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​Spun off from 'A Not-Quite-Newb's Read-through of Ex3' - Sidereal Excellency

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  • ​Spun off from 'A Not-Quite-Newb's Read-through of Ex3' - Sidereal Excellency

    First- CODE AND NUMBERS

    Das (corrected) code
    Code:
    public class Dice {
    
        private static final int ROLLS = 10000;
    
        private static enum Actor {
            SOLAR("Solar", 10, 0, 7, 10, 1, 10),
            SIDEREAL_W_0_BONUS("Sidereal wtih 0 bonus dice", 0, 0, 4, 10, 1, 10),
            SIDEREAL_W_1_BONUS("Sidereal with 1 bonus dice", 1, 0, 4, 10, 1, 10),
            SIDEREAL_W_2_BONUS("Sidereal with 2 bonus dice", 2, 0, 4, 10, 1, 10),
            SIDEREAL_W_3_BONUS("Sidereal with 3 bonus dice", 3, 0, 4, 10, 1, 10),
            SIDEREAL_W_4_BONUS("Sidereal with 4 bonus dice", 4, 0, 4, 10, 1, 10),
            SIDEREAL_W_5_BONUS("Sidereal with 5 bonus dice", 5, 0, 4, 10, 1, 10),
            SOLAR_W_EXCELLENT_STRIKE("Solar with Excellent Strike", 8, 1, 7, 10, 2, 10);
            
            private int bonusDice;
            private int bonusSuccesses;
            private int targetNumber;
            private String actorName;
            private int doubleNumber;
            private int min;
            private int max;
    
            private Actor(String actorName, int bonusDice, int bonusSuccesses, int targetNumber, int doubleNumber, int min, int max) {
                this.actorName = actorName;
                this.bonusDice = bonusDice;
                this.bonusSuccesses = bonusSuccesses;
                this.targetNumber = targetNumber;
                this.doubleNumber = doubleNumber;
                this.min = min;
                this.max = max;
            }
            
            @Override
            public String toString() {
                return "target number: " + targetNumber + " double number: " + doubleNumber + " bonus dice: " + bonusDice + " bonus successes: " + bonusSuccesses + " dice min/max " + min + "/" + max;
            }
        }
        
        public static void main(String a[]) {
            int[] successes = new int[50];
            int numberOfDice = 13;
            Actor actor = Actor.SOLAR_W_EXCELLENT_STRIKE;
            for(int i=0;i<ROLLS;i++) {
                successes[roll(actor.min, actor.max, numberOfDice + actor.bonusDice, actor.targetNumber, actor.doubleNumber)+actor.bonusSuccesses]++;
            }
            System.out.println("Test for " + actor.actorName);
            System.out.println("
    Code:
    ");
            System.out.println("Out of " + ROLLS + " attempts");
            for(int i =0;i<successes.length;i++) {
                int successesRolled = successes[i];
                if(successesRolled > 0) {
                    BigDecimal percentage = new BigDecimal(successesRolled).divide(new BigDecimal(ROLLS));
                    System.out.println(StringUtils.rightPad(Integer.toString(i), 3) +": " + StringUtils.leftPad(Integer.toString(successesRolled), 4) + " " + StringUtils.leftPad("(" + NumberFormat.getPercentInstance().format(percentage.doubleValue()) +")", 5));
                }
            }
            System.out.println("----");
            System.out.println("Number of dice: " + numberOfDice + " " + actor.toString());
            System.out.println("Top  5%: " + printTop(.05d, successes));
            System.out.println("Top 20%: " + printTop(.20d, successes));
            System.out.println("Top 33%: " + printTop(.33d, successes));
            System.out.println("Top 50%: " + printTop(.50d, successes));
            System.out.println("Top 67%: " + printTop(.67d, successes));
            System.out.println("
    "); } private static int printTop(double percentage, int[] successes) { int minimumNumberOfRolls = new Double(ROLLS * percentage).intValue(); int count = 0; for(int i=successes.length-1;i>0;i--) { count += successes[i]; if(count >= minimumNumberOfRolls) { return i; } } throw new IllegalStateException("Minimum percentage never found"); } private static int roll(int min, int max, int numberOfDice, int targetNumber, int doubleNumber) { int successes = 0; for(int i=0;i<numberOfDice;i++) { int roll = rollDie(min, max+1); if(roll >= targetNumber) { successes++; } if(roll >= doubleNumber) { successes++; } } return successes; } private static int rollDie(int min, int max) { return RandomUtils.nextInt(min, max); } }


    Results:

    ​Test for Sidereal wtih 0 bonus dice
    Code:
    Out of 10000 attempts
    2  :    1  (0%)
    3  :    4  (0%)
    4  :   18  (0%)
    5  :   63  (1%)
    6  :  254  (3%)
    7  :  603  (6%)
    8  :  967 (10%)
    9  : 1456 (15%)
    10 : 1818 (18%)
    11 : 1758 (18%)
    12 : 1406 (14%)
    13 :  920  (9%)
    14 :  454  (5%)
    15 :  211  (2%)
    16 :   56  (1%)
    17 :    8  (0%)
    18 :    3  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 0 bonus successes: 0 dice min/max 1/10
    Top  5%: 14
    Top 20%: 12
    Top 33%: 11
    Top 50%: 10
    Top 67%: 9


    Test for Sidereal with 1 bonus dice
    Code:
    Out of 10000 attempts
    3  :    1  (0%)
    4  :   12  (0%)
    5  :   34  (0%)
    6  :  123  (1%)
    7  :  324  (3%)
    8  :  657  (7%)
    9  : 1127 (11%)
    10 : 1533 (15%)
    11 : 1787 (18%)
    12 : 1675 (17%)
    13 : 1245 (12%)
    14 :  804  (8%)
    15 :  411  (4%)
    16 :  194  (2%)
    17 :   50  (0%)
    18 :   18  (0%)
    19 :    4  (0%)
    20 :    1  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 1 bonus successes: 0 dice min/max 1/10
    Top  5%: 15
    Top 20%: 13
    Top 33%: 12
    Top 50%: 11
    Top 67%: 10


    Test for Sidereal with 2 bonus dice
    Code:
    Out of 10000 attempts
    3  :    1  (0%)
    4  :    6  (0%)
    5  :   14  (0%)
    6  :   55  (1%)
    7  :  181  (2%)
    8  :  382  (4%)
    9  :  745  (7%)
    10 : 1194 (12%)
    11 : 1564 (16%)
    12 : 1729 (17%)
    13 : 1585 (16%)
    14 : 1108 (11%)
    15 :  751  (8%)
    16 :  408  (4%)
    17 :  192  (2%)
    18 :   64  (1%)
    19 :   17  (0%)
    20 :    3  (0%)
    21 :    1  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 2 bonus successes: 0 dice min/max 1/10
    Top  5%: 16
    Top 20%: 14
    Top 33%: 13
    Top 50%: 12
    Top 67%: 11


    Test for Sidereal with 3 bonus dice
    Code:
    Out of 10000 attempts
    4  :    1  (0%)
    5  :    6  (0%)
    6  :   24  (0%)
    7  :   84  (1%)
    8  :  213  (2%)
    9  :  460  (5%)
    10 :  915  (9%)
    11 : 1249 (12%)
    12 : 1547 (15%)
    13 : 1673 (17%)
    14 : 1471 (15%)
    15 : 1114 (11%)
    16 :  645  (6%)
    17 :  350  (4%)
    18 :  171  (2%)
    19 :   50  (0%)
    20 :   15  (0%)
    21 :   10  (0%)
    22 :    2  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 3 bonus successes: 0 dice min/max 1/10
    Top  5%: 17
    Top 20%: 15
    Top 33%: 14
    Top 50%: 13
    Top 67%: 12


    Test for Sidereal with 4 bonus dice
    Code:
    Out of 10000 attempts
    5  :    1  (0%)
    6  :   15  (0%)
    7  :   44  (0%)
    8  :  119  (1%)
    9  :  312  (3%)
    10 :  560  (6%)
    11 :  951 (10%)
    12 : 1356 (14%)
    13 : 1554 (16%)
    14 : 1531 (15%)
    15 : 1318 (13%)
    16 : 1037 (10%)
    17 :  614  (6%)
    18 :  350  (4%)
    19 :  149  (1%)
    20 :   67  (1%)
    21 :   14  (0%)
    22 :    7  (0%)
    23 :    1  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 4 bonus successes: 0 dice min/max 1/10
    Top  5%: 18
    Top 20%: 16
    Top 33%: 15
    Top 50%: 14
    Top 67%: 12


    Test for Sidereal with 5 bonus dice
    Code:
    Out of 10000 attempts
    3  :    1  (0%)
    5  :    2  (0%)
    6  :    7  (0%)
    7  :   19  (0%)
    8  :   59  (1%)
    9  :  184  (2%)
    10 :  319  (3%)
    11 :  652  (7%)
    12 : 1033 (10%)
    13 : 1330 (13%)
    14 : 1578 (16%)
    15 : 1521 (15%)
    16 : 1275 (13%)
    17 :  952 (10%)
    18 :  530  (5%)
    19 :  330  (3%)
    20 :  131  (1%)
    21 :   54  (1%)
    22 :   17  (0%)
    23 :    4  (0%)
    24 :    2  (0%)
    ----
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 5 bonus successes: 0 dice min/max 1/10
    Top  5%: 19
    Top 20%: 17
    Top 33%: 15
    Top 50%: 14
    Top 67%: 13


    Test for Solar
    Code:
    Out of 10000 attempts
    2  :    4  (0%)
    3  :   15  (0%)
    4  :   55  (1%)
    5  :  134  (1%)
    6  :  278  (3%)
    7  :  518  (5%)
    8  :  745  (7%)
    9  :  990 (10%)
    10 : 1186 (12%)
    11 : 1240 (12%)
    12 : 1113 (11%)
    13 : 1063 (11%)
    14 :  872  (9%)
    15 :  679  (7%)
    16 :  438  (4%)
    17 :  287  (3%)
    18 :  191  (2%)
    19 :  102  (1%)
    20 :   46  (0%)
    21 :   25  (0%)
    22 :   11  (0%)
    23 :    5  (0%)
    24 :    2  (0%)
    25 :    1  (0%)
    ----
    Number of dice: 13 target number: 7 double number: 10 bonus dice: 10 bonus successes: 0 dice min/max 1/10
    Top  5%: 17
    Top 20%: 14
    Top 33%: 13
    Top 50%: 11
    Top 67%: 10


    Test for Solar with Excellent Strike
    Code:
    Out of 10000 attempts
    3  :    3  (0%)
    4  :   13  (0%)
    5  :   49  (0%)
    6  :  118  (1%)
    7  :  234  (2%)
    8  :  482  (5%)
    9  :  760  (8%)
    10 :  934  (9%)
    11 : 1161 (12%)
    12 : 1288 (13%)
    13 : 1240 (12%)
    14 : 1106 (11%)
    15 :  879  (9%)
    16 :  626  (6%)
    17 :  446  (4%)
    18 :  295  (3%)
    19 :  200  (2%)
    20 :  101  (1%)
    21 :   31  (0%)
    22 :   17  (0%)
    23 :   11  (0%)
    24 :    4  (0%)
    26 :    2  (0%)
    ----
    Number of dice: 13 target number: 7 double number: 10 bonus dice: 8 bonus successes: 1 dice min/max 2/10
    Top  5%: 18
    Top 20%: 15
    Top 33%: 14
    Top 50%: 12
    Top 67%: 11


    Summary of the top results for each
    Code:
    ​Test for Sidereal wtih 0 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 0 bonus successes: 0 dice min/max 1/10
    Top  5%: 14
    Top 20%: 12
    Top 33%: 11
    Top 50%: 10
    Top 67%: 9
    
    Test for Sidereal with 1 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 1 bonus successes: 0 dice min/max 1/10
    Top  5%: 15
    Top 20%: 13
    Top 33%: 12
    Top 50%: 11
    Top 67%: 10
    
    Test for Sidereal with 2 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 2 bonus successes: 0 dice min/max 1/10
    Top  5%: 16
    Top 20%: 14
    Top 33%: 13
    Top 50%: 12
    Top 67%: 11
    
    Test for Sidereal with 3 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 3 bonus successes: 0 dice min/max 1/10
    Top  5%: 17
    Top 20%: 15
    Top 33%: 14
    Top 50%: 13
    Top 67%: 12
    
    Test for Sidereal with 4 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 4 bonus successes: 0 dice min/max 1/10
    Top  5%: 18
    Top 20%: 16
    Top 33%: 15
    Top 50%: 14
    Top 67%: 12
    
    Test for Sidereal with 5 bonus dice
    Number of dice: 13 target number: 4 double number: 10 bonus dice: 5 bonus successes: 0 dice min/max 1/10
    Top  5%: 19
    Top 20%: 17
    Top 33%: 15
    Top 50%: 14
    Top 67%: 13
    
    Test for Solar
    Number of dice: 13 target number: 7 double number: 10 bonus dice: 10 bonus successes: 0 dice min/max 1/10
    Top  5%: 17
    Top 20%: 14
    Top 33%: 13
    Top 50%: 11
    Top 67%: 10
    
    Test for Solar with Excellent Strike
    Number of dice: 13 target number: 7 double number: 10 bonus dice: 8 bonus successes: 1 dice min/max 2/10
    Top  5%: 18
    Top 20%: 15
    Top 33%: 14
    Top 50%: 12
    Top 67%: 11
    Current implementation of Sidereal Excellency is: Spend 1m to reduce TN by (to a minimum of 4), spend 1m to add dice (to a maximum of Essence).

    So- the trickiness

    In an ideal world, the Sidereal Excellency increases reliability at the relative tradeoff of having a lower ceiling than the Solar Excellency.
    As the Sidereal Excellency scales up with Essence, however, it starts to shoot past the Solar in both reliability and ceiling- *Technically* the Solar with 23 dice has a higher ceiling than the Sidereal with 18, but in experienced terms, the Sidereal is going to be almost always rolling higher.

    Solutions:
    * Sidereals don't get bonus dice, they only get TN reduction.
    PROS: Easy.
    CONS: The Sidereal becomes materially worse on average than the Solar- they don't gain reliability at the cost of a lower ceiling. Also, it's going to feel very 'samey' across different abilities.

    * Sidereals get (Essence) points to distribute across TN and bonus dice; at Essence 5, they effectively have 2 bonus dice.
    PROS: Best fit for the 'trade lower ceiling for increased competence'
    CONS: ...at Essence 5. Until then, the Sidereal is notably worse off. Also, more math tricky.

    Thoughts?


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  • #2
    Dislike math tricky. Easy plan is best plan.


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    Comment


    • #3
      The sidereal excellency is too strong for a player character with a bucket of charms, but its fine for antagonist quick characters where their powers are even more abstracted than a normal PC. Luckily, Vance confirmed that all the antagonist excellencies are provisional and subject to change.

      Comment


      • #4
        Meh, make the Sidereal excellency similar to the Lunar: normally you can add, say, +Essence, but if you stunt you can add +College or something.

        Comment


        • #5
          I lean towards the Second option. Sidereals should be weaker than Solars on average, IIRC. The Unconquered Sun is the god of unsurpassed excellence, while the Five Maidens aren't.

          Maybe make it E+1 points to use between Dice and TN?

          Comment


          • #6
            I don't think this is really a problem that needs solving provided that the proportionately greater power of adding dice to Attribute+Ability rolls is kept in mind in Sidereal Charm design. I have seen E2 Dragon-Bloods give Solars a run for their money with only excellencies in play, it's really not that big a deal.

            If I were compelled to make a fix, I would increase the cost of TN reduction in some fashion. Either increasing the mote cost for each TN reduction (1m for TN6, 3m for TN5, 6m for TN4), making it a flat 2m per point of reduction or requiring a point of willpower to reduce TN.


            Currently writing for Exigents.

            Comment


            • #7
              I like the willpower idea.

              Comment


              • #8
                Initial thought: overprice TN reduction - say, 3m for TN 6, 7m total for TN 5, 12m total for TN 4. Sidereals can pull enormous successes out, but they can't do it reliably, particularly with their small mote pools.

                Not sure I love that, though, because for me the biggest question is, "How do they do at hitting Def 12 with a Decisive?" That's the point where things will come crashing down, if they do. ("How do they do with a light Withering weapon?" is right behind it.) And even if it's pricey to throw a TN 4 attack, if you can do it and virtually guarantee a hit - I mean, you may be broke, but the other guy is plausibly dead.


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                Solar Charm Rewrite (Complete) (Now with Charm cards!)

                Comment


                • #9
                  Originally posted by Irked View Post
                  Not sure I love that, though, because for me the biggest question is, "How do they do at hitting Def 12 with a Decisive?" That's the point where things will come crashing down, if they do. ("How do they do with a light Withering weapon?" is right behind it.) And even if it's pricey to throw a TN 4 attack, if you can do it and virtually guarantee a hit - I mean, you may be broke, but the other guy is plausibly dead.
                  I've done some test cases with 11 dice and TN 4. The second roll had 12 successes. Most of the time it rakes in around 10 sux. I've only done about 5 tests tho', so take my results with appropriate salt.

                  Comment


                  • #10
                    Originally posted by Aranfan View Post

                    I've done some test cases with 11 dice and TN 4. The second roll had 12 successes. Most of the time it rakes in around 10 sux. I've only done about 5 tests tho', so take my results with appropriate salt.
                    The stats above suggest that 13 dice hits TN 12 only 20% of the time, which feels safe; on the other hand, 16 dice (at E3) hits 2/3 of the time, which feels a little strong, even at a high price.


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                    Solar Charm Rewrite (Complete) (Now with Charm cards!)

                    Comment


                    • #11
                      Useless comment: In an ideal world, I think this would solve more by making that technically higher ceiling the Solar has really count; so it can give them advantages they can really press when they roll higher than anyone else can, and they can downplay the consequences of the corresponding lower reliability through defenses and general ass saving Charms. High risk, high reward, with superb recovery Charms negating much of the risk part of it to leave them all round quite a bit better.

                      That said, this is fundamentally a useless comment (that I nevertheless felt compelled to make) because the Solars are done and if they're not like that (presumably for good reason!), they're not like that.

                      Comment


                      • #12
                        Other musing-

                        What if TN reduction is decoupled from Essence entirely, and is based on Ability rating?

                        * Max you can reduce TN = Ability rating. At Ability 5, can instead purchase 'perfect' success (all dice are treated as successes, costs a Willpower or something).

                        PROS: Easy, more similar to other Exalt types (coupled to ability instead of Essence); fits the 'lower ceiling but more consistent result' very cleanly.
                        CONS: Ability 4 puts you in an odd space; at TN 3, successes > dice become a non-trivial probability (which is presumably why perfect success was previously at 'If TN would be reduced below 4')

                        Test for Sidereal with 0 bonus dice (TN 3)
                        Code:
                        Out of 10000 attempts
                        4  :    2  (0%)
                        5  :   11  (0%)
                        6  :   26  (0%)
                        7  :  126  (1%)
                        8  :  302  (3%)
                        9  :  835  (8%)
                        10 : 1406 (14%)
                        11 : 1923 (19%)
                        12 : 1995 (20%)
                        13 : 1614 (16%)
                        14 : 1026 (10%)
                        15 :  488  (5%)
                        16 :  178  (2%)
                        17 :   47  (0%)
                        18 :   19  (0%)
                        19 :    2  (0%)
                        ----
                        Number of dice: 13, target number: 3, double number: 10, bonus dice: 0, bonus successes: 0, dice min/max 1/10
                        Top  5%: 15
                        Top 20%: 13
                        Top 33%: 13
                        Top 50%: 12
                        Top 67%: 11


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                        Comment


                        • #13
                          Originally posted by Irked View Post
                          Initial thought: overprice TN reduction - say, 3m for TN 6, 7m total for TN 5, 12m total for TN 4. Sidereals can pull enormous successes out, but they can't do it reliably, particularly with their small mote pools.

                          Not sure I love that, though, because for me the biggest question is, "How do they do at hitting Def 12 with a Decisive?" That's the point where things will come crashing down, if they do. ("How do they do with a light Withering weapon?" is right behind it.) And even if it's pricey to throw a TN 4 attack, if you can do it and virtually guarantee a hit - I mean, you may be broke, but the other guy is plausibly dead.
                          This is why I think something as fundamental to Exalted math as Excellencies / dice caps is the worst possible place to put wonky mechanics like TN reduction.

                          Comment


                          • #14
                            Originally posted by wastevens View Post
                            Other musing-

                            What if TN reduction is decoupled from Essence entirely, and is based on Ability rating?

                            * Max you can reduce TN = Ability rating. At Ability 5, can instead purchase 'perfect' success (all dice are treated as successes, costs a Willpower or something).

                            PROS: Easy, more similar to other Exalt types (coupled to ability instead of Essence); fits the 'lower ceiling but more consistent result' very cleanly.
                            CONS: Ability 4 puts you in an odd space; at TN 3, successes > dice become a non-trivial probability (which is presumably why perfect success was previously at 'If TN would be reduced below 4')

                            Test for Sidereal with 0 bonus dice (TN 3)
                            Code:
                            Out of 10000 attempts
                            4  :    2  (0%)
                            5  :   11  (0%)
                            6  :   26  (0%)
                            7  :  126  (1%)
                            8  :  302  (3%)
                            9  :  835  (8%)
                            10 : 1406 (14%)
                            11 : 1923 (19%)
                            12 : 1995 (20%)
                            13 : 1614 (16%)
                            14 : 1026 (10%)
                            15 :  488  (5%)
                            16 :  178  (2%)
                            17 :   47  (0%)
                            18 :   19  (0%)
                            19 :    2  (0%)
                            ----
                            Number of dice: 13, target number: 3, double number: 10, bonus dice: 0, bonus successes: 0, dice min/max 1/10
                            Top  5%: 15
                            Top 20%: 13
                            Top 33%: 13
                            Top 50%: 12
                            Top 67%: 11
                            What if we combine this with an earlier thought? Example Sidereal has (Ability) points to distribute between TN reduction (to TN 4) and adding dice. How does that math out?

                            Comment


                            • #15
                              Originally posted by wastevens View Post
                              Other musing-

                              * Max you can reduce TN = Ability rating. At Ability 5, can instead purchase 'perfect' success (all dice are treated as successes, costs a Willpower or something).
                              If I recall correctly, in 2e Sidereals could spend 10m, 1wp for an "Auspicious Success." meaning all dice are treated as successes.

                              Comment

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