Randomness is a major part of many games, whether board games, computer/video games, or physical games (such as sports). While many games do not have any randomization elements in their mechanics, such as Chess, I'd say that the majority of games do rely on randomness to some degree.
Let's take a moment to define randomness. For the purposes of games, it is an element built directly into the mechanics for the purposes of generating a set of unpredictable values, which will influence the outcomes of any in-game action. One effect of having randomness in a game is forcing players to weigh risk-reward in a given situation (such as in Blackjack and derivatives). Because it specifically involves a mechanic built directly in the rules, natural randomly occurring events, such as weather in a game meant to be played outdoors, is not counted in this definition despite the fact that it can alter the outcome of a game.
In my studies, I have distilled four general categories for randomness found in games, illustrated in basic examples.
-Ranged Randomness: Dice
-Fixed Randomness: Cards
-Player Randomness: Rock-Paper-Sissors
-No Randomness: Tic-Tac-Toe
When dealing with randomness in games, it's important to note that all randomly-generated values are within a fixed range between two values, and at least one party is aware of what, exactly, that range is, even if that party is only the designer/programmer.
Ranged Randomness involves all parties involved, player and non-player, knowing exactly what the range is. However, each time a value is generated, no party can know for certain which value in that range it will be. This is most exemplified in dice, which will always generate a number unpredictably (unless it's weighted).
Fixed Randomness involves organizing a set of values in a given range to an unpredictable order. Even though a third (non-player) party can look at the values and know exactly which ones will come up in what order, the players involved are completely unaware of the order. Cards are the quintessential example of this type of randomness, which are shuffled before play into a random order.
Player Randomness differs from both Fixed and Ranged Randomness, in that the value is generated by the player. Players will generate the value in question, and keep that value hidden from all the other players until the rules dictate when the reveal happens. Rock-Paper-Sissors is the most illustrative example of this type, as players will generate one of the eponymous values, which have cyclical win-loss relationships.
No Randomness is just what that is: a game without any built-in random element. All the values of the game are known to all parties at all times, and the only aspect of unpredictability is in the specific action of the player. While Chess is a great example of such a game, Tic-Tac-Toe is perhaps the simplest example where both players know exactly what values each other has.
No single one of these types is inherently superior or inferior to another; each one can be utilized in appropriate situations, or combined to create complexity. However, as games are a form of imitative art (that is to say, games are imitative of real-world experiences), certain types of randomness are more appropriate than others for certain experiences.
As an illustration, let's separately add Fixed and Ranged Randomness to Chess, and see how the experience changes. First, a clarification: Chess is a game designed to immitate warfare as a test of a general's ability to strategize in a hypothetical situation where all other elements are equal and transparent.
Let's first add Ranged Randomness by applying die rolls to captures. For our purposes, each piece will be given a set number of dice. Pawns will get one die, Rooks and Bishops will get two dice, Knights will get three dice, the Queen will get four dice, and the King will get five dice. Each time a capture is made, both players roll the number of dice appropriate to the participating pieces. If the capturing piece rolls higher, or there is a tie, the capture succeeds as normal. If the defending piece manages to roll higher, however, the capture fails and the turn passes. A check can only happen if the checking piece rolls higher than, or ties, the five-dice roll of the King. Otherwise, the checking piece moves back to its previous position (any captures made still apply). Pawn-promotion also uses dice: the player rolls the single dice, and whatever number comes up determines the piece it becomes by corresponding to the number of dice a piece has; 1 fails the promotion, while 5 and 6 call for a reroll.
How this additional set of dice-rules effects the Chess experience might be seen in which element of warfare is being imitated. Here, the hypothetical situation is that each piece corresponds to a unit of soldiers rather than a single soldier, and the dice simulates the play of random elements (weather, troop morale, commander competence, etc.) in any given battle. This adds an element of realism to the game, as no non-participatory army commander can be considered in 100% control of all battles. Certain elements will always be unpredictable.
Now, let's add Fixed Randomness to Chess and see what happens. (I should first note that this variant on Chess can add several hours to the game, and so is not recommended for quick, casual play.) This time, captures involve a quick variation round of Texas Holdem Poker, using only A-7 cards of all four suits. Similar to before, each piece is dealt a certain number of cards: Pawns 2, Rooks and Bishops 3, Knights 4, and the Queen gets 5. Here, the King will also get 5, as well as an option to discard up to 3 cards per check attempt. Each time a capture is made, or a check on the King attempted, the deck is shuffled and the appropriate number of cards are dealt to the players, while 3 cards are placed face-up next to the board. (Field cards are always placed BEFORE being dealt to the players.) Similar to before, the player has to build the best Poker hand from the available cards. If the capturing piece wins, or there is a tie, the capture goes through as normal; if the defending piece wins, the capture fails and the turn passes. Check attempts are also as before, but pawn promotion behaves just like regular Chess, with the player simply choosing what piece to promote to.
In traditional Poker fashion, capture attempts also involve an element of bluffing and betting. However, instead of using Poker Chips to bluff, an element of the card game Cheat (also known colloquially as Bull****) is utilized. The player can fold as normal, state exactly what hand can be built with their cards, or just by stating that the hand present is higher than a certain one (for example, "My hand is higher than a Two-Pair"). The other player can then respond by believing the statement and folding, declare the other player a liar, or by declaring the possession of a larger hand, either specifically or not. The first player now only has two options: fold, or declare the other player a liar. Any time a player is accused of being a liar, the hands are revealed.
Finally, there's an Oracle element to this variation. During a capture or check attempt, once all cards have been dealt, a player can, only once in a round and only three times per game, sacrifice one of their pieces to see a certain number of cards in the opponent's hand: a Pawn shows 1, Rooks and Bishops show 2, Knights show 3, and the Queen shows 4. The player whose cards are being revealed does not know which cards were seen. This can also happen during normal play to see the same top corresponding number of cards in the deck (not revealed to the other player), but causes the turn to pass.
This time, while the element of unpredictability remains, the players are forced to watch each other as much as the board. The focus of this variation is placed on the immitation of wartime diplomacy. Parties that have gone to war will generally still communicate with each other in taunts and statements of superior might, which, when tactfully declared, can make all the difference. The Oracle element could be thought of as immitating one of two things: spy-networks gathering intel on the enemy, or in the ancient practice of sacrificing to the Gods to gain information on the enemy. This gives each player the potential for a small edge in determining whether the other is lying.
Both of these examples emphasize different aspects of warfare imitation, neither one inherently standing above the other in terms of validity. Using dice with Chess imitates random elements in the battle itself, while using cards with Texas Holdem Poker rules imitates wartime diplomacy. Using other variations and combinations of these types of randomness on games can create a potentially infinite variety of experiences. Game Design is an alchemy as much as anything, so to any who are budding Designers like myself, I urge you to come up with your own variations of games and see what happens.
After all, consider this: what do you get when you add 3 Parts No Randomness, 4 Parts Ranged Randomness, 2 Parts Fixed Randomness, and 7 Parts Player Randomness? Well, I'm sure people will disagree with me on the result I got, but by my reckoning, that formula will give you a Pokemon Battle.
I hope you enjoyed reading this, and that you found it useful. Let me know what you think.