 7+/-2 gives more fidelity for various modifiers but is still something that can be easily computed in your nugget. Given that I want complex options and modifiers to be possible, I think 7+/-2 is the right way to go. So, on our "daily" movement chart, each hex should be 4 to 6 miles across. I like 6 miles because its two leagues -- nice and easy to remember! That means a typical character on foot covers 3-4 hexes each day on easy terrain. An example could be an unburdened peasant walking a hex or so to the market on good roads, doing their business, then walking back (in a long day). I want to use 4 hexes, even though 24 miles is on the upper end of plausible, because it allows for more penalties to be applied and it keeps to our 4+/-MOD formula that I use in so many other places. The other option would be to go with 3 hexes base move and give a bonus for improved roads.

This allows for some modifiers. The most common modifier would be being mounted. Mounted troops would often move at speeds up to ~12 miles per hour in combat, but on the march movement would be significantly slower.
From wikipedia:

The speed of travel varied greatly. Large retinues could be slowed by the presence of slow-paced carts and litters, or by servants and attendants on foot, and could rarely cover more than fifteen to twenty miles a day. Small mounted companies might travel 30 miles a day. However, there were exceptions: stopping only for a change of horses midway, Richard II of England once managed the 70 miles between Daventry and Westminster in a night.

Not the most reputable source, but this squares with what I recall from earlier research and we're only interested in a ballpark estimate here. So, for game purposes, one could say that light cavalry is perhaps capable of 5-6 hexes each day under the best circumstances; that's 30-36 miles. Heavier cavalry or beasts such as mules will move slower. Let's go with 6 hexes as its easy to remember (+50% vs. foot movement) and again allows wiggle room for modifiers.

So, to sum up, for daily movement we have hexes two leagues across. Best case (good terrain, unencumbered) foot march rates are 3-4 hexes. Best case mounted march rates are 5-6 hexes. Obviously we can come up with a list of modifiers to take into account encumbrance, racial advantages/disadvantages, terrain, roads, etc -- but, our baseline numbers are reasonable enough to allow for such modifiers.

ZOOMING OUT: CAMPAIGN HEX SIZES

Now let's extrapolate out to a campaign map scale. We will need to decide if time is measured in weeks, fortnights, or months. I tend to think months are a bit long for this scale so I automatically lean towards weeks or fortnights. Again, we'll want to keep movement rates consistent (foot at 4 hexes, mounted at 6 hexes) so as to allow easy extrapolation between scales.

If we assume 8 leagues per day, then in a week we'll cover 56 leagues (168 miles). This is ambitious. I've done a fair amount of backpacking, and while its possible to march over twenty miles a day for a week straight with a moderate load it sucks a lot. Its much more realistic to have at least one or two slow or rest days in there. So I'd be fine with reducing the weekly move rate to either an easily remembered round number like 50 leagues, or to a number easily divisible by 4 (so as to make nicely sized hexes). Luckily, 50 leagues does that as well -- it results in hexes that are 12.5 leagues or about 24 miles across.

So, make the campaign hexes 12 leagues across, and normal foot will cover 4 hexes a week, while mounted moves remain 6 hexes. This is great as many old school products use hexes 24 miles across. Tre bien! So, we'll stick with the week time scale.

ZOOMING OUT: SUPER-CAMPAIGN HEX SIZES

One can zoom out one final time for month-sized campaign hexes. Without going into too much detail, you could have hexes about 48 leagues across. You could either round up to 50 leagues for ease of memorization (although that's again ambitious), or down to 40 or 45 for a bit more realism. Again, foot travel covers 4 hexes and mounted 6.

ZOOMING IN: HOURLY HEX SIZES

Sometimes you need to get more detail than daily moves but less detail than turn based moves. For this scenario, you can go to hourly or two-hourly chunks of time. We basically want a unit of time that is a reasonable number of turns in length (hopefully 7+/-2) but also splits the day into no more than 7+/-2 chunks.

Two hour chunks are 10-12 turns (depending on whether your turns are 10 minutes or 12.5 minutes in length), and split an 8 hour day into 4 chunks (or a 10 hour day into 5 chunks, or a 12 hour day into 6 chunks). That's pretty manageable -- more so than one hour chunks or three hour chunks -- so let's run with that for now.

Our daily foot movement rate is 12 leagues. That should be total movement over a 12 hour day of activity rather than an 8 hour march day -- it assumes time factored in to make and break camp, eat food, relieve one's self, etc. So, let's say that in each two hour chunk of time, 2 leagues are covered. That means hexes need to be 1.5 miles across.

If, however, we use an 8 hour march day and somehow otherwise charge characters for errands and camp time, then in each two hour chunk of time 3 leagues or ~6 miles are covered by foot. That means hexes of 2.25 miles across.

Clearly hexes of 1 league across are probably too big -- then players will cover 4 leagues in 2 hours, or 16 leagues in 8 hours, which is too fast compared to our daily established movement rate of 12 leagues/day. I think a good compromise may be either 2 miles, or 0.5 leagues (1.5 miles). With 2 mile hexes, foot covers 2.66 leagues in 2 hours or 10.66 leagues in 8 hours. With 0.5 league hexes, foot covers 2 leagues in 2 hours, or 8 leagues in 8 hours (12 leagues in 12 hours).

So, basically, we have:
- 2 mile hexes if you plan on requiring a "chunk" or two of time each day be spent on camp chores, or...
- 0.5 league hexes if you want to abstract out the down time

ZOOMING IN: TURN HEX SIZES

Finally, you can get turn based hexploration. Let's say that turns are 10-12.5 minutes. 10 minutes is the traditional AD&D turn. 12.5 minutes allows for 5 turns per hour, which may be easier to add up. Either works out similarly for distance estimate purposes.

If characters are covering 3 miles per hour on foot, then that means they are covering almost 16,000 feet or 5300 yards. So, in a 10 minute period of time they cover around 900 yards. In a 12.5 minute period of time its around 1000 yards. Again, we want to stick with 4 hexes of movement, so that means hexes need to be around 200 to 250 yards in size. Conveniently, the old imperial unit of measure for this distance fits just right: a furlong is 220 yards! So, our hexes are one furlong in size. Perfect.


UNDER A MICROSCOPE: ROUND HEX SIZES

Ok, let's start getting tactical just for a sense of scale here. If we can cover 4 furlongs in a turn, and a turn has 10 rounds, then in a round we're covering 0.4 furlongs or around 88 yards. That means each hex needs to be ~22 yards in size.

Going to our old imperial units, this is about 4 rods (a rod was 5.5 yards).

LOOKING AT THE ATOM: SEGMENT HEX SIZES

Let's split the one minute round up now. We can split it into ten easy to measure segments of six seconds length. Or we can go to six segments of ten seconds each (mirroring the six turns to an hour).

If we go with the traditional 6-second segment, then we get a movement rate of about 9 yards/segment. This requires hexes of 2.2 yards in size -- which is just a bit larger than a Roman Pace (of 5 feet).

If we go with six segments of ten seconds each, then we get a movement rate of about 15 yards per segment. That requires hexes of about 3.75 yards, which is a bit over two paces.

PUTTING IT ALL TOGETHER

This is what we've got, put into tabular format. Base movement rates are 4 hexes for foot and 6 for horse. I've also included the area that you can depict on an 8.5 x 11" sheet of paper, assuming 1" margins and 1" hexes. That's six hexes across and nine hexes tall.

• 1 month: 48 leagues (consider rounding to 40, 45, or 50) -- ~850 x 1300 miles (empire or small continent)
  
• 1 week: 12 leagues -- ~215 x 325 miles (kingdom)
  
• 1 day: 2 leagues -- 36 x 54 miles (duchy?)
  
• 2 hour "chunks:" 2 miles (if you require 2 chunks/day for downtime)...or 0.5 leagues (if downtime is abstracted -- 12 x 18 miles or 9 x 13.5 miles (barony?)
  
• 1 turn (~10 mins): 1 furlong (220 yards) -- 6/8 mile x 9/8 mile (manor)
  
• 1 round (~1 min): 4 rods (22 yards) -- ~130 x 200 yards (5 acres)
  
• 1 segment (~10 seconds): 2 paces (10' or ~3 yards) -- 20 x 30 yards (1/2 rood; about 1/8 acre)
  
• 1 segment (~6 seconds): 1 pace (5' or ~1.5 yards) -- 10 x 15 yards (perch, or 1/160th of an acre)
  

This table makes it easy to see that if exploring a small manor or village, a turn based scale is most appropriate. If exploring a barony, you can use two hour chunks. If traveling across a duchy, then a scale of days is most appropriate. And so on.

Note that if combat occurs in rounds, this leads to large battle spaces. If characters can cover 4 x 20 yard hexes/squares at a walking pace without hustling in a one-minute round, then your battlefield needs to be at LEAST 80 yards across! That's a far cry from the 20' x 20' dungeon room! Its interesting that 3.5, with its six-second combat rounds and 5' square grid, really gets the most "realistic" for tactical movement.

In AD&D, ranges outside were measured at 1" per 10 yards. If you allowed 12" of movement (or 120 yards) in a one minute round, its also pretty accurate. My system lets someone cover about 2/3 that at a walking pace, so 120 yards at a hustle is reasonable.

However, its hard to have dungeon rooms that are 240 yards across, so AD&D had to include an arbitrary 1/3 reduction in speed to make combat on the smaller dungeon scale work well while retaining one minute combat rounds -- that reduced the distance covered in one minute to 120 feet, which is really slow when you think about it in context. While you might be able to justify that sort of movement rate on "difficult terrain" (like, say, inside a slippery, dark, dank, trapped, cramped dungeon), its hard to justify it on a wide open plaza, an open field, or other open terrain.

ADDENDUM: RATIOS BETWEEN TIME UNITS

It'd be very useful to have a relatively consistent ratio between units. This allows for some common formulas that allow conversion between different time scales at relative ease. Here's one system that tries to preserve a 1/10 (or close to it) ratio:

• 1 month:1 week = 1/4
  
• 1 week:1 day = 1/7
• 1 day:10 x 2 hour chunks (the other 2 chunks assumed to be used for sleeping or otherwise wasted -- or you can pad the chunks to make them 2.4 hours long instead of 2 hours long) = 1/10
  
• 1 2 x hour chunk:10 turns of 12 minutes each = 1/10
• 1 turn:10 rounds of one minute each = 1/10
• 1 round:10 segments of six seconds each = 1/10

Not bad! This works nicely up until the higher levels of the campaign. So you could come up with a rule of thumb that covers conversions between almost all time/distance scales.