Oddly, in my limited experience, it is very effective.
I can't say it's the right pattern for every game but for the current roguelike I've been working on in my spare time it's been the best thing since sliced bread. I use the Reader and State Transformer monads in a pattern similar to the Elm Architecture that results in my engine being completely deterministic.
This allows me to dump all of the initial state of the game and all of the serialized inputs to it. I can then take that dump and step through that entire game session. This is great for debugging with friends and stuff: when they encounter an error or something they don't like they can just send me the dump file and I can replay their entire session. It's been pretty cool being able to do that.
Another thing I didn't understand at first was that immutability seemed like an egregious waste of resources. It might still be for some applications but it has much better performance characteristics than my intuition had led me to believe... because structural sharing. You can have this big blob of state that looks like it's being copied every where but it's not -- under the hood you're actually sharing 99% of the previous state and not copying anything.
It's not likely you're going to be writing a bleeding-edge rendering engine in a pure FP language on any current generation hardware platforms but you can get quite far with it.
"A Worst Case for Functional Programming?"
http://prog21.dadgum.com/189.html
Previous HN discussion: https://news.ycombinator.com/item?id=7043644
Nearly none of the traditional game-based OOP design patterns map cleanly into F# (or any functional lang for that matter) - I often had to get creative but the results were very interesting.
Take an OOP based game for an example; tracking where your game state is, how it's being mutated, and figuring out exactly what entities have been mutated can be a nightmare. With F# I ended up with a single large data structure to store the game state, and because of F#'s pedantic immutability, it's very easy to find where that game state is modified.
The only issue with the scheme above is that there are some cases where you NEED to store game state as a variable captured by a closure. That might sound really awful, but in practice variables captured by a closure are always read-only, so unless you're replacing that closure, you don't have to worry about some weird mutability sneaking up on you.
Here's my first F# minigame, a mostly-finished breakout clone: https://github.com/bsamuels453/BreakoutFSharp
Here's the second game that uses units of measure - it was supposed to be an asteroids clone but is mostly unfinished: https://github.com/bsamuels453/X81-Prototype
Type declarations for the units of measure/data structures I used: https://github.com/bsamuels453/X81-Prototype/blob/rts/X-81_P...
let mutable greeting = ""
let btn_say_hi = new Button(Text = "Say Hi", Parent = frm_main)
btn_say_hi.Click.Add(fun _ -> greeting <- "Hi!")