Calculating Expected Worth

[DoomYoshi]

Let's say it's a 20 round limit no spoils game on Feudal Epic (I don't really like the other Feudal map). This is a really simple example, and helps me illustrate a concept.

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.[/spoiler]

A bonus of 1 requires killing 4 troops spread over 2 territories. So, it takes 5 troops. It is only worth it in the first 15 rounds. There is no excuse to not take your entire 1-6 of the kingdom.

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.

[DoomYoshi]

In case you are wondering, the next statistical analysis I am going to do will be establishing a benchmark for how secure a territory or bonus is.

E.g. You have a bonus with 1 stack that has one bordering territory (e.g. Australia).
Your opponent has a bonus with 1 stack that has 2 bordering territories. That is a less defensible position. Natty dread says it isn't. I am going to prove it (or disprove it) using a unique path analysis.

[rhp 1]

In case you are wondering, the next statistical analysis I am going to do will be establishing a benchmark for how secure a territory or bonus is.

E.g. You have a bonus with 1 stack that has one bordering territory (e.g. Australia).
Your opponent has a bonus with 1 stack that has 2 bordering territories. That is a less defensible position. Natty dread says it isn't. I am going to prove it (or disprove it) using a unique path analysis.

you need a better hobby...

obviously your "statistical analysis" is not working for you

[KraphtOne]

Let's say it's a 20 round limit no spoils game on Feudal Epic (I don't really like the other Feudal map). This is a really simple example, and helps me illustrate a concept.

First, assume the game will go to round limit. How many spaces do you want to attack?



Do you use expected worth calculations in your day-to-day games?

1. As many fucking spaces as you can as quickly as you can, the faster i get to that +3 bonus the better...

2. Yes i use expected worth calculation, but this is what we Laymen refer to as the "no-shit" principle

[#1_stunna]

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[/img]

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