M57 wrote:

Mongrel wrote:

A site-wide luck graph for each player. One chart, all your rolls.

I don't imagine this as being very helpful or interesting. I'm thinking that over time it will look the similar for every player.  I think it will be a meandering line that slides between a positive and negative score for most players.  And again, an overall number will have no meaning unless # of games is taken into account.

I think there's some room for improvement.  My backdoor stDev idea was shot down.  Alpha understood it so I'm sure it was given due consideration. And I do like the LS number that is being produced, but working on an additional stat based on the LS number that gives it time sensitive context.

For each board, a calculation of average luck of winner (> n games played on the board total). This could be split up over m-player games.

I like.  Some boards will undoubtedly have a stronger correlation between luck and winning than others.

 

For the overall luck of a player, I agree with what Mongrel said; most people will have a total luck that is near zero, but there should be some that are perpetually lucky players and then there should be RiskyBack; he already knows the dice are against him.
I also think it would be interesting to see the graph, since it would be interesting to see how periodic it is, that is if it is periodic, but I imagine it would also be a lot of data to tabulate.
Lastly, I think that the overall luck of a player, without any normalization does have a meaning.  The expected result is for the overall luck of a player to be zero, so having an overall luck of 50, 500, or 5000 are vastly different results regardless of the number of games the player has been in.

Your standard deviation based stat is a good idea and I apologize, but I haven't had the time to give it the consideration it needs; real life gets in the way.  Prior to that discussion, I had sent tom all of the information for calculating the current stat.  I think that the look up tables for standard deviations and such that are required will require the site to do more work than the current stat, but I am not sure how bad it would be (time wise/number of calculations).  For the current luck stat Mongrel and I created, there is a very minimal load on the system in calculating this based on the number of kills.

I am all for a second measure of luck and would certainly like to see the average luck of the winner on a particular board.

Cyan-ide wrote:

Mongrel wrote:

Not singling you out, cyanide. I've b*tched about luck once or twice.

I'd like to think I can whine like the best of them!  By all means, single me out!  And really, don't hesitate to ask if you're ever in need for a real sob-story about how mean the RNG is to me.

I'm also in favor of your 'global' statistic showing a luck score and graph for all your rolls across all your games combined together.  M57 doesn't see the value of it... but even single-game luck stats really have no bearing on the game, it's just nice to know and helps to confirm the debacle of dice rolling that seems to plague me.  I realize that implementing it might be infeasible and that bigger things are probably on the agenda, but I like the idea.

"3vs1 and I lose 9:1?"  ... cover the children's ears.

 

Believe me, if I see somebody is on a lucky streak I'm steering clear of the games they're in.  No matter what the theory behind randomness is.

Sorry, but the luck stats make no sense at all to me.  I've been trying to figure out how they are calculated, and I can find no math that works.

And the "explanation" text is not very descriptive at all.

Does anyone understand how to read the Luck Stats ?

Thanks.

Assuming you are familiar with the standard rules of risk and how dice rolls are resolved... The most common example is 3 six-sided attacker dice against 2 six-sided defender dice. So we'll do that. Running through all combinations and comparisons, one can calculate the per-roll probabilities an attacker

takes 2 armies = .37 ish

takes 1 and loses 1 army = .30 ish,

or loses 2 armies = .33 ish. I forget the exact decimals for each.

Form this, one can determine that an attacker should take approximately 2*.37+1*.30 = 1.04 armies on average, per roll. Since two armies are at stake, this implies the defender takes .96 armies on average, per roll. For a single roll, luck measures the difference between the ACTUAL armies killed from ACTUAL dice rolls and the EXPECTED armies killed from calculating the theoretical average above. The overall luck stat adds up these per-roll changes; it is a running tab of what extent you are outperforming or underperforming the average number of kills.

So, luck = (total ACTUAL units you kill) - (total EXPECTED units you should kill)

After all, if you kill two armies as an attacker on a 3v2 roll, that should be considered lucky, right? The luck stat calculates this as

ACTUAL kills - EXPECTED kills = 2 - 1.04 =  .96

For your defending opponent, their luck would be

ACTUAL kills - EXPECTED kills = 0 - .96 =  -.96

So your luckiness is at the cost of your opponent.

Another example: As a defender, lets say you lose 200 units in 100 consecutive 3v2 rolls against you. So you killed 0 units while defending- the worst possible outcome (for you). You would expect to kill .96*100 = 96 units, on average. So, the luck stat calculates your luck during this span as

ACTUAL kills - EXPECTED kills = 0 - .96*100 = -96

which is very negative, hence very bad luck.

Visually, the height of your luck graph goes down 96 points from its current position, to reflect the fact you just had terrible luck during your last 100 rolls.

To know your current overall luck, look just at the end of your graph- the path shows you how you got there. In particular, you can see lucky/unlucky streaks, by the up/down fluctuations in your luck path. It goes up when you are killing more than you should, it goes down when you are killing less than you should.

The luck graph updates based off these per-roll calculations. As such, the expected number of kills used in the per-roll calculation depends on the number of dice used (we used 3v2 in our example, but there are 2v2,2v1,1v2,1v1,3v1 options available), the number of sides on each dice (we used 6 sided attack dice against 6 sided defense dice in our example, but sides can vary with border mods), and whether you are attacking of defending.

Hope that helped.

tldr

heh

I'm gonna try a minimalist explanation (this goes against my very core):

There is an expected number of armies you should lose with "average rolling". Luck stats tells you how many armies above (+) or below (-) this average you have after rolling.

he asked for math. he got math.

oh i read it; just being a smart ass... :^)

: ) 

This is why I typically wait for Hugh to swoop in.

Mongrel:  That was awesome.  Thanks for the math -- makes total sense.