Todd,
Tickets to an assigned game are to an assigned game as per the original schedule. This info may be found on retrosheet.org by following the links to "schedule" and it is a raw data feed, but can be followed.
BTW, inclement weather does not always result in a patron having the ticket torn. As a season ticket holder, I have had games that were never played, or attempted to be played, due to extreme weather snow-blizzard, very heavy rain, etc.
Anyway, for the sake of argument, lets say that two games in a series were attended by a patron that were called on account of rain. Not wanting to lose their portion of the attendance gate for the rainouts, both teams decide that they will play back-to-back unscheduled day/day double headers (no night games in 1918!
). Your torn rain check for one of the games could be used to gain admission for the unscheduled double header game not on the schedule.
"Rain checks" may be used typically for any other game moving forward in the (1918 in this case) schedule.
Here is a real example of a situation that actually happened to net54 board member Randall Hahn and me in 2008:
SF's Randy Johnson was in Washington to play the Nationals and go after his 300th career win. Randall & I are both in town to hopefully see history.
The day of RJ's 300th win game it absolutely just poured rain all day- all night. We went to the game anyway, but it never got played due to the relentless rain.
The game was played the next day as an unscheduled early day game prior to the scheduled game later that night. The ticket from the rainout could be exchanged for a ticket to the early makeup game. The patrons that had tickets to the regularly scheduled night game were not allowed to go to the early game without purchasing the other ticket. Anyway RJ did get his 300th win and the rest is history. Randall Hahn saw RJ get the 300th win, but I could not because I had an earlier flight the morning of.
BTW, Emergency tickets or "E tickets" were used by teams to sell for use in unscheduled games, although I don't know if that practice dated back to the early 1900's.