def prior_knolwedge_categorized(price, n_bins = 12):
    """
    function of prior knowledge for categorized price
    :param price: input price - this price should already be bucketized. The value is in the range [0, n_bin)
    :param n_bins: number of bins
    :return: expected prob.
    """
    # The winning probably is linearly proportional to the inverse of price
    winning_prob = 1. - (1.) / (n_bins -1) * price # linear function
    return winning_prob