Algoritmo resuelto

gistfile1.txt

function playing(list,times){
	var newArray = [];
	var x = 0;

	for(i=0;i<list.length;i++){

		// console.log(list.length);
		if(times > 0){
			if(list.length%2 == 1){
			// impar debemos eliminar desde el 0
				if(i>0)
					x = (2*i);
				else 
					x = 0;
			}else{
				//arreglo es par
				x = (2*i)+1
			}

		}else{
			x= list[(2*i)];
		}
		if(list[x]!= undefined)
			newArray.push(list[x]);	
	}

	console.log(newArray);
	return newArray;

}

function playTheGame(number){

	var list = [];
	
	for(var i=0;i<number;i++){
		list.push(i);
	}

	console.log(list);

	times = 0;

	while(list.length > 1){

		list = playing(list,times);
		times++;


	}
	


}

playTheGame(process.argv[2]);

i don't know if this work well in all the cases, i don't have the time to probe xD