So, how unlucky do people get?  This is the worst game that I can remember.

Anyone else have abysmal games to share?

Lol, I've had much worse than that...in fact, that looks like it would be one of my better games. 

That might be one of the best games I've seen neutral have in a while...

As has been mentioned before, luck stats are meaningless to compare unless you take into account the length of the game in some way.  For example, this game has -138 luck for Aduse:

http://www.wargear.net/games/luck/150954/luckstats

Which is probably pretty bad, but probably not 10x worse than your luck.

Besides dice luck, how about placement luck.  This game is my worst for really bad starting setup & dice :

http://www.wargear.net/games/player/232497

2v2.    The opposing team, as a team starts with all of Australia as well as Siam, India & China!  If that wasn't bad enough, they go first and by the end of their first turn (before my team even gets to go) they also control (as a team) all of Europe.

And then on top of that, look at our team dice luck:

http://www.wargear.net/games/luck/232497/luckchart

Ozyman wrote:

As has been mentioned before, luck stats are meaningless to compare unless you take into account the length of the game in some way.  For example, this game has -138 luck for Aduse:

http://www.wargear.net/games/luck/150954/luckstats

Which is probably pretty bad, but probably not 10x worse than your luck.

Indeed.  A back of the envelope estimate says that I'm probably a standard deviation or two worse.

It shouldn't be hard to improve luck stats to give your current luck percentile, which would nicely account for the length of the game and for your luck score.

In fact here is exactly how you do it.  For each possible attack right now, they know how to compute the average you should lose in the battle.  The difference between that and your actual loss is your luck.

Add to this the ability to compute the variance for the amount you lose per dice roll.

The sum of the variance across all battles is the variance.  Your luck divided by the square root of the variance is how many standard deviations you are from the mean.  Use that number to do a lookup into the normal distribution and you have a very good approximation of the probability that, across all of the possible scenarios where you have all of those individual attacks and defends, that your luck would have been worse or better than it currently is.

(Look up the Central Limit Theorem for details on why this works.)

btilly wrote:

Ozyman wrote:

As has been mentioned before, luck stats are meaningless to compare unless you take into account the length of the game in some way.  For example, this game has -138 luck for Aduse:

http://www.wargear.net/games/luck/150954/luckstats

Which is probably pretty bad, but probably not 10x worse than your luck.

In fact here is exactly how you do it.  For each possible attack right now, they know how to compute the average you should lose in the battle.  The difference between that and your actual loss is your luck.

Add to this the ability to compute the variance for the amount you lose per dice roll.

The sum of the variance across all battles is the variance.  Your luck divided by the square root of the variance is how many standard deviations you are from the mean.  Use that number to do a lookup into the normal distribution and you have a very good approximation of the probability that, across all of the possible scenarios where you have all of those individual attacks and defends, that your luck would have been worse or better than it currently is.

btilly, this subject has been covered/undertaken quite a bit in other threads here. Yet we been somewhat at a loss to come up with an accurate and easy way to determine z-scores for die rolls for inclusion in the stats.

Here is a summary link..

http://www.wargear.net/forum/showthread/1950/Including_measured_luck_in_the_luck_stats

M57 wrote:

btilly wrote:

Ozyman wrote:

As has been mentioned before, luck stats are meaningless to compare unless you take into account the length of the game in some way.  For example, this game has -138 luck for Aduse:

http://www.wargear.net/games/luck/150954/luckstats

Which is probably pretty bad, but probably not 10x worse than your luck.

In fact here is exactly how you do it.  For each possible attack right now, they know how to compute the average you should lose in the battle.  The difference between that and your actual loss is your luck.

Add to this the ability to compute the variance for the amount you lose per dice roll.

The sum of the variance across all battles is the variance.  Your luck divided by the square root of the variance is how many standard deviations you are from the mean.  Use that number to do a lookup into the normal distribution and you have a very good approximation of the probability that, across all of the possible scenarios where you have all of those individual attacks and defends, that your luck would have been worse or better than it currently is.

btilly, this subject has been covered/undertaken quite a bit in other threads here. Yet we been somewhat at a loss to come up with an accurate and easy way to determine z-scores for die rolls for inclusion in the stats.

Here is a summary link..

http://www.wargear.net/forum/showthread/1950/Including_measured_luck_in_the_luck_stats

 

I don't care about dice rolls.  I would like attack loss/defend distribution.

I know how to calculate those numbers.  For instance if you're attacking 3d6 vs 2d6 then the attacker loses an average of 0.920910493827162 with a variance of 0.657968101042143.  Those numbers aren't the fastest things in the world to calculate, but they are not too bad.  Tell me the programming language and I can write you a function to calculate those numbers.  Whenever you first encounter a particular combination of dice rolls, you work it out, store the numbers in a lookup table/hash/dictionary/whatever, and then use that the next time.  In practice it will be fast enough.

After that knowing all of the attacks, and knowing the combination of dice used in each one, you can compute the variance of the total, and therefore the standard deviation.  Which then lets you do the luck percentile calculation.

(The game that I'm complaining about is going to be somewhere in the 1-2% range.  So it wouldn't surprise me if it was, indeed, my unluckiest game ever.)

M57 wrote:

btilly, this subject has been covered/undertaken quite a bit in other threads here. Yet we been somewhat at a loss to come up with an accurate and easy way to determine z-scores for die rolls for inclusion in the stats.

Here is a summary link..

http://www.wargear.net/forum/showthread/1950/Including_measured_luck_in_the_luck_stats

Actually, the point of the summary link is that there IS an accurate and easy way to compute percentiles.

I did not stress enough in that link that the computing technology to do this quickly and accurately already exists. And, we could code this up somewhat quickly for tom in whatever language would be required.

btilly wrote:

I don't care about dice rolls.  I would like attack loss/defend distribution.

If you click on the link that M57 quoted, you'll see that this is what we're talking about. No one cares about the specific dice rolls. Using the standard .3717/.3358/.2926 numbers, the q(1-q) + 4pq formula of that post gives  the variance you just gave in your post.

It absolutely can be done. It just hasn't been done.

Hugh wrote:

M57 wrote:

btilly, this subject has been covered/undertaken quite a bit in other threads here. Yet we been somewhat at a loss to come up with an accurate and easy way to determine z-scores for die rolls for inclusion in the stats.

Here is a summary link..

http://www.wargear.net/forum/showthread/1950/Including_measured_luck_in_the_luck_stats

Actually, the point of the summary link is that there IS an accurate and easy way to compute percentiles.

I did not stress enough in that link that the computing technology to do this quickly and accurately already exists. And, we could code this up somewhat quickly for tom in whatever language would be required.

(I believe we had another thread where the idea was presented more clearly and had widespread support, but no action resulted. I won't speak for others, but I am lazy and unmotivated.)

That was what I got from that summary.  Doubly so because I know exactly how to do it.

Seriously, I do this sort of stuff for a living.  See http://elem.com/~btilly/effective-ab-testing/ for proof of that.  I'd like to have this, and I'm willing to put in the elbow grease.

How cool would it have to be a Luck 'O Meter? ..at least on a per game basis.  I can barely parse the high-end math stuff you guys are talking about, but I know enough to know that I'd love to see a Z-score.  Thing is, I doubt most people would want or appreciate such a number. What do you all think is the best way to present it?  I'd be curious to hear your suggestion, btilly.

btilly wrote:

Seriously, I do this sort of stuff for a living.  See http://elem.com/~btilly/effective-ab-testing/ for proof of that.  I'd like to have this, and I'm willing to put in the elbow grease.

Awesome! There is a list of requested features somewhere. So, if calculating percentiles for the luckstat isn't there, we need to get it on the list of requested features.

Then we have to make it clear to tom that we have code and can get code to him in whatever form he needs. I did this long ago for the card deck simulator. It was PHP back then. It might still be PHP. I'm sure Oz has done this sort of thing too. Anyway, this step will ensure a quicker (though not necessarily quick) implementation time.

Hugh wrote:

btilly wrote:

I don't care about dice rolls.  I would like attack loss/defend distribution.

If you click on the link that M57 quoted, you'll see that this is what we're talking about. No one cares about the specific dice rolls. Using the standard .3717/.3358/.2926 numbers, the q(1-q) + 4pq formula of that post gives  the variance you just gave in your post.

It absolutely can be done. It just hasn't been done.

Those number are just for 3v2 attacks, right?  Would it be possible to "somewhat easily" include all attack types ..and dice mods?

M57 wrote:

Those number are just for 3v2 attacks, right?  Would it be possible to "somewhat easily" include all attack types ..and dice mods?

Yes! The whole point of that summary post that you linked to was that we can do this for arbitrary dice types and arbitrary numbers of rolls of each type. Right now, luckstats computes an update for the mean based on the dice percentages.

We just need to do an update for variance (details given in the summary post). Variance, even for mixed roll-types, is additive. So, we just add the single roll variance to update the total variance. This directly gives a z-score. We would then translate the result to a percentile. And yes, most people, myself included, would prefer to see a percentile over a z-score. Most people know how to interpret a percentile.

M57 wrote:

Hugh wrote:

btilly wrote:

I don't care about dice rolls.  I would like attack loss/defend distribution.

If you click on the link that M57 quoted, you'll see that this is what we're talking about. No one cares about the specific dice rolls. Using the standard .3717/.3358/.2926 numbers, the q(1-q) + 4pq formula of that post gives  the variance you just gave in your post.

It absolutely can be done. It just hasn't been done.

Those number are just for 3v2 attacks, right?  Would it be possible to "somewhat easily" include all attack types ..and dice mods?

Absolutely.

In fact to get that number I wrote a program this morning before my son got up to calculate average and variance.  My understanding is that a +1 defensive bonus means that the defender gets to roll 7-sided dice while the attacker still only has 6-sided.  If that assumption is correct then 3d6 vs 2d7 gives an average attack loss of 1.10515873015873 with a variance of 0.640207703451751.

Tell me the programming language.  Tell me how you want to tell me what dice were available, along with bonuses, different numbers of sides, etc.  I can write code to give you back averages and variances for the result of that dice roll.  I'll even write the caching layer to make it fast in practice.

So, to be clear, what you guys are discussing is a luck stat that is dice-based. Other factors of luck, as Ozy pointed out, are initial placement as well as how often you are attacked. If I'm in a game in which I might go last in turn order, I would think I was pretty unlucky if I lost half my territories before taking my turn. A comprehensive luck stat would need to take these and other factors into account and attempt to weigh all the factors appropriately, with the dice luck having the largest weighting most likely.

M57 wrote:

How cool would it have to be a Luck 'O Meter? ..at least on a per game basis.  I can barely parse the high-end math stuff you guys are talking about, but I know enough to know that I'd love to see a Z-score.  Thing is, I doubt most people would want or appreciate such a number. What do you all think is the best way to present it?  I'd be curious to hear your suggestion, btilly.

The way that I'd like to see it presented is that there is a combat luck percentile.  A number like 56.5% or in the case of the above game probably something like 1.6%.

It can be explained as, "How lucky were your combat rolls?  If every combat roll was redone, this estimates how likely it is you would have done worse."

Thingol wrote: So, to be clear, what you guys are discussing is a luck stat that is dice-based. Other factors of luck, as Ozy pointed out, are initial placement as well as how often you are attacked. If I'm in a game in which I might go last in turn order, I would think I was pretty unlucky if I lost half my territories before taking my turn. A comprehensive luck stat would need to take these and other factors into account and attempt to weigh all the factors appropriately, with the dice luck having the largest weighting most likely.

Yes.

The other luck factors are much, much harder to estimate.  If someone attacks me because of what is a coin flip, I'm unlucky.  If they attack me because I'm dominating the game, I'm not at all unlucky.  There is no way for an algorithm to distinguish those without having a good knowledge of strategy.

btilly wrote:

The way that I'd like to see it presented is that there is a combat luck percentile.  A number like 56.5% or in the case of the above game probably something like 1.6%.

It can be explained as, "How lucky were your combat rolls?  If every combat roll was redone, this estimates how likely it is you would have done worse."

What would the 56.6% mean? ..that 6.6% of your rolls were better than expected?

What might a standard deviation look like?

I feel obligated to make an argument for a "dramatic" system.  If 1.6% is "really unlucky," it doesn't sound like it.

For example, something more like Z-score * 50, expressed as a whole number.  -100 would be 2 Standard deviations, and be very unlucky..