Score system for "little bit more complex" snake game

Question

I have created snake game. I can't think of good score system so that is is fair.

There is only one highscore list for all modes.

Player can choose any size of board - Let's call that param "Board area", it is defined in cells. One snake segment takes one cell.

Player can choose any speed of snake - Speed, in cells per second

I don't know how to calculate it so that score is fair for all players.

Firstly I thought of this: score = length * speed But is is not fair for players that reach end of board (nearly no free spaces to go, careful planing is needed to survive).

Then I thought that I need somehow award players that can survive for long in small amount of free place. The new formula looks like that: score = (length/board size) * (length * speed) But I still don't like it.

My score should reward players for: Longest snake, tight turning and planning (bigger multiplier when board is full), and speed at which they are playing.

Answer 1

I'd squeeze in another variable - cells travelled - it could act as your "planning" score.

Base

Given the core variables speed, length, cells travelled, the main formula could be:

score = base * (length * speed)

With base being:

base = cells traveled; // basically, this could prove enough

// optionally
base *= board size coefficient; // a coefficient based on board size could apply to base, this is for you to judge, but generally the idea is that the larger the board, the smaller the coefficient.
base *= prohibited cells; // prohibited cells ("walls") also being an applier - the larger the prohibited cells, the larger the coefficient.

Tight turn

I'd give tight turn a constant value. So, once a tight turn happens: score += tight turn * speed. Though, length could act as a modifier again - base += tight turn * (length * speed).
You could also apply a modifier to tight turn based on how tight it was by checking the distance between head and tail after turn.

Fruits

In case you have "fruits" there, lets give them a constant value again fruit, once we eat one: base += fruit * speed.

Extra mechanics

You can also implement extra mechanics. One variable being cells travelled to get the fruit.

The other being, tail kiss - gives extra points once head, being perpendicular to tail, exchanges the last tail block.