Each Major League team plays 162 games. There are 30 MLB teams and each game involves two teams which gives us:
MLB Games = 162 * 30 = 4,860 Games
There is no reason to divide games by 2 as a game is defined as played by 2 teams. Each MLB team plays 162 games.
In an actual season this will vary as some games are rained out and never rescheduled while on occasion an extra game is played to settle a tie (last year San Diego & Colorado each played 163 games due to tieing for the NL Wildcard after 162 games). In 2007 due to the one extra game to settle the NL Wildcard, 2,431 Regular Season Games were played in Major League Baseball.
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Using the 2008 Chicago Cubs as an example, they played their first regular season game on March 31 and are scheduled to play their final regular season game on September 28. That is a span of 182 days.
In 1961, the American League increased its season from 154 games to 162. In 1962, the National League followed suit. This was done in order to generate additional revenue for the owners.