Thursday, February 05, 2009

Luck-Based Gaming

I'm sure I've written on this before, but it's always good to fill time while I'm waiting for a phone call. So here we go with an essay on the role of luck in games.

Luck in gaming takes many forms, but usually it boils down to one of three situations:
  1. Take one of  a limited pool of options/resources, which is now not available for some period of time that may include the remainder of the game. Chit pools, cards, etc.
  2. Take one of a limited number of results, which are always available. Usually in the form of rolling dice to achieve a specific result (e.g.; hit on every '6') or on some sort of results table (e.g; a combat results table).
  3. A combination of the above, usually in the form of a random events table where once a specific event has been rolled you ignore it (or roll again). Much rarer in practice.
To my knowledge, luck is ubiquitous in gaming. Even games that don't seem to have any luck element at all (the 18xx series of games, chess, etc) actually have a strong luck element in the form of who goes first, which in these games tends to generate a person who drives the game forward early or a set pattern of moves, at least with experienced players. 

Luck is used to achieve several design goals depending upon the game. Most wargames use luck to select from a potential number of outcomes to an action. For example, the result of entering into combat is often achieved by rolling one or more dice and referring to a table of results based on the specific situation such as a ratio of the combat capabilities of the forces involved. Using an odds-based combat results table (CRT) as implemented in 60's-era Avalon Hill wargames, you refer to the column that matches the attacker:defender strength ratio (e.g.; 3-1), roll a d6, and get a result ranging from one side being destroyed to one side retreating to somewhere in between. 

A popular trend in wargaming has been the so-called "card-driven" wargame, or CDG, which uses cards to "drive" the game forward by making them the basis for not only activation of units, but also to reflect socio-political events of the period. Where the combat is usually resolved via dice, the flow of the game is dictated to some extent by the cards in play and how each player uses the hand they are dealt. Often, you must draw and play specific cards in order to receive additional combat units, or to allow specific actions on the board. This sort of luck element can be thought of as "front-end" luck, or luck that dictates player actions, whereas the CRT tends to produce "back-end" or "results-based" luck as an end product of the player's actions. 

Some games use cards to dictate front- and/or back-end luck, but when you get down to it, all luck is simply a matter of probability, so long as you consider the design intent. Fields of Fire is an excellent example of a game that uses cards to generate all probability, even though in almost every case the intent is that the success of a given action is based on all of the cards being present in the deck at the time of drawing. By this, I mean that even if you are halfway through the deck, the intent is not that you would remember that X cards have included the "Cover" keyword that have been discarded out of Y cards available in a full deck, although there are players who might be able to recall that sort of detail on cards that can have as many as 25 bits of information on them. The reason cards are used is not to fulfill a goal of having a closed pool of resources/results, but to easily generate random numbers in ranges that are difficult to generate with regular or semi-regular polyhedrons such as cubes and decahedrons (10-sided dice, which aren't Euclidean, but work just as well as their more regular brethren). If you need to generate a number between 1 and 7, you have to either roll a d8 and reroll the '8' result, or else find another way to generate it such as a card pull. Interestingly, given that the Action Deck in FoF doesn't have a number of cards that divides evenly into 7, you will get an uneven distribution of probability using this method, and in fact will run into this situation for almost any number of cards other than 60 in the deck (which will support even distribution of the ranges of 1 to 2, 3, 4, 5, 6, and 10, but not 7, 8, or 9). 

On the other hand, you have a game like Combat Commander, which also uses cards to generate actions (although, in a strict sense, this is not a CDG as defined by games such as We the People and Hannibal: Rome vs Carthage). In this case, however, the cards are convenient not because of non-Euclidean probabilities, but because they are used as "money" and collected and spent over time. FoF, on the other hand, generates a probability that exists at a specific instant in time with no resource management element. At the same time, the cards are also used to generate "instant" probability, in this case not only a 2d6 result, but also die "triggers" that can take effect if generating this specific bell curve, and also random hexes on a map. By using a 72-card deck, all of the 36 different possible 2d6 dice results are represented equally, although it's pretty easy to keep track of how many 12 results show up if you're paying close attention. 

Let's examine the use of the varying methods of resolving combat, which generally boil down to one of three methods:
  1. CRTs based on odds, strength, or differentials,
  2. Rolls "to hit" based on a target number, occasionally resulting in "buckets o' dice",
  3. Differential combat using rolls to augment combat strengths, which are then compared.
CRTs have been around forever, but they are continually used in interesting ways. For example, Advanced Squad Leader, which resolves combat based on one unit firing on another (common in tactical level combat), uses the actual combat strength to determine the column in use. Waterloo 20 uses a differential (-1, 0, +1, +2) between fighting units to determine column. In all cases, it's fairly easy for players to understand which column a given combat will take place on (barring the use of action or combat cards that will create SNAFUs for one or both sides) and judge their actions accordingly. Also, this tends to generate a relatively small set of results. In Paths of Glory, where both sides roll dice based on their combat strength, then compare those numbers, it requires more work to figure out what percentage of the time you are likely to get a larger result than your opponent, but it's manageable. With a game like Successors, where the Battle Rating of your general will determine the lowest possible individual die results when rolling a 2d6 result (a '4' rating would change a roll of 1,6 to 4,6, for example), things get a little more complex. The important element remains that the bounds on the results are fairly set. 

With the "to hit" method, you roll dice based on your combat factor, usually one die per point, and achieve successes based on how many dice meet the necessary criteria. War at Sea is a seminal game that used this method - If you fired on an enemy ship and your ship had four attack factors, you'd roll four dice and every '6' result (taking into account die roll modifiers, or DRMs) resulted in a point of damage for the target. Great War at Sea takes that model and adds in various other elements such as what part of a ship was hit, the size of gun firing compared to the armor of the target that was hit, etc. Other games, such as Wellington and Kutuzov, use both the hits to determine how much damage happens to the target, but also who wins the battle by comparing total hit/disruption results. 

The "to-hit" method has it's advantages and disadvantages. For one thing, it's easy to compute the number of successes you should have given the number of dice that you're rolling and the range that results in success. In War at Sea, for example, assuming no modifiers such as the Germans getting a +1 drm and a 6 being a success, you should see one success on average for every six dice you roll, thus a ship with a firepower factor of three should score one hit every two times it fires, or a 50% of scoring at least one hit (more or less - I understand that the math gets a little more involved). Also, because you are rolling a lot more dice, you should see a much more normal bell curve over time. 

The disadvantage, of course, is that you can get results that fall far outside of the standard deviation, both in and out of your favor. Rolling eighteen d6 for a 5-6 result gives an average result of six successes, but you may get as many as 18 or as few as 0. Where the CRT gives you a limited range of results but potentially skewed results with fewer rolls, the to-hit method gives you a more statistically balanced result over the course of the game, but with the chance (admittedly small, but present) of a wider range of results. 

Differential combat, such as is used in Unhappy King Charles and Combat Commander, has it's own danger. In a game such as We the People or Hannibal, where combat is relatively rare (these are games of maneuver, bluff, and combat is resolved through the use of battle cards, an entirely different method), the opportunity to see games go south through consistently bad die rolls is more likely. I played a game of Storm Over Stalingrad, which uses this method, and my dice were either in the 10-12 range or the 2-5 range throughout the game. In fact, I won largely on getting a lucky roll or 12 at exactly the right time to kick the Russians out of the final victory area I needed to take on the last turn. The problem wasn't that you could end up with a 12 result that would accomplish your goals, it was that you rolled 2d6 roughly 25 times in a game. Unhappy King Charles has gotten the same complaint - not *enough* luck in a game where you can be devastated with an unlucky roll at a key moment. 

Of course, any game that involves luck also contains that caveat - some rolls/draws are more important than others. In a game like Paths of Glory, the common wisdom is that you prepare for the worst and hope for the best, and some games allow you to do that to a great extent. Still, I've lost games of Paths when my opponent went for that 1-36 chance at the end of a turn, and if it worked then I'd have half of my army out of supply and thus lose them permanently, effectively ending the game. While it's arguable that players should be aware of those possibilities and guard against them, it's also true that in many cases there is no way you can effectively do that (I'm thinking about the Near East map in particular, where the Turks can barely guard all of their fronts at once, and the MEF is more effective as a threat than as an actual played event). 

There is, to the best of my knowledge, no real way to mitigate luck at that particular level. You will always have critical points where an outlier result will determine a winner, and wargames are complex enough that it's nearly impossible to design the game so that those events don't occur. If you can't handle that sort of result, it's best for you to not play that particular game if who wins is important to you. While I understand that it's frustrating to play a long game that is well played by both sides throughout, only to result in a series of chance events that hands the game to one side or the other, at the same time wargames are about history and story and understanding the situation. If you are playing solely for competitive purposes, you will often find yourself frustrated with the results. 

On the other hand, some of us seem to consistently run afoul of chance elements in games, as Mike did in his game of Storm Over Stalingrad (not the same game as I played), where he rolled an average of 4 on 2d6 over several attacks at the start of the game, while his opponent rolled an average of 10. This sort of thing seems to happen to Mike on an astonishingly regular basis, to a point where you have to wonder if he didn't do something really bad in a past life. Multiple games of Glory III were ruined for him through consistent bad die rolling. 

Of course, the components you use for chance elements need to be of a certain quality. I've gotten dice in games that clearly favored specific rolls (the German die in WW2: Barbarossa to Berlin, for example, rolled one number higher than a 3 an average of once in ten rolls over a couple of games, indicating that it was off-balance), but you can always buy balanced dice or make sure that your card decks are thoroughly shuffled (or use a electronic die roller, such as the excellent Dicenomicon app for the iPhone, which will generate any range or result set you wish). 

I've been talking about wargames, where the point is to simulate a potential range of results based on the historical record as well as weapon system capabilities. There are many games that introduce a luck element solely to balance the playing field between experienced gamers and those with less experience or cognitive skills (such as children). These games tend to have different design goals, such as to teach basic skills such as numbers, colors, set collecting, etc, or to be experiential in nature, where it's the ride that's important more than who gets to the finish line first. Others try to evoke a particular theme or mood, and so the luck element tends to be more capricious and (if done correctly) entertaining. However, since my focus is on luck as a design element intended to encourage specific play styles or to generate a set of results, I'll ignore these for this essay.

Finally, I'll mention the appropriateness of luck in game design. On occasion, a designer will insert a luck element into a game for no other reason than what seems to me to be laziness. Two games that I'm less interested in playing because of poor design are Agricola and Age of Empires III. Agricola is a tight design with a lot of thought and preparation required of the players, but that inexplicably added in a major random element in the Minor Improvement cards. Because the luck in this case can't be mitigated (you get random cards dealt to you, and it's what you get to work with), and because it's player specific (you can get great cards while your opponent gets a handful of crap), the net result is that the game can buff or nerf players right out of the gate. Fortunately, there is a drafting variant for this cardset that fixes the problem. 

Age of Empires, on the other hand, uses a heavy luck element for it's Discovery mechanism. Not only do you take a chance if you don't go strong with your units if you try to discover new areas, but you may have gone strong to get a nearly useless result. At the end of the game, there often isn't much you can do other than take a chance on whether or not you find a Discovery card that pays off well (there are two in that particular deck), so an identical investment in resources can benefit one player much more than another. The designer isn't exactly known for his tight efforts, so this isn't a big surprise, but in a game that was otherwise very well thought out, this was lazy design. I spent some time trying to come up with a more equitable way to implement discovering new territory, but was unable to do so within the design itself. A better solution would have been to have discoveries made on a timetable, and then allow the various players to take advantage or not, rather than to force them to devote resources to the crapshoot in order to move the game along.

I'm sure there are other aspects to luck in gaming that I haven't touched on, but I'm also fairly sure that I've lost most of my readers who started out this post with me, so it's time to stop typing. May your dice never fail you in the breach, and may all of your event cards be timely.

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