Seven competitive bidding strategies for optimizing profits in construction contracting are developed; namely: (1) Lone Bidder Strategy—no competitors; (2) Two Bidders Strategy—one competitor; (3) Many Bidders Strategy—more than one competitor, number and identity of competitors not known; (4) All Bidders Known Strategy—more than one competitor, number and identity of competitors known; (5) Number of Bidders Known Strategy—more than one competitor, number of competitors known but identity of competitors not known; (6) Least Spread Strategy—minimizing money left on the table; and (7) Unbalanced Bidding—maximizing competitive position through quantity change. In addition, the following statistical distributions and applications are investigated: (1) Binomial Distribution—forecasting the frequency of winning; (2) Gaussian Distribution—precision of bidding; and (3) Poisson Distribution—forecasting of number of competitors. Other related topics are examined briefly.