End it all now

Some wins are better than others.  Today I won a game in my online Thurn and Taxis league because one of my opponents decided to end the game despite being solidly in last place.  I spent a lot of time thinking about my final turn because I saw that position coming.  The player in last was so far behind that even closing the final route and claiming their seven carriage put them last by a big margin.  In theory there might be some set of events that gets them out of last place if the game keeps going, but it seemed far fetched.  

I had the chance to close my route and get a solid lead, which locks in my victory if the person in last ends the game.  If the person in last decides to keep the game going, this almost certainly gets me second place instead, because I don't get to do anything useful on the following turns and someone else does.

If I keep my route open, I have a shot at first place if the game continues, but this gives someone playing after me the chance to close a crappy route, and then they get first place instead if the person in last ends the game.

I find these kinds of calculations really frustrating.  Sometimes it is just something like 'Is this opponent going to gamble to try to advance, and make a crazy play for first?' which isn't great, but isn't so terrible.  At least I can try to figure all that out.  But how should I play against someone who is totally screwed, but has maybe 1/1000 chance of getting out of last if they keep the game going?  Are they the sort who never gives up, and never surrenders?  Or are they the sort of person who values their time and who won't continue a game that is obviously over?  That is the sort of calculation I can't do anything with in terms of game theory.

In the end I decided that the person in last was so far behind they were just going to end the game and be done with it.  I closed my route, got a few points, and the game did indeed end.  I don't feel great about it though.  Knowing that I locked in the victory because someone decided it wasn't worth trying anymore isn't quite the glorious victory march I had envisioned.

But I do want to advance, so I guess I will take what I can get.  :)  I have a first and two seconds now, so advancing is totally plausible.  I usually end up needing three first place finishes to advance in these things though, so I am not all that optimistic.  (I figure most of the time two firsts and two seconds should do it, but I have been beaten with two firsts and two seconds most of the time I have gotten there, whatever the odds are.)

I am curious what other people think of the etiquette of ending games when you guarantee yourself last place.  How much of a chance of improving that position do you need in order to stick in a game?  Personally my answer is anything greater than zero - I won't give in until there is truly no way out.  How do you behave in that situation?