... G(a
∗
, b) for the bidding game in which Alice starts with a bidding chips and
the tie-breaking advantage, and Bob starts with b bidding chips. Similarly, G(a, b
∗
) is the
bidding game in which ... of the total bidding
resources is greater than R(G), and she does not have a winning strategy if her proportion
of the bidding resources is less than R(G). If her proportion of the bi...