If you’re right handed, the right side of your body is probably a bit stronger than the left side. For a cross-country bike ride, this can be a problem. Your left leg is weaker and tends to tire out more quickly — putting more strain on your right leg.
So, every time I approach a stair case, I take the first step with my left leg. This means I often take more steps with my left leg than with my right — which tends to balance out my strength.