Counting unique occurrences with multiple criteria

I'm trying to count unique occurrences based on multiple criteria.

Specifically, I have text in column A and column B (over 200,000 rows) and I want to be able to use/create a function that counts the unique combinations of the data in both columns while specifying the value in column b to count.

Even more specifically, the data below are a sample of the data set. Column A contains game IDs for an NBA basketball game. Column B is the name of the player who participated in the game in some way. I'm trying to count the number of games players have played in over the entire season. So I want to be able to specify the player in column b that I want to count unique game IDs for in column A for which that player participated in at least once. Does that make sense? Sorry, its a little wordy.

A B
20091027BOSCLE Varejao
20091027BOSCLE R. Allen
20091027BOSCLE O'Neal
20091027BOSCLE James
20091027BOSCLE Garnett
20091027BOSCLE Varejao
20091027HOUPOR Aldridge
20091027HOUPOR Battier
20091027HOUPOR Scola
20091027HOUPOR
20091027HOUPOR Scola
20091027HOUPOR Aldridge

No. Sorry, let me try and clarify. If a player played in a game, his name will show up somewhere in column B for that game specified in column A. For any given game ID (column A) there are several occurrences of a players name for a particular game ID (column B). But if a player did not play in a game, his name will not show up anywhere for the particular game id. I want to count simply how many games a player I specify played in. So the 2 criteria are the players name in column b and the game id in column a--but I want only the unique number of combinations. Does that make sense? Thanks for the help.