BTW, I purchased one of the game 61 tickets (different game in which was a WaJo 14 inning win) from the 1918 season from Ray Holmes (nice guy BTW) here on net54.
These tickets were removed from a 1918 scrapbook according to Ray and were surrounded by other items related to 1918. Additionally, there is a yet to be released terrific book on Washington Senators tickets coming out that is written by baseball ticket super collector & historian Dan Busby. I have a pre-release copy of this book in hand.
Ray's tickets are consistent with Senators tickets from 1918 based on Team President, font, ticket price, etc. I truly believe these to be from the 1918 season & the rest of the research can be done looking at game log notes....
Ticket dates did not appear on any Nats tickets until the mid- 1920's, BTW. They simply did not exist yet. The only way to nail down years and dates for the earlier Nats games comes from a situation where you are fortunate enough to find that the patron wrote info on the ticket or in a scrapbook...