In algorithms you can trade space for randomness. I don't know if there are some precise generic theorems about this as opposed to theorems about specific families of algorithms. But that's not why I'm here...

There's a similar trade you can make in games, TTRPGs in particular.

For example, you could go old school and track how long everyone's torches have been alight as they explore their dungeon. But it's tedious to track that state.

There's another extreme where you can say a torch has a fixed probability of going out each turn. But that's unrealistic in a way that's not fun. You don't get the anticipation, or dread, of your torches slowly burning down.

Today I learnt about another approach to torches that uses a middle ground. You roll D12 every so often to see if the torch burns down. When you roll a 1 you now switch to rolling D10. When you roll a 1 you switch to D8 and so on. When you roll a 1 on D4 (say) the torch goes out. There are far fewer state updates. You can even store that state as a choice of die sitting in front of you.

There's probably also a connection here to DSP with the fixed probability case acting like a one pole filter.