Dice and probability are an inevitability in any war game, however a distressing number of games include it simply because "war games include probability". There are three good reasons to include probability:
1) To provide constant interesting tactical choices. Without random events skirmish games would be little more than sloppy games of chess, predictable but without the strictures that make such predictability interesting. Chance allows a skirmish game to have a player formulate a plan, see it go wrong and build a new plan on the fly, which is fun. It is vital though that such probability allows enough predictability to formulate plans.
2) To keep hope alive. Outnumbered or outclassed troops should still have a lucky shot at defeating their opponents. Each player should have good reason to keep playing until the play is done and not before. The added advantage is that forces can begin games with lots of small chances of victory or a few large chances. It is vital however that chasing hope for a losing player does not result in destroying any point of playing well for the winning player. If every player constantly has a reasonable chance of victory whatever they do there is very little point paying any attention to the game itself.
3) In the interests of simulation. Battle, as with much in life, is never certain so it is more accurate to real life to add in random elements. That said some things are fairly certain, enough so that including their failure in a simulation is either pointless or likely to annoy. It is a strange obsession with war game designers to put in the automatic fail result so that even the most highly skilled individual performing the simplest act occasionally fails badly enough to slice their own nose off, but more about that later.
If your game's dice or other random elements aren't there to fulfill one of these three criteria seriously consider replacing them with a definite event.
The Third Circle Of Hell: Punishment Without The Chance Of Rehabilitation
It is a truism, but an important one in games design, that you get the behaviour you reward. The flip side of that coin is that you do not get the behaviour you punish. The worst extension of this idea is in punishing behaviour that you have forced players into. Many games include a "fumble" system, creating a worse than failure option. For example, Test Of Honour is a genuinely excellent system but it has a fumble system whereby characters can hurt themselves if they fail a roll badly enough. In cases of hand to hand combat this can be imagined as a last minute parry but in the case of firing a bow it seems to indicate a combatant shooting themselves in the foot for no earthly reason. This event can occur to the game's most skilled samurai bowman shooting a stationary target in clear view on a well lit day, not only can it happen it happens quite regularly. This would be fine if it were an avoidable tactic to attack the enemy but it isn't, it is a behaviour that the game forces you to adopt and occasionally punishes you for adopting. When you punish a player with a reaction to an event you are, for want of a better term, teaching them a lesson. Punishment teaches your players how to play your game and if you punish them for what they are meant to do or have to do you're not teaching them any more, you're bulling them. Worse is when you punish players for attempting what the game should be making fun. The hugely successful Frostgrave has a system where its most enjoyable and exciting element, casting spells, occasionally wounds your leader. The result is that sometimes when you do what the game was built to let you do, it punishes you for doing it.
If your chances involve punishing events, have them occur when a player does something wrong or chooses to exchange risk for reward. If your game has events it is meant to be about, include rewards for doing them well rather than punishments for doing them badly. When working on Gaslands there was an early version where the car in the lead at the start of a race never won the game. We had to fix that because otherwise the behaviour you were rewarding was not trying to win the race. Always reward the behaviour you want. Of course to do that you need to know clearly which behaviour you desire.
Mo' Dice Mo' Problems
Some designers have the odd impression that everyone is thrilled to roll lots and lots of dice with lots and lots of results. In truth those over the age of 12 generally don't find this much fun. Dice are fiddly, especially if a system has a range of types and stacking results. Rolling to hit, rolling to wound then rolling to save is practically a war games cliche, it would be the central system to any generic skirmish system. While the process is widespread, its a pain, roll a handful of dice, pick out some without disturbing the others after making sure all players have checked all results, then do it again. Then do it again. If it weren't so widely accepted no-one would suggest it, "you just picked up an X" is the argument most often had at gaming tables and the etiquette of removing fails before re-rolling hits is probably the most vital unwritten rule of modern tournament gaming. Just because its an assumption don't believe that stacking dice results is a good idea.
The only very good reason to ever have a player roll more than a couple of dice at a time is to employ the "bucket of dice" method of probability control. If an event occurs based on a single D6 score it is very hard to predict and control, if it occurs based on how often a score occurs across ten, twenty or thirty dice it becomes much more controllable. However this control only kicks in if you have a lot of dice a lot of the time, if the system rolls six or seven dice a few times (more with a dice of more than six faces) it might as well just roll one or two. If your system rolls D12 or D20s it will need to roll actual buckets of them to provide any level of probability control. If you ask players to roll two D10 for five damage each just roll one for ten.
Rolling one D6 needing a six is a moment of excitement. Rolling twelve needing four sixes with a re-roll to achieve the same goal is much less exciting. You can see this in that if you give this event to a player they will tend to roll the last few of the twelve dice one at a time, just in case they end up needing one six on one dice, because players will make their own fun if they have to. Oddly while four sixes on twelve dice is more likely than one on one dice it feels less likely, it feels like failure is a depressingly forgone conclusion in fact. Dice should be fewer with clearly defined results.
Additionally, the reward for both setting up and beating the odds must always be commensurate. If a player lines up an attack that generates an unusually large number of dice for your system they should be rewarded by having a lot of stuff happen, or at least a few really big things. Also if they make an extraordinary number of saves they should come out better than expected. Nothing is less satisfying than a huge number of dice that end up doing little or nothing of significant effect.
Tables Embedded In My Heart
Another oft given justification for a lot of random probability in a game, particularly a narrative skirmish game is to allow for "fun" story events to trigger at various steps. This is usually a place to pull out a table and then, oh horror, an embedded table. Designers of a certain type delight in a table that triggers off a rare event with a rare result that triggers another roll on another table. This is, as a rule, a very bad idea. There are two possibilities. One is that what happens on the embedded table is not interesting enough for it to be worth the effort of triggering it and looking it up, which is bad, what's worse is that sometimes it is worth the effort. For an event to be worth trawling through two or three tables mid game it has to be really fun, and if your hiding the really fun bits of the game in a table that rarely ever triggers then your putting a lot of work into something that never gets seen and producing a game that's less fun than you put the work in to make it be. I personally have a nasty suspicion that designers who know they've missed their promised target of narrative involvement then embed a set of tables deep in their games full of promised but never reached carnivals of narrative excitement, so that when they don't come up players think the excitement is in there somewhere and bad luck alone means that they miss it.
The worst crime of table embedding is that it not only hides excitement away but that it hands it over to pure chance, it removes player agency. Players engage with games for a sense of control, interaction and agency. If an event is exciting or enjoyable players should be able to trigger it by their actions, not by chancing down a table, they should be able to play for and get it. If its not exciting or enjoyable it should be removed.
The fact is that rarely triggered events just get plain forgotten by most players, tables that don't get referred to regularly or triggered at very specific known events get forgotten. One or two triggering events is a good maximum and embedded tables should just be avoided if at all possible.
Write in rules which produce real and exciting moments because players choose them and unexpected moments because of emergent and synergistic engagement of player actions.