What percentage is luck involved in a games outcome?



  • Not quite sure what you’re talking about but I’ve tested my random number generator and it will average a roll of 3.5 on a d6.

    That’s the thing with odds, in real life you can’t actually roll a 3.5. For instance if you’re fighting a tank, you have to kind of think of what happens when it hits, and when it doesn’t, because you can’t exactly go on the math which says it will kill half a unit on average, since you can’t kill half a unit (bb ships excluded lmao).


  • Moderator

    Just out of curiosity.

    Rolling 100d6:
    (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6)


  • Moderator

    I forgot about the ording function.  LOL!  😄

    At least it’ll be easy to count.

    1’s:  14
    2’s:  13
    3’s:  21
    4’s:  15
    5’s:  22
    6’s:  15

    1-3:  48
    4-6:  52

    Little high on the 3 and 5’s, but close enough for me.



  • Lmao I too, at first, was like wtf  😮 😮 😮 you rolled it exactly in order on individual dice?



  • @Frood:

    Not quite sure what you’re talking about but I’ve tested my random number generator and it will average a roll of 3.5 on a d6.

    I am not sure of being able to explain it better Frood! But I will try.

    First I am not saying that dice rollers are not working well.
    Really a dice roller, generating number from a pseudo random sequence, it is more “precise” than a real dice.
    DarthMaximus showed with the test of 100 dices.
    The problem I am trying to describe is related with the sequence of results, that is not possible to see from the preceding post because dice results are re-ordered, in ascending order.

    I am trying to say that observing the results on a smaller period  (for example every 10 results) it could be possible to found that results are almost all above the average. While in the following period they are almost all under the average.
    If you roll dices and get in the "above average " sub-period you has been screewed.
    If you roll dices and get in the “under average” sub-period then you have been lucky soring more hits.

    I am not saying that the dice rollers are not correct. The nature of pesudo casual sequences grant that the average is 3.5 but may arise problem with smaller sequence of the results.
    I try to explain it with a simulated experiment. Consider the following sequences of results :
    (a) 1 6 2 4 3 5 2 4 1 5 3 6 3 5 2 6 1 4: Average 3.5

    (b) 4 6 5 4 6 6 5 5 4 3 1 2 3 1 2 1 2 3: Average 3.5

    © 3 3 3 4 4 4 5 5 5 6 6 6 1 1 1 2 2 2 : Average 3.5

    All the above sequences have the same average but going in combat with the last one © is not a beutiful thing! If I attack with 6 inf and 6 tanks I score 0 hits. Then defender defends with 6 infantry and score 6 hits!
    The second sequence (b) has the same problem, having in the first half sequence (4 6 5 4 6 6 5 5 4 ) with an average of 5. The second half sequence is (3 1 2 3 1 2 1 2 3) with an average of 2.
    The first sequence (a) suffers less from this problem, first sub sequence is (1 6 2 4 3 5 2 4 1)  averaging 3,11 the second subsequence is (5 3 6 3 5 2 6 1 4) averaging 3,88.

    So my point is: pseudo random sequences have such kinds of oscillation? I mean on the long run they are almost “perfect dices” but analyzing the sequence in smaller segments has ever been made?
    This is only an hypotesis, I may be wrong and this is not a real problem.

    Addendum:

    I made an experiment in the threads regarding dice roller, using 100 dices@1, that are not reoredered. Results are:
    Considering sub sequences of 10 results, and calculating the number of values between 1 and 3 and the avereage of each sub sequence, we have:

    Average  hits (1,2,3)
    3,1 0
    2,8 3
    3,4 2
    3,6 2
    3,3 2
    4 1
    3,4 2
    2,7 3
    3,8 2
    3,2 3

    Each sequence of 10 numbers is “well equilibrated” (never more than 3 hits)
    there are sequences like the sixth that averages 4 and get only one hit. But it seems that my hypothesis is not completely true.
    There is an oscillation of the averages but its seems not a problem that may really hurt.



  • Of course the averages are going to vary with small er numbers of dice… each die is weighted more heavily in a smaller sample size, and thus any single die will skew the dice far more than it could in a larger sample.

    It is the nature of dice for that to happen.



  • I make a premise. I prefer to play with ordinary luck. In our face2face games we have not problem with dice.
    I prefer the risk of the dice and the uncrtainity of the random results that allow for more challenging planning.

    My idea was only about the fact that the “precision” of dice rollers in averaging more precisely than a real dice, may influence the results.
    I mean the pesudo sequence is built (before the numbers are generated) in order to as near as possible to the average of 3.5. Now, what happens if the average go down (below 3.5) the only possible thing is that in the next dice results extracted from the sequence (they are alredy ordered and ready to be used) the results are “forced” to raise the average.
    So we have an influence on the current results by the past results. I am still not able to quantify this phenomena, so I asked if someone eve tried to make sampling evaluation and running averages of the result of the dice rollers.


  • 2007 AAR League

    The nice thing with dice is that, when your ego is hung up on being a good strategist, you can lose a game without losing your sense of self-worth. Bah, it was just dice! It does add an element of excitement, and a lot of good war stories come out of it -“I attacked Egypt with 14 Inf and 9 Fighters and 6 battleships, and I only scored two hits! zomgzorz!!”


  • 2007 AAR League

    @Romulus:

    My idea was only about the fact that the “precision” of dice rollers in averaging more precisely than a real dice, may influence the results.
    I mean the pesudo sequence is built (before the numbers are generated) in order to as near as possible to the average of 3.5. Now, what happens if the average go down (below 3.5) the only possible thing is that in the next dice results extracted from the sequence (they are alredy ordered and ready to be used) the results are “forced” to raise the average.
    So we have an influence on the current results by the past results. I am still not able to quantify this phenomena, so I asked if someone eve tried to make sampling evaluation and running averages of the result of the dice rollers.

    All I can say is that frood.net/aacalc/ rolls each die without any knowledge or reference to any previous dice.



  • Ender, I do not know how frood.net/aacalc/ roll the dice.
    I am not saying that they are wrong in rolling.

    Sometime I use pseudo random number in Java and I used them in C/C++.
    Being the computer unable to make random choices there are pseudo random sequences that are used.
    A pseudo random sequence is a sequence of number built in order to be as near is possible to a Gaussian distribution. So sometime the results may “suffer” from periodic effects.

    But frood.net/aacalc may use another method to generate the random number singularly. In which case the “rolled” numbers are completely random.


  • 2007 AAR League

    @Romulus:

    Ender, I do not know how frood.net/aacalc/ roll the dice.
    I am not saying that they are wrong in rolling.

    Sometime I use pseudo random number in Java and I used them in C/C++.
    Being the computer unable to make random choices there are pseudo random sequences that are used.
    A pseudo random sequence is a sequence of number built in order to be as near is possible to a Gaussian distribution. So sometime the results may “suffer” from periodic effects.

    But frood.net/aacalc may use another method to generate the random number singularly. In which case the “rolled” numbers are completely random.

    It rolls the dice one at a time using the mt_rand() function in PHP, which is reportedly better than the regular rand() function (or is it random()?). Each time it rolls it takes the time in microseconds as a random number seed that mt_rand uses to do what ever it does and creates a random number from 1-6. That’s as much as I can tell you, cuz I don’t know anything more about it.



  • @Ender:

    It rolls the dice one at a time using the mt_rand() function in PHP, which is reportedly better than the regular rand() function (or is it random()?). Each time it rolls it takes the time in microseconds as a random number seed that mt_rand uses to do what ever it does and creates a random number from 1-6. That’s as much as I can tell you, cuz I don’t know anything more about it.

    It is more than sufficient to understood how its work!

    mt_rand() should “randomize”, using the time as seed, every time the number a number is generated. Randomize means initialize the random generator, so as you already said each number generated is completely independent form the preceding!

    Tanhs Ender!


  • 2007 AAR League

    I’ve just wondered how it works that when the dice are rolled within the same microsecond as each other, so the same time seed, that it rolls a different number.  :?



  • I suppose that such operation are “serialized”, i.e. executed one after the other even if for us they appear simultaneous. Is one of the things that makes computers so intriguing!



  • Whats with everyone changing there name? First Jenn and now you Frod. I like it anyways.



  • @cyan:

    Whats with everyone changing there name? First Jenn and now you Frod. I like it anyways.

    we are training in teh wayz of ninjazorz

    poof


  • 2007 AAR League

    @Commander:

    @cyan:

    Whats with everyone changing there name? First Jenn and now you Frod. I like it anyways.

    we are training in teh wayz of ninjazorz

    poof

    That should be Emperor Ender Ivanova perhaps?



  • I just can;t bring myself to give up my Avatar…

    Though the name, I am ready to change…  The trouble is, the name change would demand a new Avatar as well…  So I am stuck…



  • I’m just lazy. i used to change my avatar with each promotion.



  • Yes, but former USAFA Zoomie Pride is tied up in mine…



  • i just realized i’m a bomber! yeah


  • 2007 AAR League

    @ncscswitch:

    I just can;t bring myself to give up my Avatar…

    Though the name, I am ready to change…  The trouble is, the name change would demand a new Avatar as well…  So I am stuck…

    I don’t see why you’d have to change both - and besides, ncscswitch is hard to remember how to spell, let alone pronounce… can’t you cook up some cool pagan name. I’ll just call you Bacchus.



  • I may surprise you all soon…

    I am less than an hour away from logging 100 DAYS of active posting on the site (in 2 years).  That may be worth an update…


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