To estimate the luck:
* each time a player wins an attack that is statistically against him, he is lucky
* each time a player defends against an attack that is statistically against him, he is lucky

Then you make a ratio:
(lucky attack + lucky defence) / (number of attack and defence)

And you compare with others players.


Soda you're a mexican

Wouldn't it be far simpler to count up the number of 1s,2s,3s,4s,5s and 6s that each player got and make a graph? Think about it, a 2vs3 defense is "luckier" than a 7vs8 defense, simply adding it all up doesn't make much sense.

i never lose.

For the luck-o-meter, you need to controll for differences in attacking chances. Means: There are people who only attack with at least 2 more dice - and others who take the risky way. So the luck-o-meter would go:
SUM(chances of winning for every battle you won)/nr. of won battles - SUM(chances of losing for every battle you lost)/nr. of lost battles
And if we compute all that we'd find that basically everybody has got more or 0 (apart from rOn who never loses). So we don't need the luck-o-meter. It would be a fun thing to have, though.
On the other hand, if we only look at luck statistics for single games we could find out whether winning is down to luck or not.

Better yet, eliminate chance altogether. For instance, when I attack I should always win, and so on for defense as well.

The luck issue is even more complicated. Just a few examples:

1. It should include the probabilities of success in a given attack (a person winning 6:8 is luckier than the one winning 8:8, even if in both attacks its more probable he should lose)

2. Say there are players A and B with the same "elo". Both of them have a series of bad games and a series of great games, but A has great series first, and bad later, B - bad series first, great later. As a result A would gain much more in rank than B, so he is luckier...

3. And what about "social luck"? Player A may attack either B or C. There is no strategical difference. None of them is his pga, OTF etc. So he choses randomly to attack B, which makes B more lucky than C.

4. Different attacks have different strategical significance. There may be 5:4 attack in the beginning of the game deciding the whole outcome of the game. There may be 5:4 attack with no strategical significance whatsoever. The luck in first of them is much more lucky than in the second....

Ufff - I got tired... I will be lucky if anyone has patience to read up to this point... so let here be the end.

The Convolution Integral (CI) is the non-luck component of the Elo gain per game, so the luck component would be Elo gain per game minus the CI. The CI is explained in the comment on my profile page.

Other random elements of the game that contribute to luck are the initial assignment of countries, the initial placement of dice, and subsequent restacks.

In-game luck in rolling would be fairly simple to come up with a good formula for. For every attack or defense you win, give yourself 1 luck point per % chance that you should have lost. For every one you lose, subtract a point per % chance you should have won.

The math works out well. If you win 7/10 rolls that you have a 70% chance of winning, the 7 wins x 30% loss chance is +210 luck, while the 3 loses x 70% win chance is -210 luck, leaving you at 0, which is what you'd expect gonig 7/10 on a 70%.

OTOH, winning all 10 rolls would give you +30 luck, and losing all 10 would give you -70 luck.

RYAN.. please make a luck-o-meter!!

Sinth, you're pretty much right. But you have to controll for the number of battles you had - otherwise people with a lot of battles will almost always have a very positive or very negative balance (even though the odds are pretty even when measured per attack). My formula incorporates that ...