Here are versions of 154 and 156 games with no interleague, 2 16-team leagues, no divisions. I had the preferred start day on Thursday while I made them, but they're intended to start on a Monday and end on a Sunday. So set the preferred start day to Thursday in your league.
I'll try to get to the 156-gamer with interleague play in the next couple of days.
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Is that the real reason why way back MLB landed at 162?
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Actually, the schedule went from 154 to 162 in 1961 in the AL when the Angels and new Senators (now the Rangers, the old Senators moved to Minnesota as the Twins that season) were born. At that point, the AL had 10 teams, so they played 9 opponents 18 times for 162. The NL did the same the next year when the Astros and Mets came aboard. It's been 162 in both leagues since.