else:
        pairs.sort(key=operator.itemgetter(0), reverse=True)
        average = 0
        seen = 0
        norm = 1
        for pair in pairs:
            price = pair[0]
            chance = pair[1]
            average += price * (1 - ((1-seen-chance)/(1-seen)) ** 4) * norm
            norm *= (((1-seen-chance)/(1-seen)) ** 4)
            seen += chance

        return average