  In two-player games on graphs, the players move a token through a graph to
produce an infinite path, which determines the winner or payoff of the game.
Such games are central in formal verification since they model the interaction
between a non-terminating system and its environment. We study {\em bidding
games} in which the players bid for the right to move the token. Two bidding
rules have been defined. In {\em Richman} bidding, in each round, the players
simultaneously submit bids, and the higher bidder moves the token and pays the
other player. {\em Poorman} bidding is similar except that the winner of the
bidding pays the "bank" rather than the other player. While poorman
reachability games have been studied before, we present, for the first time,
results on {\em infinite-duration} poorman games. A central quantity in these
games is the {\em ratio} between the two players' initial budgets. The
questions we study concern a necessary and sufficient ratio with which a player
can achieve a goal. For reachability objectives, such {\em threshold ratios}
are known to exist for both bidding rules. We show that the properties of
poorman reachability games extend to complex qualitative objectives such as
parity, similarly to the Richman case. Our most interesting results concern
quantitative poorman games, namely poorman mean-payoff games, where we
construct optimal strategies depending on the initial ratio, by showing a
connection with {\em random-turn based games}. The connection in itself is
interesting, because it does not hold for reachability poorman games. We also
solve the complexity problems that arise in poorman bidding games.
