Alpha wrote:

I do from a practical standpoint feel the need to point out when my attacks have landed me in the 1 in 10000 range (like losing a 12 v 1 or winning a 20 v 40), but this is not whining or complaining, I intend only to point out that an event worth taking note of has just occurred.

Yeah - this I can get behind.

Of course the dice luck chart doesn't capture all the luck in a game.  Sometimes starting position is even more important and in a "deterministic" game like seven it is the only luck.  Of course, it would be a lot harder to measure that luck.

If you got a proposal, I am more the willing to hear it.  This is something I have thought about and have some ideas, but they would be computationally intensive.

A, I'm curious what your ideas are.

I'll throw one out there to let you mathematician's ponder.  God, I wish I were geeky enough to do this myself.  Anyways, this one is regarding starting position..

As boards get played, the statistics of Local (individual boards) and Global (all boards) accumulate over time and determine the probability that a given seat will win given any number of criteria (# of players, # of territories, #of borders, board type, etc..)

Local stats are the most appropriate, but until a large number of games have been played on any given board, their sample sizes will be much too small to be valid. On the other hand, there’s already a significant amount of existing Global data, which is of course less relevant for individual boards.

My idea is to use both.  As a board starts out, Global stats are consulted, and as the # of games played in respective categories hit thresholds, which are either incrementally or linearly determined, Local stats are given more and more weight.  The stat could even include a “reliability/significance” number that expresses how heavily weighted the local data is as a percentage.

Yeah - starting position can definitely be important.   Ideally the map maker would tweak initial bonuses so that any seat is equally good, but that would probably require 100s of test games to get right.

As far as initial position luck, that one is really tricky, and honestly I don't have any good answers, but was kind of hoping others might.  I have some thoughts:

#1 -  If we had several million games played on a relatively small map you could correlate every possible starting position and the % win chance for that position.  This is pretty much impossible for the foreseeable future.

#2 - So given that is impossible, you could instead correlate individual territories with win %.  Maybe in 3 player games the player who starts with Brazil wins 50% of the time or something.  Then combine the percentages based upon all the territories you start with.  This solves the combination explosion of #1 at the expense of being less accurate.  Still not a very good solution.

#3 - You could try and assign value to territories based upon map characteristics.  Things like border modifiers.   Sum of continent values / continent member count  for all continents it is part of.  etc.  Then players luck is based upon how good the individual territories they start with are.  One statistic I have been thinking of calculating is some kind of centrality (http://en.wikipedia.org/wiki/Centrality) for territories.  Probably the Betweenness centrality, but maybe some of the others also.

#4 - In addition to #3, something like how many territories you start with that are touching another territory of yours, and maybe some value for territories that are only 1 away from each other.

Anyway, just some random thoughts - I'm curious what you have thought of.

O, I like your ideas. #2 is my favorite.  I'm pretty sure it would be a relatively easy stat to calculate because it's just a matter of finding the mean for the values of all the territories held.  Only problem I can see is if one or some players start with more territories than others.

#4 should also be pretty easy to calculate, which makes me think that some kind of subjective number could be derived using independent data sources.  The question is whether to use the mean these numbers or weight them.

My ideas from post #44 could still apply.

#2 is one of the ideas I had in mind.  For each territory on the map, give it a plus 1 if it was in the starting territories for the winner of any completed game.  After each game, the territory would get a luck percentage:
  option 1: (total times that territory was in a winning starting scenario)/(total number of completed games).  The average of all starting territories luck percentages would be your starting position luck.

In games where there is a scenario start, say like five, this would end up being exactly the overall luck of going first or second for the board.

Option 2: Alternatively you could assign a luck percentage to each territory based on (total times that territory was in a winning starting scenario)/(total times any territory was in a winning scenario).  Then starting luck would be the sum of all territory luck percentages. 

This would work better for the boards where the placement is always random (like the standard map or from my world Seven).

For Five, the luck stat would be skewed with option 2 since one player starts with 3 territories and the other with two territories.  (You could use some sort of weighted average to account for this, but it gets difficult for it to work globally).

For Seven, the luck stat would be skewed in option 1 from the fact that certain territories are always assigned to one player or the other.

These could of course be fixed in some other manner by keeping track of information based on seats, not just territories.  Anything along these lines would require many more games played before it had any meaning.  Those are my thoughts on that idea and I believe it is too complicated to make an algorithm that will require a few games played (say 20) and be global and still have some meaning (hopefully I am wrong).

I have some other luck ideas, but they will have to wait til later.

We've totally hi-jacked this thread - I'm going to start another one.

yes, I find that I do not pay attention to the thread name only the discussion.  Sorry.