  Motivated by recent insights into the online bipartite matching problem
(\textsc{OBM}), our goal was to extend the optimal algorithm for it, namely
\textsc{Ranking}, all the way to the special case of adwords problem, called
\textsc{Small}, in which bids are small compared to budgets; the latter has
been of considerable practical significance in ad auctions \cite{MSVV}. The
attractive feature of our approach was that it would yield a {\em
budget-oblivious algorithm}, i.e., the algorithm would not need to know budgets
of advertisers and therefore could be used in autobidding platforms.
  We were successful in obtaining an optimal, budget-oblivious algorithm for
\textsc{Single-Valued}, under which each advertiser can make bids of one value
only. However, our next extension, to \textsc{Small}, failed because of a
fundamental reason, namely failure of the {\em No-Surpassing Property}. Since
the probabilistic ideas underlying our algorithm are quite substantial, we have
stated them formally, after assuming the No-Surpassing Property, and we leave
the open problem of removing this assumption.
  With the help of two undergrads, we conducted extensive experiments on our
algorithm on randomly generated instances. Our findings are that the
No-Surpassing Property fails less than $2\%$ of the time and that the
performance of our algorithms for \textsc{Single-Valued} and \textsc{Small} are
comparable to that of \cite{MSVV}. If further experiments confirm this, our
algorithm may be useful as such in practice, especially because of its
budget-obliviousness.
