Arduino2Max Problems

Projects General Guidance
3 
          x = map(analogRead(pin), 1023, 0, 0, 1023);

This is an expensive way to accomplish:

 x = 1023 - analogRead(pin);

        if(serialvalue == 0){
          digitalWrite(12, LOW);
        }
        else if(serialvalue == 1){
          digitalWrite(13, HIGH);
        }
        else if(serialvalue == 2){
          digitalWrite(12, LOW);
        }
        else if(serialvalue == 3){
          digitalWrite(13, HIGH);
        }

So, you are sending 0, 1, 2, 3, or 'r'. Really?

Or, are you sending '0', '1', '2', '3', or 'r'?

void sendValue (int x){              // function to send the pin value followed by a "space". 
 Serial.print(x);
 Serial.write(byte(32)); 
}

Serial.print(" "); would be a whole lot clearer.

You know that this is converting the integer to a string, right? Are you expecting a string in Max?