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    Pseudo Random Distribution - ituturo ni Wazzy!

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    Wazzynator
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    Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Wed May 13, 2009 3:59 pm

    Pseudo Random Distribution
    A Pseudo Random Distribution refers to the Warcraft III engine's dynamic probability calculations for certain percentage-based attack modifiers. Rather than using a static percentage, the probability is first set to a small initial value, then gradually increased with each consecutive attack for which the modifier does not occur. The probability then drops back to the initial value when the attack modifier does apply. Not only does this system make long strings of successful modifiers unlikely, but it also makes going an entire game without an attack modifier occurring impossible, as eventually the dynamic probability exceeds 100% and "forces" a modifier on the next attack. The distribution of attack modifiers is therefore not truly random, hence the term Pseudo Random Distribution. In general, all abilities that are rounded to the nearest 5% in the
    Warcraft III engine follow this probability distribution.
    Pseudo Random Abilities
    The list of all currently known base abilities that follow this system of balanced randomness is shown below. Triggered abilities notably do not fall in this list.

    Critical Strike (ex. Coup de Graçe, Crystalys)

    Bash (ex. Time Lock, Slithereen Guard's Bash. Since its remake, Cranium Basher no longer follows this distribution.)

    Pulverize (ex. Flaming Fists, Anchor Smash)

    Orb of Slow (ex. Maim, Maelstrom)

    Hardened Skin (ex. Stout Shield, Vanguard)
    Probability Mechanics
    Critical Strike Example
    Consider the case of a 20% chance to Critical Strike. If the game were truly random, then for each attack there would be a 20% chance for the unit to land a Critical Strike, regardless of how many Critical Strikes had been performed in the past. A simple implementation would therefore be to select a random integer between 1 and 100, and if the integer was less than or equal to 20, then the engine would cause that attack to be a Critical (which is the usual construct used by triggered percentage-based abilities). While this implementation would, in the long run, average out to 20% of attacks being Criticals, there is nothing preventing an infinite series of Critical Strikes or, conversely, an absence of Critical Strikes for the entire game, although the chance is rather insignificant. To prevent the ensuing complaints and balance this random game mechanic, the Warcraft III developers implemented a Pseudo Random Probability Distribution.
    Instead of there being a 20% chance to Critical Strike with every attack, the first attack made actually has a 5.57% chance to Critical Strike. If that is not a Critical Strike, then the second attack has a 11.14% chance to Critical. If that is also not a Critical Strike, then the third has a 16.71% chance to Critical, and so on, adding 5.57% for each consecutive non-Critical. When a Critical Strike does occur, however, the chance for the next attack resets to 5.57%. In the long run, the number of Critical Strikes divided by the total number of attacks somewhat approximates the stated 20%, but now it is extremely difficult to have a series of Critical Strikes, and also impossible to go more than 17 attacks without a Critical, because the percentage for the 18th attack (assuming 17 previous consecutive non-Critical attacks) is 100.26%. In effect, the game causes the number of attacks between Criticals to be skewed towards 1 / 20% = 5, with a maximum limit of 17.
    Probability Formulas
    For all of the abilities stated above, the Warcraft III engine uses an initial percentage (%) value that linearly increases with each consecutive attack for which the attack modifier does not apply. The probability formula for an attack modifier to occur is therefore:
    P(N) = C * N
    In this formula, P(N) is the % probability for the modifier to occur on the Nth attack, N is the number of attacks since the last attack modifier (minimum value of 1), and C is a constant that serves as both the initial % and the increase in % with each attack (Note: In the forum topic linked below, a slightly different formula is used in which N is defined as the number of in-between attacks, which has a minimum value of 0. For ease of comprehension, this article defines N as the number of attacks since the last attack modifier, with a minimum value of 1). Since this is a linear formula, when N reaches a high enough value, P(N) will exceed 1 and the next attack is guaranteed to have an attack modifier. Simple algebra shows this N value to be equal to 1 / C.
    The value of C in turn depends on the probability stated in the World Editor for that skill; for the rest of this article, this stated probability will be referred to as P(E), the expected probability.
    For obvious reasons, the overall probability of the attack modifier occurring should be as close as possible to P(E). In other words, after an infinite series of attacks, the number of attack modifiers that occurred divided by the total number of attacks should ideally be equal to P(E). However, Warcraft III's Pseudo Random Distribution actually results in an overall probability that is less than P(E). While this negative deviation is insignificant at low P(E), differing by less than a percent for P(E) = 30%, the error increases sharply for higher percentages: a P(E) of 80% actually has a probability of only ~66%. This error likely results from two factors:
    1.
    A truncation in C. Without an infinite number of digits available for C, it is virtually impossible for a linear probability formula to accurately model a random distribution for a given P(E). Simply calculating C requires a significant amount of computing time, considering that it has to match an entire probability distribution to a single constant. This is the reason why all of the above skills are rounded to the nearest 5%: instead of dynamically calculating C as well, which would take up far too many CPU resources for each attack, the developers were able to create a static table of C values for 5%, 10%, 15%, ...95%, which could then be substituted into the above formula to determine P(N). The truncation of these defined values, which always results in smaller values, then leads to actual probabilities that are less than P(E).
    2.
    Ladder P(E) values. Blizzard tailored Warcraft for Ladder play, not custom maps, and the highest P(E) in Ladder is the Tauren's Pulverize, with a probability of 25%. It is likely not a coincidence that the error in P(E) increases significantly after this point. When Blizzard implemented the PRD, they probably only calculated C values for the percentages that they knew they'd use in Ladder, and all other values were simply estimated from those results (e.g. with a fitted exponential curve). Apparently they didn't care to check whether those values actually worked, leading to the current situation.
    A table of C values is shown below for percentages up to 45%. The maximum number of consecutive attacks that can occur without the attack modifier is also listed for each C value. So for a Critical Strike with a value of 45%, a series of four normal attacks can occur, but the fifth attack will then have to be a Critical.
    Note: For P(E) > 30%, C was estimated from in-game testing rather than a fitted probability distribution, in order to better reflect the rising error in P(E) after that point.

    Pseudo Random Probability Constants
    Expected Probability P(E) Constant (C) Max # of Consecutive Attacks without modifier


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Wed May 13, 2009 4:12 pm

    tsk, di pa tapos........ na pindot ko kasi yung send... tae...

    Expected Probability P(E) Constant(C) Max# Of consecutive attacks without modifier
    5% 0.00380 263
    10% 0.01475 67
    15% 0.03221 31
    20% 0.05570 17
    25% 0.08475 11
    30% 0.11895 8
    35% 0.14628 6
    40% 0.18128 4
    45% 0.21867 4

    Applications
    The Pseudo Random Distribution has clear gameplay uses and implications. A hero with a Critical Strike ability could fight creeps until a long string of non-Criticals occurred, then head into a team battle or gank with an increased Critical Strike chance for his first attack(s). Such a tactic, while time consuming, could significantly increase the hero's DPS for that battle. The applications are even greater for Bash heroes, who could build up the same string of non-Bashes in order to maximize their chances of landing a Bash in the beginning of battle. Furthermore, the fact that consecutive Bashes are discouraged by the Pseudo Random Distribution benefits Bash heroes greatly in that Stun times will not overlap as much as in a true random distribution, making Permabashing a distinct possibility.
    While not completely confirmed, it would be logical to assume that the counter of consecutive attacks does not increase when attacking units against whom the attack modifier can not apply. So attacking an enemy building repeatedly would not increase the chance of a Critical Strike on the first subsequent attack(s) against an enemy unit.


    Credits goes to Dotationary v3.06
    ^_^


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Thu May 14, 2009 5:21 pm

    wow!!Sa tingin ko nasobrahan ka sa kape!Daming letters nyan oh!Nagawa mong i-type lahat yan o Copy-Paste Process lang? tongue


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Thu May 14, 2009 5:46 pm

    SINclare21 wrote:wow!!Sa tingin ko nasobrahan ka sa kape!Daming letters nyan oh!Nagawa mong i-type lahat yan o Copy-Paste Process lang? tongue

    no comment.....xD



    to be honest, copy-paste lng, kaya nga credits goes to dotationary


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Thu May 14, 2009 6:09 pm

    Hehehe...Oo nganaman no!?


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Thu May 14, 2009 9:20 pm

    bakit ko naman isusulat ang ganyan ka lahabang wall of text?


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Thu May 14, 2009 9:36 pm

    @Wazzy
    para ma exercise yung mga fingers mo!


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Thu May 14, 2009 9:50 pm

    puyat noh!


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Thu May 14, 2009 10:15 pm

    Gabi na tulog na kayo mga kids!


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by sopas111 on Fri May 15, 2009 8:17 am

    Wazzynator wrote:
    SINclare21 wrote:wow!!Sa tingin ko nasobrahan ka sa kape!Daming letters nyan oh!Nagawa mong i-type lahat yan o Copy-Paste Process lang? tongue

    no comment.....xD



    to be honest, copy-paste lng, kaya nga credits goes to dotationary

    lol, pero nakasulat ituturo ni Wazzy! haha.
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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Fri May 15, 2009 9:17 am

    wala pa kasing topic about dito eh....

    pero mentioned naman ang dotationary....


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Qwatro Bente on Fri May 15, 2009 1:02 pm

    kala ko ba ituturo mo? eh copy paste lang yan eh! translation naman. di ko maintindihan Shocked
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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Fri May 15, 2009 1:08 pm

    CONCLUSION:
    you may want to hit a creep before you hit the hero for the actual stun|crit


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Fri May 15, 2009 6:16 pm

    Ahhh!Hit muna creeps bago hit hero para mag crit o di kaya stun!Ganun ba!?


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Fri May 15, 2009 6:19 pm

    ganun na nga...

    pero ako, personally di ko to inaaply, basta hit lng ako sa hero.... xD


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Fri May 15, 2009 6:24 pm

    Halos lahat naman yata ng manlalaro ganun ginagawa imbes na hit muna creeps bago hero!


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Fri May 15, 2009 6:26 pm

    kaya nga....


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by SINclare21 on Fri May 15, 2009 6:28 pm

    Pero Ok din to know na kung paano yun gumagana!


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    Re: Pseudo Random Distribution - ituturo ni Wazzy!

    Post by Wazzynator on Fri May 15, 2009 6:30 pm

    yes... maganda rin naman may malaman kay facts..


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