First, assume the game will go to round limit. How many spaces do you want to attack?
So, calculate how many rounds of deploy you will get for a bonus. On round 1, its 19. Then calculate expected lost troops.
Spoiler
0.8534144 N - 0.2213413 (1 - (-0.525359)^N)
N=# of defenders
Or, more a more simple approximation is 5/6 # of defenders in all territories + 7/9 # of territories + 1/18 # of territories that have exactly 2 defenders - 1/9 # of terts with 1 army.
This simple approximation includes troops lost due to territory spread. Those troops still count for victory at round limit, so my model is overly conservative.
N=# of defenders
Or, more a more simple approximation is 5/6 # of defenders in all territories + 7/9 # of territories + 1/18 # of territories that have exactly 2 defenders - 1/9 # of terts with 1 army.
This simple approximation includes troops lost due to territory spread. Those troops still count for victory at round limit, so my model is overly conservative.
The map is symmetrical in that everyone has the same 10-1-1-1-5 to get through for the village bonus. That would lose an estimated 18.5 troops. It only takes 7 rounds of village bonus to win that back.
The real question is: if everyone goes for village bonus, how do you deal with it?
I would say that if the first person to arrive at the village takes it for 8-10 rounds and then pulls out to let the other guy get the bonus for a bit, that would be the optimal strategy. What does game theory say about the likelihood of this?
Do you use expected worth calculations in your day-to-day games?
In non-round limit games, its pretty simple except you can only calculate relative worth, not absolute.
