Approaches to random elements in games

I've been thinking a lot about luck lately. Specifically, I've been thinking a lot about how elements of luck are approached in games. Not so much specific randomizers, but structurally speaking. And I've come up with three basic approaches to luck that I think all games fall into. And of course, most games fall into multiple categories. The three categories as I see them are:

• Deterministic - in which the mechanics have no inherent random element. Any feeling of randomness comes from player interaction or hidden information.
• Uncertain Actions - in which player make a choice and then some sort of randomizer affects the result of that choice.
• Random Events - in which a random element takes effect and then players make choices in response to that event.

Deterministic

The best example I can think of for a deterministic approach to randomness is Chess. Although basically any abstract game could be plugged in to replace Chess as the example. There are two potential elements of luck in a deterministic game, information and player action. In Chess, like most abstracts, the players have perfect information so the only real randomizer is the skill level of your opponent.

In terms of my own designs:

• Europan Wars (still in development) is a deterministic war game with hidden action selection. It plays sort of like an RTS (real time strategy) but instead of real-time it uses simultaneous action selection. The random element is that I don't know what you will do and have to make a decision at the same time as you. 
• Battle of 4 Armies (out of print) is a lightly themed abstract. Players have complete information but need to be able to see chains of moves to really play well. It also has a randomizer which falls under the Uncertain Actions umbrella, but it's not used every game.
• Swytch (out of print) is a solid abstract with just a bit of hidden information/memory as the orientation of pieces within a stack can be important for advanced play because the directions a stack can move are based on the orientation of the top piece and the stacks can be split in various ways.
• Symmetric (out of print) is an abstract game in which the movement of a player's pieces can affect the position of their opponent's pieces. Ultimately it is about out maneuvering your opponent. It has perfect information, so it is probably solvable but I haven't solved it. 

Deterministic games are pretty much the ultimate in player agency. What they want to do, they do with no random chance of failure. But, a purely deterministic game can have a downside in that if there is perfect information they also have the potential to be solvable. That is to say, there can be a right move in a given situation and in fact every move of a game. Granted this is usually an issue with particularly simple games such as Tic Tac Toe but if a game is solvable and that becomes common knowledge that is the opposite of agency, as the game basically plays itself.

Uncertain Actions

A good example of this would be Risk. In Risk, players may choose to attack a province and if they do both sides roll some dice to determine what happens. Because of the nature of dice, it's possible then for an overwhelming force to fail.

In my designs:

• The Chosin Few is a simple solitaire wargame. One of the actions players can take is attacking enemies. The success of an attack is based on a die roll compared to the strength of the attacking unit.
• Surrounded with a Shotgun (unreleased) also uses dice for its combat resolution. To simulate the effect and feel of a shotgun when you fire into a group you roll a number of dice equal to the number of enemies in the group (to a max of 5) and compare each result to a simple table. Enemies can either be killed (removed from the game) run off (removed from the board) or scared (pushed back one space)
• Federation of Sol (unreleased) uses a success system where you may roll up to 5 dice and individual results of 5+ result in pushing enemy fleets, but if they get pushed far enough they get removed from the board. Federation of Sol also has a Technology system where you can spend a tech resource to roll for all the technologies you are currently working on. And they are more likely to advance than not, but the further along you go with each tech the harder it is to make progress.
• Battle of 4 Armies (out of print) has one mechanism that is Uncertain. If you have captured at least one enemy and one or more of your regular units have been captured, as your turn, you may use the captured enemy as a binomial randomizer (flip it like a coin) to try to get one of your regulars units back into your pool to place later. Since it costs you a turn, it is a costly move but sometimes worth it.

The strength of uncertain actions is that they are uncertain. And as such should only be used to simulate things that would be uncertain. If for example, you were playing a worker placement game in which you had to feed your workers at the end of a round. If you had to roll to see if you succeeded in eating, that would probably upset you because eating isn't something that you can really fail at. You either have food and eat or you don't. At the same time, if you have to roll to see how much food you gather with placed worker that maybe doesn't upset you because the action doesn't feel like it's representing something inherently easy.

Random Events

A good example of this would be Catan. The basic structure of a turn is you roll some dice which causes resources to be generated or the robber moved. Then, the player gets to decide how to best utilize their resources.

Another good example is Carcassonne. In that game, players draw a tile at the start of their turn and must place it. The event is drawing a tile, then their decision is how to best use that tile.

In my own designs I've used this approach to randomness a couple of ways:

• In several of my games (Why?!, The Chosin Few, and Surrounded with a Shotgun) this takes the form of a random event card drawn at the start of the turn followed by a number of player actions also determined on the card.
• In Federation of Sol, I instead use a set of 7 custom dice that are checked against various game states to manipulate the board before allowing the player to spend gathered resources to affect the game.

I really like this approach for a number of reasons. The biggest is probably that it gives players a sense of agency that is hard to get using the uncertain actions approach, while still having enough uncertainty to keep it from having any kind of solvability.