Here is an implementation of a linearly recursive bowling scorer following the rules from Wikipedia.

It does not use mutable state. Once created values don’t change.

The main entrypoint is the Game.score() function which accepts rolls from one player as a sequence of arguments. The Game.score() function delegates work to the recursive Game._scorer(). This iterates over all provided rolls keeping track of any bonuses which are due.

Game._scorer = function(previousShot, rolls) {
    var roll = rolls[0];
    if (roll === undefined) {
        return previousShot.score;
    } else {
        var bonus = this._bonus(previousShot, roll, rolls);
        return this._scorer(previousShot.next(roll, bonus),
                            rolls.slice(1));
    }
};

The variadic Game.score() function is implemented using the arguments object.

Game.score = function() {
    var init = new Shot(0, 0, 0, 0);
    return this._scorer(init, [].slice.call(arguments));
};

To Run Tests

npm test

On Recursion

For more information on recursion, consult the Factorial example from SICP.