It's widely (although not universally) accepted in tabletop gaming that it's fun to roll dice. Broadly speaking, that tends to be correct. There's a guarantee in rolling dice. You're either going to be happy because you get what you want, or else you're going to be surprised. We humans like getting what we want, but also we like to be surprised. It seems like a winning formula, but here are 5 important hidden costs to dice rolls that game designers ought to keep in mind.
Every dice roll has a rule associated with it. You don't just roll dice to roll dice. You roll a die, and then you do something based on the result. Every die roll represents at least a binary condition, but because there are lots of sides on most popular dice, there are probably more than just two results.
When you tell a player to roll a die, you're generally asking the player to recall a ruleset governing how the game proceeds based on the dice result. Back in the bad old days of traditional board games, the rule was probably roll a six-sided dice and then move your player token that number of spaces along the path. But modern games can get complex, so very often there's a different ruleset governing different "kinds" of dice rolls. Roll this die and add this number for combat. Roll that die and add that number for defence. Roll this other die and add something else for a skill check. And so on, and that's assuming the player is only playing one or two games.
It can get to the point that players dread picking up dice.
Some games are all about strategy. A player is provided resources, and must spend those resources to outsmart another player or the game engine. The exciting element in this kind of game is the set of known factors. It's a puzzle that needs solving.
Dice rolls are never known factors. Randomness is the point of a dice roll. A dice roll brings the unexpected into a game, and that can be frustrating for a player who thinks the game is about strategy.
In [the mostly defunct] Magic: The Gathering (MTG) game, there was a set developed as a tie-in to [the mostly defunct] Dungeons & Dragons universe, and it introduced dice rolls to some of the cards. (There'd been dice rolls in some of "Un" sets before, but the pretense of "Un" sets is that game play is intentionally silly.) In the D&D set of MTG, a card requiring a dice roll made the card almost useless because, after all, the very definition of what the card could do was variable. MTG has a catalogue of over 25,000 cards, so why would you ever use a card that might do a thing when you can almost certainly find a card that definitely does a thing?
To off-set this frustration, the dice rolls never worked against you, and instead you only ever stood to benefit from the roll. But that meant that a card with a dice roll was only "valued" (in game terms) at its lowest effect, because a smart player doesn't bank on a roll of the die. On the contrary, a common strategy in MTG deck building is to reduce variables by including the maximum number of the same cards in a deck. Many winning deck lists are surprisingly short because they include four copies of literally every card so the player is drawing known factors.
Dice rolls and strategy aren't entirely at odds, though. Wargaming and RPG can be extremely strategic, but players of those games tend to value (and plan on) surprise. A recognized part of the game experience is to deal with blocked attacks, counter-attacks, attacks of opportunity, near-misses, unexpectedly powerful hits, and all manner of unforessen circumstances.
Rolling dice can have an effect on a game's pace. In many wargames, there are defence rolls that verify the effectiveness of a hit. That makes at least two rolls, one for each player, for every troop attack. One player rolls dice to make the attack, and then the other player rolls dice to confirm that the hit was damaging. A third roll is often required to establish how much damage was dealt. That's three rolls for the most important action in the game.
This is an "expensive" roll that functionally presses pause on an exciting moment in the game. Imagine it. You move in for the attack. Your squad fires 15 dice worth of artillery. You get 9 hits!
That's exciting! Except now stop, and pass control to your opponent. Wait for the defence roll. Your opponent shrugs off 2 hits, so your 9 is now a 7. Roll again to deal damage.
It's not a crushing blow to the pace of the game, but the game is definitely at its mercy. In a wargame ruleset I developed, I offset this interruption by using a successful hit to award the attacker with bonus "hit die" that they can choose to roll on their next turn in hopes of making a "kill". Obviously, the more hit die you have, the better chance you have to score a kill and remove a soldier from your enemy's squad. There's no damage in the game, you're just rewarded with hit die. Whether collecting hit die is as satisfying as seeing your opponent's wound allowance go down depends on the player. Whether waiting until your next turn (the game uses squad activation, not sides) is better than just waiting for more dice rolls also depends on the player. I obviously think it's a superiour play experience (if I didn't, I wouldn't have written the rules.)
Gamers love to game, and the "problem" is that gamers can find games in unexpected places. If you've got a dice roll set up as a barrier to a thing a player wants, then to some players that's an invitation to find a way around rolling dice. And that's fair play.
Gaming is all about finding a creative solution to problems. If you've got dice set up to determine the speed of running toward a finish line, then you're effectively broadcasting to players that running is a gamble. Some players are happy to gamble, but other players take it as an invitation to avoid running.
But when you roll dice, you feel like you have agency. You're taking your fate into your own hands by...surrendering your fate to chance. OK, it doesn't make all that much sense, but something doesn't have to make sense to be true.
Sometimes as a game designer you use dice because you want to communicate to the players that there's a barrier. Success depends on a dice roll. Just be prepared for players to potentially try to avoid dice rolls, especially when there can be negative results from a bad roll.
In Blackstone Fortress, there's a challenge in which player characters have a chance to acquire some rewards by rolling dice. However, a failed roll results in 1 point of damage. I think the designers understood that the potential damage would cause some players to essentially opt out of the challenge altogether, and the mechanic successfully makes it an intrguing individual risk in an otherwise co-op game.
A sometimes underrated source of pseudo-randomness is a card deck. When a player rolls dice, probability takes over. It's possible for a player to roll six 1s in a row. If you're designing a game where 1 is the absolute worst result, then your game also needs to be prepared for the possiblity of lots of failure. More importantly, your players need to be prepared for failure, and they aren't always willing to endure that.
Games like Pandemic: Reign of Cthulhu, Forbidden Island, Pathfinder Adventure Card Game, and Battle in Balin's Tomb use a shuffled deck to impose penalties. To increase the probability of a bad event, cards are either stacked in some portion of the deck, or they're placed back on the top of the deck under certain circumstances.
A deck of cards cycles through conditions in a surprising but ultimately evenly-distributed way. If you have a deck of six cards numbered 1 to 6, then you know you're only going to get a 1 once out of every 6 draws. It's not just improbable, it's impossible to draw six 1s.
Rolling dice is fun, but there's a cost. Sometimes, the cost may be acceptable to you as a designer. Other times, it helps to consider fewer rolls, or alternatives to dice. Playtest your game, find out whether you're accidentally designing a Yahtzee clone or whether you're designing something fun. No mechanic appeals equally to every player, so use your own definition of fun as the ultimate guide.