CSubP19 - Why good players SHOULD get bad dice


  • CSubP19: A conversation about mean/mode divergence with Mr. T

    Read what people are saying about the latest Caspian Sub paper:

    This is the NEW operating system for operational strategy.
    -Bill Gates, MicroSoft founder

    I feel I should throw away my books; Mr. T’s brilliance has put my work to shame.
    -Stephen Hawkings, SupraGenius

    Before reading this paper I was nothing but a hobo; now I’m a GENERAL!
    -Tom Cruise, aspiring tall-man

    A voice has been found.  One crying in the wilderness has called an audience to himself with a cry of knowledge and a cry of betterment.  Eloquence, thy name is T!
    -James Lipton, host of Inside the Actor’s Studio

    This magnum opus, this illuminating treatise, this revelation of hitherto secret cognition stands apart as a sentinel event in human history - an event whose significance is not unlike that of the Isle of Atlantis risen from the depths with the bones of her kings new-clothed in flesh.
    -George F. Will, pundit

    There was before the paper and then there was after the paper.  I don’t remember anything of value before the paper.
    -NewPaintBrush, Scientologist

    That’s hot.
    Paris Hilton, flotsam

    Get it here:
    http://games.groups.yahoo.com/group/Caspian_Sub/files/1PolicyPapers/


  • :lol: Wouldn’t it have been easier to just say “Good players should generally avoid battles with questionable outcomes” and leave it at that.  Entertaining read, but not sure I understand what makes that a “policy paper”.

    You explain why avoiding questionable outcomes results in what seems to be more “bad dice” results than “good dice” results, but you really don’t explain why that is an advantageous strategy over aggressively pushing more battles each with slightly lower odds.  I’m not saying you’re necessarily wrong, just that you don’t show why that approach is better (unless that’s what the whole “Tanks are STRONG!” thing was all about and I just missed it). :shrug:


  • Interesting response  :-D

    Considering how much of the game discussions revolve around dice, bad dice, and low luck, I think there are some rather important points in the paper.

    Not only do bad outcomes occur, but they should occur more often than good outcomes.  Essentially, good players are facing a negative-sum game with the dice.

    The vast majority of conversations on dice have missed the central fact that when “luck” occurs, it is more likely to be bad than good.

    And that is yet another reason why low luck is so different than regular Axis.  The risk management angle is pivotal to the standard game because the dice don’t deviate in a standard manner; they will tend to deviate negatively.

    Peace


  • @Mazer:

    Interesting response  :-D

    Considering how much of the game discussions revolve around dice, bad dice, and low luck, I think there are some rather important points in the paper.

    Not only do bad outcomes occur, but they should occur more often than good outcomes.  Essentially, good players are facing a negative-sum game with the dice.

    The vast majority of conversations on dice have missed the central fact that when “luck” occurs, it is more likely to be bad than good.

    And that is yet another reason why low luck is so different than regular Axis.  The risk management angle is pivotal to the standard game because the dice don’t deviate in a standard manner; they will tend to deviate negatively.

    Peace

    “Always the negative waves Moriarty…”


  • This isn’t in the traditional vein of policy papers, but it’s definitely making my head hurt, so regardless, it’s pretty important.@Mazer:

    The vast majority of conversations on dice have missed the central fact that when “luck” occurs, it is more likely to be bad than good.

    I don’t think that’s necessarily true. I mean, wouldn’t you have to look at the odds for every battle for many, many games before you could say that?

    I slapped 2inf 1ftr vs 1inf into frood (all rounds, 5k, LL) and the “most likely outcome” was like 65%. Sure, in that example, bad dice were more likely than good dice, although the chance of bad dice was still outnumbered by the most likely outcome. I upped it to 4inf 1ftr vs 3inf and the “most likely outcome” was 50%. A better outcome had 40% and the two worse outcomes were at 20%. So, for that battle, bad dice were less likely than good dice.

    4inf 1ftr vs 3inf ain’t gonna happen that much, but who’s to say that common battles (maybe territory-trading battles can be ruled out because of the 2inf 1ftr vs inf example?) aren’t similar–in that good dice is more likely than bad dice? I’d want to see hard numbers. Maybe by listing the odds for different variants of round 1 battles we could get an idea whether bad dice or good dice really are more likely in a typical AAR game.


  • Hey Hyo.

    Solid concerns.  Let me address a couple of them.

    I mean, wouldn’t you have to look at the odds for every battle for many, many games before you could say that?

    1. The start of this paper actually began with the question of analyzing the role of luck in an individual game.  One of the other editors and I played a 6rnd game and then counted up the actual outcome vs. the calculated outcome for EVERY battle in the game (took a couple hours to do it right).  On the whole, we both thought the dice were quite unremarkable; neither of us thought we had experienced unusually bad outcomes (with the exception of one naval battle that was a major statistical outlier - this was a <=1% outcome that was removed from the stats).

    But when we looked at the aggregate outcome for the game with the outlier battle removed, we BOTH had highly negative scores.  We were both surprised by that, and the result of that surprising finding was an analysis of outcome distributions as represtented in the paper.  BTW - there is a second paper in the works that talks about the role of luck at the game level instead of the battle level.

    2. The data in the paper does cover a large number of tests.  All of the battle grids come from 10,000 runs of a battle under standard rules.  So by finding the median and then looking at possible deviations, you will find that in a favorable battle there is much more room for negative deviation than for positive deviation.  That is why the 10th percentile outcome hurts much worse than the 90th percentile outcome helps.

    3. You mentioned you ran a 5k trial under LL.  That doesn’t compare to regular rules because LL flattens out the deviations.  LL dramatically compresses the results, and it is the peak-and-trough effect of the dice that is really signficant in showing the aggregate negative outcomes.  The point of LL is to “norm” the dice.

    Does that explain the trials a bit better?  I could elaborate more if it would help.

    Peace


  • :|
    I am supposing that the luck factor being discussed is as it it affects the attacker, and not the defender.
    Long charts of info on die results hide one factor, and that is how much one decisive battle can change the whole course of the game should it go real bad in the first round of combat.
    I’ve seen more than my share of winning games turn around on one throw of the die.
        :-o :cry: :roll: :-o :-P :x :wink: :-D


  • [The vast majority of conversations on dice have missed the central fact that when “luck” occurs, it is more likely to be bad than good.]

    For ‘normally’ favourable attacks the distribution of outcomes is skewed with a ‘long left tail’.
    That means good luck is MORE frequent than bad luck - but the rare bad luck can be much farther from the average than the good cases.
    Attackers also have the really useful option to stop an attack and withdraw after 1, 2… rounds. Defenders don’t. I estimated the option value at some +5% in attacking forces.

    The practical psychology thing is: the human brain is more of an unfairness detector than a general-purpose logic device. Careful tests have shown bad events are easier detected and more memorable. All games involving some luck are great examples…

    (Backgammon) is a game of skill and luck.
    If you win it’s skill; if you lose it’s luck.


  • Tanks are STRONG.

    ==OOOO
    OOOOOOO
    OOOOOO


  • NPB: Well said.


  • @Magister:

    That means good luck is MORE frequent than bad luck - but the rare bad luck can be much farther from the average than the good cases.

    Good post!

    You are close to the position of the paper, but I think we have to tighten up the terms.

    When you write “good luck is MORE frequent than bad luck”, I’d argue that isn’t true if you take the median outcome as your starting point.  By definition, the median is the spot where the luck is neutral - half the outcomes are same/better, half the outcomes are same/worse.

    The point is that the magnitude of the good luck is much smaller than the magnitude of the bad luck, so equally “lucky” dice, good or bad, will have a much bigger negative weight.  You don’t get more frequent unlucky dice, but the unlucky dice are more harmful than the good lucky dice.

    A 90th percentile good outcome could net you +$3 from the median, while a 10th percentile bad outcome could net you -$11 from the median.  Those are outcomes of equal luck in terms of frequency, but the magnitude of deviation is quite different.

    There is no psychological bias in this negative finding (though the phenomenon you mention is real and significant in its own right, and often overlooked in post-game dissections).  The point of the paper is that net bad outcomes are not imaginary; good players actually should get the shaft!

    An objective observer will find that standard, perfectly normed dice will result in a significant net loss from the median outcomes over the course of a game (or within 10,000 runs of a battle).

    This paper looked at the individual fights.  The next paper will measure the magnitude over the course of a game.

    Peace

  • 2007 AAR League

    Was the paper arguing that this is true for the first round of combat, and where smart attackers know when to call it off?  I didn’t quite follow the paper since the whole Mr T thing was distracting.

    Intuitively I’d guess that the size of bad luck depends mostly on force composition.  If the attacker uses planes, sure they can lose big.  If the defender has planes, they can lose big too.  Defenders can also lose really big if you take their capital (or to a lesser extent if you take WEU or SEU).

    For single round combats, most of the time attackers can retreat if they see their luck going bad after the first round - and that makes a huge difference.

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