mysql - Bulk converting eastern timezone to gmt using CONVERT_TZ 12k+ records

Question

UPDATE bridge_copy SET 
      game_begin = CONVERT_TZ(game_begin,'EST','GMT'), 
      game_end = CONVERT_TZ(game_end,'EST','GMT');

This is the query I attempted to run, and it failed misserably. What the end result was, was 2 columns filled with 0000-00-00 00:00:00 Rather than there conversions. Any ideas how I can update 12k+ rows without looping over them via some server side script that selects the current value, converts it, then updates it?