ABSTRACT PRINCIPLES of 40k - Luck and skill

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One of the biggest difficulties 40k players have when talking to one another is that people have a myriad understanding of what the words "luck" and "skill" mean with regard to 40k. Both of these words can be broken down and explained in a systematic way to provide for a common definition. These definitions can come from the game itself, rather than our preconceived definitions that are forced onto the game after the fact. To begin with, let's look at luck.

LUCK

For the purpose of this theory, luck is a catchword for all of the parts of the game over which a player has no control. In a tournament, this includes the order in which you play people, the list they bring, the terrain setup, etc. Of course, luck also refers to the results of individual die rolls, whether it be for mission or first turn, or for whether a plasma gun penetrated armor on a vehicle. Players have no power over this, and can't, through any amount of planning, skill, or force of will simply dictate the results.

In any game of 40k, your ability to win is going to be based on destroying (or in some other way neutralizing) your opponent's units. After all, you can not win a kill point game without killing units, and you can not win an objectives game without removing your opponent's units from the objectives. In any given event in a game, luck (especially die rolls) is going to be the determining factor of if you destroy an opponent's unit or not. The game was purposely designed in such a way that you can not ever see an opponent's unit destroyed without dice determining if they were destroyed or not. Unlike chess, which allows you to destroy your opponent's units with movement alone, 40k is solely dependent, then, on how you roll the dice.

You can do things to lengthen the odds of failure, or shorten the odds of success, but you can't remove dice as the primary mechanic of the game, and thus can not remove luck from its core.

SKILL

Just as luck is the overarching idea of uncontrollable variables, so is skill the the idea that represents all controllable variables. Skill includes such things as building a powerful list, and using them to their maximum effectiveness on the table.

Given that luck is the primary mover in the game, skill's role is entirely devoted to manipulating luck. Its role is predominantly to shorten your own odds of success, while lengthening the odds that your opponent succeeds. For example, if you move a plasma gun that was out of range of any target in such a way where they are now in range of the target, the odds that you successfully destroy that particular target with a plasma gun is shortened from a 0% chance of success to something much better. Likewise, if you move one of your units out of LOS of all your opponent's weapons, the odds that your opponent will be able to destroy that unit just lengthened from whatever it was before down to 0% (barring other circumstances like barrage or deepstriking).

Remember, that this also counts list-building skill. If you have a vehicle, and your opponent does not bring anything with a high enough strength to damage it, then the odds that the vehicle remains on the table the entire game are incredibly short. Likewise, the more you have on the table, the more power you have over changing the odds. You can not exploit the bad luck of your opponent if you have no surviving units on the board, nor can you mitigate his good luck.

THE EFFECT OF LUCK

Better players may be able to get more odds-bending power out of their units, and thus can do more with less, but while how much power a player can squeeze out of hit units may go up, it can never exceed the maximum power, which is the aggregate of all the units left on the table. After all, if someone has half their army blown off the table turn 1, they have half the potential power of their opponent. They can still win the game if, for example, they are able to get 100% out of their 50% while their opponent is only able to get 10% out of their 100%, but the maximum possible has still been determined by the luck of how hit, wounding, cover, armor penetration, leadership, etc. rolls go.

More obviously, there are several individual die rolls, over which no player has control, that can be very key rolls, and not just if one critical shot managed to destroy its target or not. This includes things such as which player goes first, and when the game ends. Most people can recall a game in which one person would have won a game, except the roll to continue ended the game one turn too early, or one turn too late.

This is very important to note: all luck is not equal. Who you get paired up with in the first round of a tournament might have a massive impact on how far you go, and, as mentioned, certain die rolls like who goes first, when the game ends, and possibly that last plasma gun shot you get against your opponent's last model on an objective will have a MUCH bigger impact on the result of the game than other die rolls. Some people like to claim that die rolls can be controlled for because you roll so many dice, but the law of large numbers doesn't apply here. Firstly because the numbers aren't actually large (a couple of hundred die rolls spread over a variety of different circumstances), and secondly because the number of die rolls that are really critical could well be very, very small indeed (I've had games that were so close that literally a single die roll determined the winner. How is that for "large numbers"?)

THE EFFECT OF SKILL

Skill allows you to change the odds of luck in an attempt to control the effect of luck. If a vehicle is destroyed or not is determined by luck (after all, if you can't roll a single successful hit against a vehicle, you will never destroy it), but you can make the odds of a vehicle destruction result go up with skill (such as moving several plasma guns into range of the vehicle, compared to only shooting a single one at it). Thus skill is able to make the results of any particular outcome more likely. Said another way, skill allows a player to play the odds better.

A better player, then, would be able to more exactingly move the odds in whatever direction he so desires. In the end, though, it's not that more skill makes the "best" result happen, rather more skill makes the "desired" result more likely.

If skill has no impact on luck itself, and luck has an impact on the game, then what impact does skill have on the game? In the end, while skill will not make results more favorable over the course of a game, skill will increase the chances that you have more relatively positive results. Luck is still the determiner, but a player can make more rolls where the end result is more likely favorable results. In short, player skill makes luck kinder.

RELATIVE SKILL

As a player's skill improves, they are able to make the battlefield more and more accurately reflect the odds they want to play. It also affects the odds that they want to play in the first place. Poorer players will tend to make decisions that, if successful, will have less strategic gain, and if they fail, will have more grave strategic consequences (much less their ability to fix odds one way or another in future turns).

This means that if you were able to completely control for the uncontrollable variables (luck), the only determiner of the game would be the relative skill of the two players. The better player would gain more from success, and lose less from failure. Of course, if you had two players who played at exactly equal skill level for any given game, AND all other variables were controlled for, the end result would always be a draw. The likelihood of victory, then would be determined by the relative skill inequality of the two players. The more one player played better relative to the other, the more likely it would be that they won the game.

But this relative skill between the two players is not, in fact, the only determiner of outcome, because there is this whole set of uncontrolled variables which also have an impact on the game. As mentioned, if the players are of very different skill level, the relative skill of the two players makes a big difference on the outcome. As such, when you have a gross disparity of player skills, player skill has an increasing impact on who wins a game relative to the uncontrolled variables (the chance a die rolls any given number being fixed).

Remember, it's the relative impact of relative skill that's important here. Take, for example, two players who were perfectly equal in skill. They had the same list, playing on a symmetrical board, playing the same odds just as successfully. In this case, the only determiner of who wins the game would be luck. If one player only rolled 6's and the other player only rolled 1's, there is a 100% chance that the lucky player would win. Likewise, if both players were equal in skill, the result of who won could be determined by just a single die roll.

If you control for one factor, it becomes less important to the outcome as the other factors. Likewise, as you control for all controllable factors, then controllable factors become less important to the outcome of the game as uncontrollable factors. As player skill approaches perfectly equal in any given game, the impact of skill on who won or lost is less. To put it another way, the closer you are in skill level to your opponent, the more that the outcome of the game is determined by luck.

SKILL ADVANCEMENT

If luck is the prime determiner of games, then, the only way to improve your chances of winning at all are to become better than your opponent. The wider you can force the skill gap, the more skill will be a determiner of the outcome compared to luck.

The problem with skill advancement, however, is that it has diminishing return. The more that you can lengthen or shorten the odds of a particular event occurring, the more difficult it is to continue to lengthen or shorten those odds. If you really want a vehicle dead, the shortening of the odds by bringing in 1 plasma gun where there was once zero is enormous. This is comparatively easy to do. However, if you're already a skilled player, and already have 20 plasma guns in range, being that little bit extra skilled so that you have 21 present isn't actually increasing the odds of a dead vehicle by very much.

Furthermore, just shortening the odds of any particular event happening is not actually necessarily the sign of a better player. In the above example, the better player would likely apply 10 plasma guns to two vehicles rather than 20 onto just one. In this case, the person who shoots all 20 at a single vehicle is suffering from overkill. While the short player is insignificantly more likely to kill the vehicle they shot at, for one dead vehicle, the "risky" player is still very likely to have 2 dead vehicles as the end result of their shooting.

As such, skill advancement doesn't really allow you to shorten or lengthen odds further (although it does this too), so much as it allows you to shorten them to exactly how short you want them, and lengthen them to the extent that you want them lengthened more exactly. As you get better in skill, the more likely that you are actually playing the the odds that you want to play.

In the end, though, you're not, over all, getting "better" odds, you are just getting more "accurate" playing of odds. This gets harder to get better at the better you get. Furthermore, it doesn't have any bearing on the actual effect of the die rolls (only shortness and length do, and even then, it's not an actual predictor).

What, then does the impact of playing exactly the odds you intended to have on the actual results of any given event or the game as a whole? None whatsoever. This means that luck is an independent variable of skill (which we already knew). It also means that the effect of more skill decreases absolutely the more skilled you get, as well as decreasing relative to that of your opponent.

THE EFFECT OF SKILL ADVANCEMENT AND LUCK

If skill allows you to play odds better, and if the better you get, the less getting better allows you to play the odds better, this means that the better you get, the closer you get in skill level to your opponent. As the closer you get in skill level to your opponent, the less skill matters, and as the higher your skill level gets, the less difference there becomes in skill level, we can conclude that the end result of increasing your skill level is to lessen the impact of skill on your games, and to increase the role that luck plays in determining the outcome of your games.

THE EFFECT OF LUCK AND SKILL

All of this means that the more one advances in skill at playing 40k, the less they will see their games determined by their increase in skill, and the more that they will see their games determined by luck. So what use does skill have at all?

40k is often compared incorrectly to other games. It's not like chess (which isn't based on random elements), and it's not like poker (where you get dealt cards, but you're not required to play them if everyone else folds), and it's not like candyland (which is completely random). The best analogy for 40k is blackjack - a game where the random element determines who wins and who loses, but better players will win more games (or more luck events, in the case of 40k) over time than will players playing worse odds. In the case of blackjack, though, the game is so simple that the best odds a player could play are well-known.

The problem, though, is that there ARE no "correct" odds to play in 40k, and if there are, they're impossible to calculate and constantly shifting over the course of the game as things move and are destroyed. There are some principles that are well established (like "bring anti-tank weapons and shoot them at tanks"), but the more detailed you get, and the smaller differentiations you're making (running a 50.0001% chance rather than a mere 50% chance that something happens), the more it all becomes guesswork.

This is for two main reasons. The first, as mentioned, is that 40k has a very coarse random mechanic based on six-sided die. Tiny changes in the odds you play (out to many decimal places, say) hardly matter when your unit has a 2/3rd chance of hitting and a 1/3rd chance of doing absolutely nothing. Likewise, there is a great deal of coarseness built into the game itself. If you have 5 plasma guns, you can't fire 3.45 of them at one target and 2.55 of them at another. You have a coarse, discrete set to deal with.

The second is because tiny differences in skill are only seen over appropriately large data sets. If you were 1% "better" than your opponent (which doesn't make sense since we're talking about playing imprecise odds in a dice game - what does "better" even really mean?), you would only be able to determine this if you played 201 games of 40k (with the same lists and same terrain and same mission, etc.), and noticed that your record was 100-101. As such, the idea of playing a tournament of a handful of games to decide who is best is flat absurd. And that's before we consider that the results can easily be poisoned by the coarse mechanic of die rolls. Even at a large number of games, you're still testing for who is consistently luckier, rather than who is consistently higher skilled. Especially since the accuracy with which one plays odds does not change the fact that its the dice that ultimately decide.

But even if you decided to use huge sample sizes, you would still run into a serious problem. The better you and your opponent get, and the smaller and more refined of odds you play, the larger and larger the data set has to get for you to be able to see the impact. Between two very good players that are able to play odds down to the 10,000ths, you may well need to have them play 10,000 games to see who is the better player. Of course, because this is also relative skill, in this case you would need to play 100,000,000 games to actually see the difference because you're really trying to see where one player played the 10,000ths and the other player only managed a 9,999.

As such, the point at which player skill fades into the sample size is shockingly quickly. For example, if you play three games against someone, they could easily be three times worse than you and still pull out an overall draw. Things are just too coarse, both in data creation (6-sided random events) and in measurement (inability to capture fine changes without lots of data points) to be able to measure the difference in player skill.

CONCLUSION

Because die rolls are the ultimate determiner of the success of events (and thus, the game), skill is defined as manipulating the odds that something will happen. Because it becomes more difficult to set these odds with greater precision, and the effect of increasingly smaller changes is itself increasingly small, it becomes more and more difficult to see the effects of skill on the outcome of a game. This is especially true as both players become more skilled (skill becoming a controlled variable), and the orders of magnitude problem quickly surpasses both the coarseness and absolute impact of luck, as well as the ability to determine player skill by empirical means.

As such, we can conclude that once a player reaches a certain level of basic proficiency, success is more determined by being lucky than good, that player skill plays an indirect, and sometimes indeterminate effect on the outcome of a game, and that 40k isn't a game that in any way accurately tests player skill.

Put another way, 40k is a dice game, not a strategy game.