Table of Contents

Sunday, 21 January 2018

Cards and Cannon

To resolve cannon fire (or other types of fire), most wargaming rules use a ruler to measure distance, followed by a die roll to determine casualties. Many variations are possible, but the basic structure of measuring the range to the target and rolling for damage is a constant in dozens of wargames rulesets.

However, other approaches are possible as well.  It is well-known that H.G.Wells used toy cannon, shooting matchsticks. Although most wargamers do not like the idea of damaging their figures this way, there is something to say for more tactile mechanisms such as the one used by Wells.

This article describes a procedure for resolving cannon fire, by using cards to lay out the firing path.

A Path of Cards

I encountered this mechanic in Miniature Wargames issue 264, April 2005 (I often look up old articles, and then happen to come across something more interesting ;-)), in an article titled "A Deck of Cards", written by Andy Philippson. The article describes playing mechanics using ordinary playing cards. It is mostly about drawing cards to activate units, but one particular mechanic about shooting cannon drew my attention.

In order to determine whether a cannon hits its target, take the cards 2-10 from one suit, plus the Joker (10 cards total). Now, shuffle the cards, and lay out the cards in a straight line lengthwise, starting from the gun towards the target:
  • If the card that reaches the target has an even number, the target is hit. If the card is odd, the target is not hit.
  • If the Joker shows up before the row of cards have reached the target, this means the shell has "exploded" prematurely, and the shot stops right there (and yes, I know that a cannonball does not really explode in mid-air :-) , but as with many mechanics, invent your own favourite explanation for this effect ...).
  • If the Joker shows up as the first card, the cannon explodes and the crew takes damage.
  • If the "2" or "10" shows up, this means the shot deviates, and you place the next card 1 card-width to the left (if the 2 is first encountered), or to the right (if the 10 is first encountered).
That's the idea. Of course, you still need to fill out some more details regarding damage etc.

I quickly set up some ACW figures to show the mechanic in action (images taken with an iPad, they could have been of better quality ...):

The path of fire is laid out, with the "2" indicating a deviation to the right. Since the last card hitting the target is odd, the shot does zero damage.
The Joker shows up, ending the shot. No damage to the target.
The "10" deviates the shot to the right, with the "2" a further deviation. The shot passes next to the target.
Discussion

The use of the Joker stopping the shot might seem a bit harsh, but actually makes this mechanic a fine-grained distance modifier. We have 10 cards, so the joker could turn up with 10% probability in any of the card positions along the firing line. You could see this as a variable range (the shot can be 1 card length long, 2 card lengths long, ... each with 10% probability of occurring), but as we have shown in a previous post, random ranges are (sometimes) equivalent to distance modifiers. So, this mechanic has a more fine-grained distance modifier compared to a single die modifier for "over half range", as is often seen in rulesets.

It might seem a bit strange not to measure the distance between the gun and the target. But actually, we do. We measure the distance in units of card length instead of inches or centimeters. That's a perfect valid measure, although perhaps a coarse one. But that doesn't really matter, since the measured distance is usually only compared to the maximum or half range of the gun. If the maximum range is, let's say 24", it isn't that important whether you measure that distance in inches, centimeters, or card lengths.

The additional feature of deviation is another (geometric) probability built in to determine whether damage is inflicted or not.

Thus, this mechanic is perfectly capable of capturing the results of a more traditional ruler-and-dice approach. It comes down to whether you like this particular mechanic better. Laying out cards like this creates a unique tension ... when you turn over the next card in the sequence, there's always the possibility that the Joker turns up and that your shot will fall short. As the sequence of cards is laid down, you know the Joker can stop your shot with increasing probability ... this suspense during the resolution is more difficult to replicate with a simple die roll.

Moreover, laying out the cards creates a nice visual mechanic, comparable to using a cone-shaped firing template. Fantasy wargaming uses this mechanic fairly often for all sorts of (magical) effects; in historical wargaming it is considered somewhat old-school, but firing templates are often described in the books by Featherstone or Grant.

Variations

The mechanic as described above uses 10 cards (including the Joker), but you could easily increase or decrease the number of cards for making the effective firing range longer or shorter. Perhaps the number of cards could depend on weapon type, or other tactical modifiers.

The number on the card that hits the target (odd or even) determines whether damage is inflicted or not. But you could also use the number itself as an indicator of damage inflicted. That would open a new set of possibilities with damage ranging from 2-10, or any other range depending on the selection of cards. Obviously, this needs to be tuned with the rules in use.

Just as the "2" and "10" indicate deviations, you could add more cards that do exactly that, or less cards ... again variations can be introduced, perhaps even by printing out custom cards specifically tuned to various weapon types.

Battlemasters

When reading the article, I remembered I had seen this mechanic before. And suddenly I remembered! The classic Games Workshop/MB game Battlemasters (1992), still fondly remembered by GW afficionados of the late eighties/early nineties.

Battlemasters is played on a hexgrid, and also includes a cannon for the Imperial army. When the cannon shoots, a path of cards is laid out, hex by hex, till the cards reach the target. Again, an explosion stops the shot early, and there is the same rule that if the explosion is the first card, the cannon takes damage. There is no deviation left or right, but there are cards that make the ball "bounce", inflicting reduced damage if any troops would be present in that location.

I still have the components of Battlemasters lying around (the figures have long been drafted for other uses), so here they are, illustrating the principle in action.

My original Battlemasters cannon, aiming at some Treemen. Put the target card at the Treemen's hex.
The path of the projectile is laid out using cards. Sometimes the ball bounces, sometimes the shot falls short.
When the shot reaches the target, turn over the aiming card, and damage is done!
The similarities between Battlemasters and the mechanics described in the Miniatures Wargames article are very obvious, even more so because the article has activation mechanics almost identical to Battlemasters. Thus, I assume that the author has drawn his inspiration from Battlemasters - 13 years later - to develop his own card-driven wargame.

Conclusion

I think this mechanic is a nice visual representation of a cannon shot, especially if you would use custom-printed cards to add to the drama. The card deck can be tuned such that in terms of to-hit probablity and amount of damage, the same effects can achieved as with a more traditional ruler-and-dice mechanic.

I wonder if any other rulesets have used something similar? Let me know!

Addenda
  • Discussion on The Wargames Website.
  • An interesting suggestion was made on TWW: you could use a suit of cards, or even a full deck, but define the effectiveness of a gun in terms of which cards would "stop the shot", just as the Joker does. So, you could have a "Queen-gun", meaning that whenever a Q, K or Joker shows up, the shot fails. Similarly, you could have a "10-gun" etc. Maximum firing ranges would not be necessary, since the shot will statistically fail sooner or later depending on its type.

Wednesday, 3 January 2018

Square Grids (2)

In a previous post ("Square Grids") we outlined several methods how to measure distances on a square grid, with the aim of approaching the Euclidean distance as closely as possible.

One of the possible solutions is to count a diagonal move as 1.5 movement points. Such a procedure allows for a more accurate movement compared to not allowing diagonals, or counting diagonals as 1 movement point.

However, one could take this a step further and also define movement points for other types of movement. E.g., we can define a number of movement points when executing a Knight's move (as in chess, 2 squares horizontally, 1 square vertically, or vice versa). Using Pythagoras' Theorem, one can easily compute that such a distance equals the square root of 2*2 + 1*1 = square root of 5 = 2.236, or approximotely 2.25.

Hence, let us define movement on a square grid as follows:
  • 1 movement point for a horizontel or vertical move;
  • 1.5 movement points for a diagonal move;
  • 2.25 movement points for a Knight's move.
The resulting movement ranges, for 3, 5 and 7 movement points, are illustrated in the diagram below. The dark shaded squares are the ones we can reach when rounding our movement allowance down, i.e. we can spend up to 3.5, 5.5 or 7.5 movement points.

Diagonal movememtn counts as 1 movement point; a Knight's move counts as 2.25 movement points.
Dark shaded squares indicate an expenditure 0.5 movement points above the nominal number.
The overal picture, especially when compared to the diagrams in the previous blogpost, is that we can approach the circle (the ideal Euclidean distance) even better.

And why stop here? We could define custom movement points for a move that would take us 3 squares forwards and 2 squares sideways ( a so-called Zebra move in chess), or a move that would take us 3 forwards, and 1 sideways (a Camel move in chess -- both Zebras and Camels are called "leapers" in the context of fairy chess pieces), etc. The more we include these special "moves", the closer we can get to approaching the ideal Euclidean distance. In the limit, every possible movement between a starting square and end square can be given its own customized movement point cost.

"But such a system would become totally unworkable!", I hear you say. Quite right, it would become unworkable, working with fractions, and remembering all those special moves with their own movement points expenditures.

That's why - in a wargame that uses a gridded playing field - we don't really want a measurement procedure, we want a counting procedure. There's a subtle difference between both. A measurement procedure would express the movement cost between two gridcells on the playing field. But a counting procedure is what we need when playing. We want to to go from gridcell to gridcell, physically moving the figures (or using our finger to point out the movement path), while counting and accumulating the spent movement points as we proceed along the movement path. Thus, complicated counts such as the Knight's move, the Camel move or the Zebra move, do not fit that pattern.

It is tempting to play around with more complicated counting procedures, but I think the game will suffer. And, the more complicated counts we include and the closer we approximate Euclidean distances, the more we should think about removing the grid and use a ruler in the first place!

What's the probability xD6 beats yD6?

What's the probability a roll of xD6 beats yD6? In other words, roll x number of D6's, add them all up, and compare to the sum of rolling a number of y D6's. I got this exact question from a long-time gaming friend some time ago.

My first question was "How large are x and y?" With small numbers, one could do the calculation by hand, but with larger numbers, finding a closed-form formula might be more difficult. "Anything from 1 to 12", was the answer.

What's the distribution of xD6?

The first thing to consider is the probability distribution of the sum of rolling x number of D6's. Most gamers know that the distribution of outcomes for a single D6 equals {1, 2, 3, 4,5 ,6}, with all outcomes having a 1/6 probability of occuring. But what is the distribution of adding multiple D6's together?

In mathematics, this is known as a convolution operator. Simply stated, a convolution adds distributions together, arriving at a final distribution that reflects the sum of various independent variables. We will not go into the mathematics of computing such convolutions for die rolls, but most wargamers are familiar with the notion that the more dice you roll and add together, the more the final result behaves like a "bell curve" (although I always like to point out that a bell curve has a precise mathematical definition, being the Gaussian normal distribution, but let's not start that discussion here :-)).

The plot below shows the resulting probability distributions for rolling 2D6, 4D6, ... , 12D6 (using the excellent tool anydice.com). As you can see, the more dice you roll, the more spread out the results become (varying between rolling all 1's or all 6's), but there's a clear "bulge" in the middle of the distribution that indicates a higher probability for those particular results. Also note that these are discrete distributions, i.e. only the dots are possible outcomes. The lines between the dots are only drawn for a nicer visualization.


Comparing xD6 to yD6

When we want to compute the probability that xD6 beats yD6, we need to consider all possible results of xD6, and compare to them all possible lower results of yD6. All combined probabilities of such combinations need to be added to arrive at the final probability.

We can illustrate this process on the graph below. The distributions for 6D6 and 10D6 are shown. Let's single out the probability that 6D6 gives 28 as a result. We now need to multiply this probability (2.5%) with all probabilities that 10D6 gives a lower result, and add them all up. Then we need to repeat the process for all other outcomes of the 6D6 roll as well.


 Especially for high numbers of x and y, this can result in quite some tedious calculations, so perhaps there is an easier way?

What's the distribution of xD6 -yD6?

What we really want to compute when comparing xD6 to yD6 is the probability that xD6 - yD6 gives us a number greater than 0. This means subtracting two distributions, which is itself a convolution operator.

But we can do something clever here. The distribution of a single D6 is exactly the same as the distribution of 7-D6 (see also "D20 = 21 - D20?").

Thus, yD6 has an identical distribution of 7y-yD6, and so we can say that:

probability xD6 - yD6 > 0
equals
probability xD6 + yD6 -7y > 0
equals
probability (x+y)D6 > 7y

Let's illustrate this using x = 6 and y = 8. The graph below shows that 6D6-8D6 has exactly the same distribution as 14D6, except it is shifted by a distance of 7*8 = 56.  The probability that 6D6 - 8D6 is greater than 0, is the same probability that 14D6 is greater than 56.


What's the probability that zD6 > some number?

So, we need to compute the probability that any distribution zD6 is larger than some number (which itself is a multiple of 7). Can we do that?

It is difficult to find a closed-form solution for this probability. It can be done, but the mathematics involved would fall outside the scope of this article. An alternative could be to approximate zD6 with a Gaussian distribution with the proper mean and deviation, and compute the integral under part of the Gaussian curve ... which involves the so-called erf or error function and is a built-in function in many numerical mathematical packages. But again, this would fall outside the scope of some simple game design calculations. And moreover, such approximation would only hold for large numbers of z.

So, what do we do?

In the end, I fear there's not much we can do than to simulate a large number of die rolls, and compute the probabilities as an average of all these simulations. You can quickly program something like that, using a proper programming language, or even something like MS Excel.

I have done exactly that, and the table below gives the final results ...


The color codings indicate the percentages: 10% and 40% intervals on both sides, and anything below 1% in grey. Draws are not included in the percentages, so that's why 2D6 only has a 44.5% probability of beating another 2D6.

But what about using this as a gaming mechanic?

The mathematics above say nothing about the elegance or usefulness of comparing xD6 to yD6 as a gaming mechanic. I fear this is where everything falls apart. It seems to me that comparing die rolls like this is quite some hassle. You need to roll multiple dice, compute the sum, and compare it to another sum. That's a lot of work for a binary decision. On the positive side, modifiers can easily be included by increasing or decreasing the number of dice.

Moreover, from the table above one can see that the "workable" range of probabilities (yellow and orange areas) is quite limited. So, although x and y vary from 1 to 12, they better do not deviate too much in order not to have a foregone conclusion.

My conclusion?

I would not recommend comparing xD6 to yD6 as a gaming mechanic ... I still prefer using single polyhedral dice for opposed die rolling.

Saturday, 25 November 2017

Airborne landings

Airborne operations are often associated with elite troops, carrying out daring missions. Eben-Emael, Crete, the D-Day landings, Arnhem, ... all of them have become the stuff of legend.

A wargame scenario involving an airborne landing always poses some interesting challenges mechanics-wise. One of the aspects of an airborne deployment is the unpredictability of where the troops will land, and I think it deserves attention in a wargame as well.

Air Assault on Crete

The first game I played (back in the 80s) that involved airborne landings was Avalon Hill's Air Assault on Crete. This is a classic hex-and-counter wargame, with a map depicting the northern coast of the island.

German airborne units were placed in a landing hex, after which a die was rolled and the counter was placed in its final landing hex using a drift diagram, as shown below.

Drift diagram for Air Assault on Crete (image from BoardGameGeek)
The die modifiers due to nearby Anti Aircraft guns always seemed very realistic to me. The non-symmetric drift diagram implied prevalent winds. And surely, given the reputation of Avalon Hill games, this whole procedure was what could be expected in a serious wargame.

Space Marine and Featherstone

I think it was in an issue of White Dwarf during the early 90s, when I read rules involving drop pods for the 6mm game Space Marine. To place the pods on the table, one had to drop paper chits from a certain height above the gaming surface, and wherever the paper chits landed, that was the location of the drop pod. The flimsy pieces of papers would "flutter" down, making the exact landing point quite unpredictable.

I still remember being surprised by such a procedure. Surely the sophisticated wargamer would not use such a "stupid" rule? This seemed so different compared to the almost precise analysis of the drift diagram in Air Assault on Crete, that I didn't realize this procedure was just another randomizer, albeit an analogue one instead of one involving hexes and dice. I could have settled for a mechanic involving a D12 clockface direction for deviation and a 2D6 for distance, as was used in some other GW scattering procedures of the time. But dropping pieces of paper?

It was only much later when I learned that this mechanic had a long history in miniature wargaming, and was described in Donald's Featherstone book Wargaming Airborne Operations (published in 1977, and reprinted by the History of Wargaming project. My version is the American version printed in 1979).


In the book, a few suggestions for airborne deployment are listed:
  • Dropping paper chits, but some chits can be heavier, simulating a more accurate drop (e.g. pathfinders that have to lay out the drop zone for the subsequent lifts). Featherstone even suggests dropping the markers with the lights out for night operations!
  • A number of adjacent virtual tables to the real wargaming table, on which the troops land. The move towards the central table on subsequent turns.
  • Moving a model airplane attached to strings across the table, while the paper chits fall out - although it is suggested it is far simpler simply to drop the paper chits from a box.
  • The chits can be color-coded or bear an ID to see what troops have landed where.
  • Various dice rolls are suggested for troops being wounded upon landing, or what to do when troops land in difficult terrain. Chance cards are mentioned as well to determine the height of the drop, deviation by winds, etc. 
Dropping paper chits above the table is great fun, and I have used it in various games set in various periods (WW2 to Scifi). Chits that don't land on the table mean the corresponding figures enter the tabel a few turns later, representing troops that were dropped outside of their designated landing zone and needed some time to get back to the main area of operations.

Dropping paper chits from a model airplane (attached to a string for the photograph). From Wargaming Airborne Operations - Don Featherstone
Dropping paper chits from a box. From Wargaming Airborne Operations - Don Featherstone
Scattering

An alternative is to use a scattering die roll, that indicates deviation from a chosen landing point. One can use a D12 die for direction, and 2D6 for distance, or something similar.

On my gaming table, I often use Kallistra hexes. The designated landing point is a hex, and then a D8 is used for devaiation. A die roll of 1-2 means that troops land in the hex, 3-8 indicate the 6 adjacent hexes. When using a D20, one can include a 2nd concentric circle of hexes as well.
 Depending on circumstances (wind, anti-aircraft, height of drop), modifiers to the die roll can be used to make the drop more accurate.

Off-table Landing Zones

The problem with dropping paper chits is that they land all over the table, and that the resulting combat becomes very chaotic, especially on a small table combined with long weapon ranges. The whole idea of regrouping your troops before engaging the enemy is very difficult to play out under such conditions.

Therefore, my preferential airborne mechanic is to use off-table landing zones. The sketch shown below, (taken from my notebook, listing all the games played in my wargaming room), illustrates the basic idea.


Various landing zones are drawn around the table, in two concentric circles. If you look at the right-hand side, zones A, B, C, D and E are adjacent to the table, and zones  I and II are one step further.
Each squad that landed in this scenario was allocated to a single landing zone. A die roll of 1, 2 or 3 indicated the unit landd in the designated zone, otherwise it landed in an adjacent random zone (possibly on the table, and then troops would be placed along the table-edge). For determing a random adjacent zone, simply roll a D6, and start counting from a designated starting point. If there are less than 6 adjacent zones and the die indicates a non-existing one, roll again.

Once the game has started, movement from zone to zone (or onto the table) takes 1 turn. Troops that are on the table can never return to any of the landing zones.

The specific diagram was drawn based on the map for the main table, with a railroad and road delineating various sectors, and a river splitting the table in half. If a different lay-out is used, the zones and connection between them should of course be redrawn.

Using such a diagram provides the player with some interesting tactical decisions. Landing zones for various units have to be decided, and at the same time, the mechanic also provides for deviations during the landing using an easy die rolling procedure. Once all landing points have been determined, various regrouping moves (on or off-table) can be spent before the assault on the actual objectives is started.

Paper airplanes

I once considered paper airplanes that would glide elegantly onto the table, but the dimensions of the typical wargaming table do not make this very practical. However, for a wargame in the outdoors, this might be a fun alternative.

Addenda
  1. Featherstone's book Wargaming Airborne Operations wasn't the first to mention the idea of dropping paper chits. His book Air Wargaming (1966) describes the same idea, and the idea has been mentioned in WRG's rules  Armour and Infantry 1925-1950 (1973) as well. I will delve a little bit deeper in my wargaming library to look for older references, but if anyone can find any, please let me know!
  2. The boardgame Memoir 44 has a mechanism to drop plastic figures onto the hex-gridded gaming board.
  3. When dropping paper chits, you can also line them up on a wooden ruler, and then flip the ruler over, recreating all paratroopers jumping in sequence along the flight path of the carrier aircraft.
    The same idea can be used when using scattering diagrams on a hexgrid, by plotting the flight path along a series of hexes, and having troops jump out in subsequent hexes along the path, each jump followed by a scattering procedure. The game Starship Troopers (Avalon Hill, 1976) used this mechanic, as is shown in the diagram below.
Scatter and flight pah diagram (Starship Troopers rulebook, 1976)

Wednesday, 13 September 2017

Situational vs Inherent die roll modifiers

Many wargaming procedures involve dice to resolve combat or test morale, and many of these dice rolls come with a list of modifiers. Typically, a die roll modifier adds or subtracts some factors to the roll, and affects the target number to beat a certain result - whether a number in a table or an opposing die roll.

When you look at older rule sets, one often encounters huge lists of modifiers. I often wonder whether such rulesets were playable at all. Below is an example from a seventies-era ruleset. Modifiers are determined not only based on a certain condition, but also on troop type. Unworkable, if you ask me!

Die roll modifiers from a 70s era ruleset. Cross reference the troop type (A, B, ...) with the situation to get a modifier to apply to the die roll. These are only the positive modifiers. The ruleset had a similar table for negative modifiers!

When writing wargaming rules, there are several things to consider when selecting die roll modifiers:
  1. Are modifiers situational or inherent? 
  2. What is the purpose of the die roll modifier?
  3. How many modifiers per roll?
  4. How significant should the modifier be?
Are modifiers situational or inherent?

A first type of die roll modifier models a variable (possibly based on historical record) reference for the specific action. E.g. one might have a specific procedure for determining the casualties due to firing, but some troops are of better quality, hence, they get a positive modifier when they fire at the enemy. I would call such modifiers inherent modifiers. They depend on troop characteristics, and are used to introduce variability between troop types.

A second type of modifier represents situational circumstances. E.g. a unit in cover might get a positive modifier when being shot at, or troops uphill get a bonus in melee, or charging gives an advantage to the attacker. Such modifiers depend on the tactical situation in which the troops are placed. They typically do not depend on troop type, but on the situation in which the troops find themselves. I call them situational modifiers.

Sometimes you have a mix between both types. E.g. in a Napoleonic game, a modifier might state that lancers have an advantage on combat, only against infantry in line or square, but not against other troop types. Such a modifier is inherent (lancers), but also situational (target must be infantry in a specific formation). So the distinction is sometimes hard to make.

What is the purpose of the die roll modifier?

Mechanically, the purpose is clear: to increase or decrease the probability of a die roll succeeding, and affecting the outcome that is linked to the die roll.

But a more important factor to consider is whether the modifier affects the decisions made by the player, or simply adds some variation to the die roll procedure (sometimes called chrome). The latter can be fun, but often slows the game down, and might give a false feeling of realism (after all, a huge list of modifiers implies the rules designer knows his history, right?). The former is - at least in my view - a much more important effect of die modifiers: do they steer the decisions made by the player?

I do think that the true purpose of modifiers should be to influence decision-making during the game. Hence, situational modifiers are preferred, and inherent modifiers to be avoided. After all, you can decide whether to put troops in cover or on a hill, but you cannot decide that your cavalry suddenly becomes equipped with lances, or is better in morale. At most you can decide where to deploy certain troop types before the game starts, but that's a pre-game decision that is different from a tactical decision in-game.

That does not mean one cannot make a distinction dependent on troop type, but it should preferably be reflected in the troop characteristics, rather than in the modifiers when resolving a die roll.

How many modifiers per roll?

If we want modifiers to guide decision-making, I think they should be limited in number such that a player can learn them by heart, rather than having to look them up in the rules all the time. Too many modifiers will simply result in a lot of random number-adding, ending with an overall +0, +1 or -1 anyway.

3 or 4 modifiers per procedure seems to be a good number. It allows players to remember them, and make each modifier significant enough such that they do not get drowned out by other effects.

I know it can be fun to distinguish between all sorts of cover, but does it really matter (unless the game considers it at the heart of its gaming engine)? Simply use one type of cover with a single modifier, and that's it. Limiting the number of modifiers to a significant set that influences actual decision making is part of designing the rules. Playtesting also might give you insight what modifiers players will use actively in their choices during the game, and what modifiers are just chrome, and subsequently, can be tossed. Also, modifiers that describe situations that are so exceptional that they happen only once during an entire game, should be avoided as well.

How significant should the modifier be?

Modifiers should also be significant. A +1 modifier on a D100 is not going to actively influence decision-making.

Some time ago, we had a discussion in my gaming group when playing a recent set of rules that used a 2D6 die roll to activate units. Most units needed a 5+, 6+ or 7+ to be activated, with 6+ being the most common number. However, none of the players felt that having 5+ or 7+ troops guided their decisions. Rather, it was the tactical situation on the field that drove the decision what unit to activate next. Thus, the activation rolls can as well be set at 6+ for all troops (it saves time!); or should be spread out to 4+, 6+ and 8+ if we want to give them a meaningful role in the game, such that the differences in probabilities become significant enough for the player to cosnider them. Modifiers should mean something, not simply add some random noise!

To conclude ...

Overall, I think that modifiers are an important aspect of game design, and it does matter what the intent is. If the intent is simply to add chrome, go wild, add lots of modifiers reflecting all sorts of different things!

But if the intent is to guide decision-making, better limit yourself to situational modifiers, keep them limited in number, and large enough in effect.

Addendum

There's some follouw-up discussion on this thread on The Wargames Website.

Tuesday, 18 July 2017

Some thoughts on the turn sequence

When discussing wargame mechanics, the turn sequence is often a subject of hot debate. In a sense, the turn sequence is the engine that drives the game forwards. Many other mechanics that deal with combat resolution or morale, are often embedded in the overarching turn sequence. The turn sequence regulates the alternating role of players, but also regulates the order in which units can act and how.

The classic IGO-UGO turn sequence

During the early days of wargaming, the turn sequence was rather simple, and is now often referred to as an “I Go, You Go” sequence (IGO-UGO). Both players take alternating turns, and within a player’s turn, the order of actions (or phases) is fixed as well. Typically, I move all my units, then I shoot with all my units, then I resolve close combat with all my units, then I resolve morale for all my units, and then you take your turn.

Let’s try to put this in a diagram. Let’s assume we have 2 sides (Red and Blue), and 3 units per side (A, B and C). A complete cycle starting with Red would mean that Red moves all of his units first, then shoots with all of his units, and so on. The fixed order in which all activities take place can then be schematically represented as follows:



Movement
Firing
Melee
Morale
Red, unit A
1
2
3
4
Red, unit B
Red, unit C
Blue, unit A
5
6
7
8
Blue, unit B
Blue, Unit C
 
The matrix above lists all possible phases for all possible units, and the numbers indicate in which order they are executed. It is a very straightforward turn sequence, and one that is still present in many wargaming designs. It is also a traditional way to play classic boardgames, such as Monopoly, Snakes and Ladders, even Chess. They all follow a similar format:  move a piece, then do something with that piece. If you follow that framework, it is quite natural that you end up with this particular turn sequence. BTW, you also often see this same turn sequence appearing in board wargames. The Avalon Hill classic hex-and-counter wargames also use the framework “move all of your pieces, then do something with them.”

The main problem with this turn sequence is there is no possibility for the opponent to react, or to do something with his troops. The classic example is so-called overwatch fire. When I move my units from one covered position to the next, you cannot shoot at my troops, although they might be vulnerable during some  part of their movement path. Another often-cited problem is that I can have a unit outside of our mutual firing ranges, I move them within range, and I blast your unit to smithereens before you have the chance to do anything.

Solutions often come in two forms: re-order the various phases of the turn, and/or introduce more sub-phases. Re-ordering is the more elegant solution. The sequence might then involve that Red moves first, then Blue shoots, then Red shoots, then a joint melee phase occurs, etc. Another often-used solution is to put the firing phase before the movement phase, such that “move and shoot to smithereens before you can do something”-tactics are not possible.

Adding more sub-phases, sometimes depending on troop-types, becomes complicated very rapidly. It results in games in which you have various movement and firing phases for each side, sometimes interspersed. In my experience, these do not play fluently, since players often not capable remembering what troop type can do something in what phase.

Any turn sequence also has implications for the underlying mechanics of the various phases, and how these phases influence each other. E.g. the morale phase might specify conditions and events that happened in the previous combat phase. A strict ordering of phases makes such interactions more easy to deal with, but also has to allow for “out of order” actions that otherwise do not fit the overall structure. E.g. when charged, troops might be allowed to counter-charge or run away, although it is not strictly their movement phase. Similarly, movement reactions often are part of the morale phase as well.

Alternating unit activation

In this turn sequence, players alternatingly activate units. Red activates a unit, then Blue activates a unit, then Red activates another unit, etc., until all units have been activated. Each player chooses what unit to activate next, and some sort of bookkeeping is needed to remember what units already have been activated. During a unit’s activation, the unit can move, shoot, fight, etc, but not necessarily in a fixed order.

We can schematically represent this turn sequence as shown below, with Red activating unit B first, then Blue activating unit A, followed by Red activating unit A and so on.



Movement
Firing
Melee
Morale
Red, unit A
3
Red, unit B
1
Red, unit C
5
Blue, unit A
2
Blue, unit B
6
Blue, unit C
4








As you can see, during a full cycle, all units still get to do all possible actions, but we have organized them in a different manner. If you are familiar with computer programming, you could see this as having two loops turned inside out. The classic sequence looped over all phases, and each unit got an action during each phase. This sequence loops over all units, and a unit gets to do all phases when it is selected. Another way to look at it is that we subdivided the matrix listing all possible actions for all possible units by rows instead of by columns.

This sequence has some consequences on the mechanics of the various phases. The mechanics of a phase cannot be strongly dependent on previous phases or the actions of other units. E.g. it becomes more difficult to have a morale phase that would take into account the actions or behaviour of nearby units.

This turn sequence is often more flexible in design than the classic sequence, since the phases themselves do not form the overarching structure of the game. Hence, it is easier to add new types of actions or phases that a unit can do. Suppose you would like to include an engineering activity in your game. The classic sequence might make this part of the movement phase – or should introduce a new "engineering phase" in the turn sequence. The alternating unit activation sequence can simply add a new type of activity that a unit might or might not do during its activation. It might seem like a subtle difference, but it works very well in e.g. roleplaying games in which each character takes a turn, and can then do a multitude of different actions available to the player.

Variants on alternating unit activation

To ensure an equal pacing of units being activated on both sides, variants often include that whatever sides has the most units left to activate, must activate the next unit. Group activations are another variant that can guarantee multi-unit coherency.

Another, more extreme variant stipulates that players cannot choose what units to activate. Often, this is implemented as some sort of draw (cards, chits, …) with each card specifying what specific unit can activate. This is not a very attractive mechanic, because it takes away important decisions that the player wishes to make. Moreover, in some scenario setups, it can clearly create bottlenecks, when e.g. a column of troops has to cross a bridge, and units simply refuse to be drawn in the correct order.

A hybrid is possible, by allowing a randomization to check what side can activate, but then leave the decision up to the player to determine what unit will activate. Such mechanisms also often include the early abortion of the entire cycle, such that neither player is certain that all his units get to be activated, and is forced to activate those units first he thinks are most important. Underlying mechanics to accomplish this often include special cards in a deck that drives the alternating activation sequence.

Unit-driven IGO-UGO sequence

This turn sequence tries to combine the best of both worlds, by using the alternating player structure of the  IGO-UGO sequence, but within each player’s turn using a unit activation mechanism. This is a turn structure that has become very popular in modern designs. During a player’s turn, the player can choose which units to activate and in what order. Often, dice control the activation sequence (command rolls), or a hand of cards might drive the player’s choices. An early abort mechanism often is included as well.

The following diagram illustrates this sequence, with units in grey not having activated due to an early abort, e.g. a failed die roll. First Red activates unit A, followed by B, and then fails to activate further units. Then it's Blue's turn, activating unit B.



Movement
Firing
Melee
Morale
Red, unit A
2
Red, unit B
1
Red, unit C

Blue, unit A

Blue, unit B
3
Blue, unit C


The advantage is that the mechanics for the different phases (movement, shooting …) can still be interlinked, since we can assume that a large number of units will get activated within the player’s turn. Hence, it might be possible to sequence the movement unit by unit, but still keep an overall morale phase at the end or the beginning of the player's turn.

Random phase sequence

The advantage of using the matrix representation to illustrate the turn sequence is that you can subdivide the matrix in different ways (i.e. organizing the turn in rows or columns as shown before), but one can also re-arrange the columns in random order.

An unusual turn structure might therefore randomize the different phases over all players. Thus, we could first have Blue firing, then Red movement, followed by Red morale etc. As a mechanic, this can be easily achieved by making a custom card deck and drawing cards to see what next phase comes up. The diagram below illustrates a possible random sequence.



Movement
Firing
Melee
Morale
Red, unit A
2
8
6
3
Red, unit B
Red, unit C
Blue, unit A
4
1
5
7
Blue, unit B
Blue, unit C

Such a sequence requires that all phases can be resolved independently, as explained before. I have only tried it once before, in a skirmish game in which many unexpected events might take place, and an emphasis is put on heroics rather than a coherent well-orchestrated battle plan.

Conclusion

There are of course many more turn sequences possible. All sorts of hybrid formats can be imagined. In the end, the turn sequence is interlinked with the underlying mechanics for the different phases and activities, since the entire gaming engine has to form a coherent whole.

As a games designer, it’s always useful to tinker with various ways in which the turn can be organized. Even if you end up with a classic IGO-UGO sequence, at least you thought about it and can defend your particular choice much better.