Since it's come up a great deal lately, I thought it would be nice to document the rationale for how luck works in Wesnoth. In particular I'm going to compare it to games like Fire Emblem which have luck as less of an influence. If people find this useful, it could go in a wiki page.
Different games have varying degrees of luck. Some games are completely deterministic, such as chess, go, and tic-tac-toe, and some trivial games such as snakes and ladders are governed entirely by luck. Most games fall between, such as Dungeons and Dragons, Settlers of Catan, Monopoly, Poker, Backgammon, Fire Emblem, and of course Wesnoth.
In Wesnoth, there is a substantial, but not huge amount of luck. The main luck limiting factor is the way in which units have multiple strikes in a battle. A unit with four attacks has four chances to hit, not just one, and so it is generally reasonably unlikely that they will either miss all four times, or hit all four times.
Of course, units have different numbers of strikes. This means different units are susceptible to luck to different degrees. This is one of the key gameplay facets of Wesnoth: managing luck. There are many opportunities to manage how much risk one exposes oneself to, and make backup plans if things go wrong.
This can be contrasted against a game like Fire Emblem. In Fire Emblem, a unit typically has one attack, though may have two in some situations, and four or more in very rare situations. Units also have a chance to hit, but it is dependent heavily on the attacker's skill, and in particular, it is common for an attacker to achieve a very high chance to hit, and a 100% chance to hit is common. (If a player wants, they can optimize to almost always have 100% chance to hit).
This approach is more satisfying for many gamers, because they feel in control of the game. They can normally achieve a 100% chance to hit, they can use units that have poor dodge abilities but high resistance to damage, and expect to usually be hit, but take relatively little damage. They can play Fire Emblem close to being a deterministic game.
This has a certain appeal to it, and is fun in its way. In particular, one can often in a turn in Fire Emblem carefully plan out one's moves, work out how many enemies one can definitively knock out, and can plan to avoid any chance of one's own characters dying.
However, in my opinion this kind of gameplay has only a limited amount of appeal. It is certainly not the kind of gameplay we want in Wesnoth. In Wesnoth we want a player to plan out a complex situation, to estimate carefully the possibilities. To have to work out a good strategy. If a player can simply rely on all sorts of assurances that their units will hit, they don't have to do any of this. Sure, there will be a certain amount of fun to planning out a situation where you can set up a cool 'domino effect' of enemy units going down as you attack them. But this is nothing to do with the skill of planning out a real strategy in a dynamic situation where you have to consider all kinds of contingencies.
Additionally, a big reason why the Fire Emblem approach works in Fire Emblem is that the Fire Emblem AI isn't...really even an AI. It is closer to being 'scripted'. The enemy doesn't move intelligently at all. Most enemy units just stand still until you move in range, then they charge forward and attack. This makes Fire Emblem closer to a puzzle game than a strategy game. If Wesnoth used a Fire Emblem-like system, there is no way you could keep all your units alive, because the AI simply wouldn't be that dumb. There would be situations that would be simply intractable for you to avoid losing units in.
Wesnoth's approach also requires a substantial amount of analytical ability from the player. In chess, and in Fire Emblem, one knows that if they lost, they made a mistake. In Wesnoth, one can occasionally play better, and still lose. Bad in many ways perhaps, but still it adds an interesting facet: it requires more analysis as a player. You have to be able to distinguish from situations where you played a good strategy but still lost, and situations where you lost because of your poor strategy. Certainly, in real games, a losing player will almost certainly have made mistakes, but working out what those mistakes were becomes difficult, and requires great analysis.
In my opinion, many people who struggle to improve at Wesnoth do so for this very reason. They fail to see strategic mistakes they make, resulting in them losing, as such, instead believing their loss was a result of luck. Other times they may blame the wrong things for their loss, and correct the wrong things. This analytical ability is a crucial skill required for Wesnoth play, and simply wouldn't be needed if luck wasn't such a big factor.
I also do not think that in fact, Wesnoth has a great deal of luck compared to many other games. Games such as backgammon, poker, bridge, and settlers of catan involve higher levels of luck. Most versions of Civilization have at least as much luck in their combat systems.
Trying to "slide down the scale" of luck would simply make Wesnoth less interesting, in my view. Suddenly the difference between a two attack unit and a four attack unit would be trifling instead of critical. Not near as much planning would be necessary. Simply, in my view, Wesnoth would become less fun.
Of course, the Wesnoth community should always be open to experimentation. Practice trumps theory. I myself have worked on an experimental change to allow an 'accuracy' feature. Other people have tried experiments too. However, so far I haven't seen any experimental evidence that points to anything but the above rationale being correct and accurate.
I think that one of the biggest problems people have with luck in Wesnoth is that it is computerized. People know how dice work. There is a certain aesthetic enjoyment to rolling dice, to feeling them in one's hand, to choosing how to roll them. One does not get this with a computer. One has to 'trust' in the fairness of the system. And heaven help us when people 'discover' that computers actually use pseudo random numbers. It doesn't matter that the 'pseudo' part is only really relevant in cryptographical applications and that for a game a pseudo random number generator is as good as a 'real' random number generator. People start to think they can see 'patterns' in the numbers. Numerous variations of the gambler's fallacy take effect. People remember times they were unlucky and ignore other times. And so on and so forth.
Time and time again people have insisted that they see all kinds of incredibly unlikely unlucky sequences, and claim to see such sequences on a regular basis. This is probably a natural human response, exaggeration of the effects of luck in one's mind. I have asked such people to send me replays of their unlucky games, and then I either never receive such replays, or when I do and I analyze them, I find that objective analysis shows that the person was not near as unlucky as they said they were, or were not unlucky at all.
In summary, luck is an important and crucial part of Wesnoth. It is certainly not some dial that can be scaled back a little without critically affecting gameplay. Players should remember something: Wesnoth is not a typical game for its genre, nor do we intend for it to become one.
“At Gambling, the deadly sin is to mistake bad play for bad luck.” -- Ian Fleming