No, I did it based on rolling sequentially. First roll: 25% (1on four chance of negation) If any of the other three rolls (on average) occur, then you move on to the second roll. And I did the conversion wrong; it was supposed to be 5/8 (37.5%), not 7/8.
I'm not seeing 5/8 doing it this way. Sticking to fractions, you have a 1/4 probability of negating, and a 3/4 probability of not negating and therefore moving to the second fortification. There, you have a 1/4 probability of negating and a 3/4 probabilty of not negating. The second result is conditional upon the first (that is, you only go to the second fortification three times out of four), so the total probability of fortification is (1/4)+(3/4 * 1/4) = 1/4+1/5 = 4/9. And, interestingly, 4/9 is 43.75%, the same result I came up with earlier.
These are NOT all my creations! The lead authors are identified as follows: [TS] Tempest Stormwind, [AR] Andarious Rosethorn, [RT] Radical Taoist, [SN] Sionnis, [DH] DisposableHero_, [SH] Seishi.
[TS] The Pinball Brothers: Large And In Charge (Melee, Lockdown, Charge, Juggling) [TS] Ashardalon Reborn: I Will Swallow Your Soul (Melee, Fear, Negative Levels, AoE, Theme) [AR] "A"-Game Paladin: Play That Funky Music, Knight Boy! (Team Support, Melee, Theme, Single-Class) [RT] Uncanny Trapsmith: Get in, make it look like an accident, get out. (Skillmonkey, Stealth/Scout/Infiltration, Unorthodox Methods, Theme) [AR] Wizsassin: *Everything* is permitted. (Spellcaster, Support, Sneak Attack, Utility) [TS] Phantom Rush: General Gish Gouda. (Gish, Theme, Setting-Specific(Eberron), Early-Entry PrC) [TS] Storm Knight: Another kind of gish. (Melee/"Gish", Theme, Setting-Specific(Eberron), Unorthodox Methods) [TS] Inevitable Nightmare: The weapon you only have to fire once. (Melee, "Unorthodox" Methods (no charging), Reliability) [AR] Captain Constitution: The number one threat to America. (Melee, TOUGHTOUGHTOUGH, Defense, Theme) [AR] Nuker: I casts the spells that makes the peoples fall down! (Spellcaster, damage, blasting, damage) [TS] Dread Lord of the Dead: Let the Reaping Begin! (NPC-only, Variable (combat/casting/leadership), Iconic Villain, Theme) [AR] Heavy Crusader: No Rest. No Mercy. No Matter What. (Melee, Damage (No charging), Variable, Theme). [TS] Gun Fu: It's bullet time (Ranged, THEORETICAL, Twin weapons, Theme) [RT] Face First: We should talk. (Psionic, social, mind-control, info-management) [SN] Chaingun Porcupine: Never Enuff Dakka. (Ranged, Skirmishing, Spike Damage, Incarnum) [RT] Always On Edge: The Mortal Draw deals death. (Melee, Generalist, Dungeoneering, Stunt) [AR] Feral Druid: Real feral taste. Zero druid calories. (Melee, offense, damage, murder) [RT] Rusty!: Man's Best Friend (Sentry, Support, Backup, Rearguard) [RT] The T3 (Tashalatora Triple Threat): My Kung Fu is More Powerful (Hybrid, Flex-Function, Melee, Caster) [RT] The #1 Snoipah: Boom. 'Eadshot. (Caster, Theme, Spike, Trapscout) [AR] Dreamblade: Rest in Pieces. (Melee, Damage, Single-Class, Combo/Momentum) [AR] Evasion Tank: “When fighting angry blind men, is best to stay out of the way.” (Melee, Tank, Unorthodox Methods (attack negation), Theme) [DH] Psycarnum Warrior: ↑↑↓↓←→←→BA Start (Melee, Tank, Psionics, Incarnum, 1337 h4x) [AR] Heavy Weapons Elf: WHO TOUCHED MY BOW? (Ranged, Cohort, Damage, Unorthodox Methods (ranged ToB)) [RT] Gnowhere Gnome: A little man who wasn't there (Caster, Stealth, Single-Class, Elusive) [AR] Uberflank: I got your back. (Melee, support, stunt, teamwork) [TS] Flip the Bird: Everyday I'm shuffling (Ranged, harrier, unorthodox methods (ranged ToB / off-turn movement), support) [DH] Eat Sleep Gank: Real Ultimate Power (Stealth, Assassination, Spike, Magic Versatility) [AR] Slash and Burn: Mind, Body, Blade, Flame / Aspects of a greater whole / which delivers death. (Melee, Theme (flex-style), Damage, Stunt) [RT] Edge of the Light: Cut, Fade to Black (Melee, Defense/Offense, Momentum, Tactical) [RT] Quiet Murder: Cut throats, not corners. (Melee, Stealth, Harrier, Tactical) [TS] Wand Overdrive: Say Hello to my little friends. (Caster, support/artillery/variable, wand specialist) [RT] God Hand: What did the five fingers say to the face? (Melee/Gish, Unarmed, SAD, Theme) [AR] Zero Buff Time Gish: Try to keep up! (Gish, Speed, Movement, Opportunity) [TS] Robo Tackle: I Am Iron Man. (Melee, setting-specific (Eberron), positioning, theme, stunt)
In that case... I don't know how the hell I came up with that number. I blame it on not dealing with math since '94.
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In that case... I don't know how the hell I came up with that number. I blame it on not dealing with math since '94.
I also didn't point out that 37.5% is 3/8, not 5/8 (that's 62.5%); I was too busy considering your method to notice.
37.5% is off by 25% of 25% - in other words, it's the probability that EITHER ONE negates BUT NOT BOTH. (This Venn, which is the correct answer minus the intersection.) 62.5% is off by 75% of 25% - in other words, you double-counted one of the fortifications somewhere. (This Venn (the correct answer) plus this Venn due to double-counting.)
Whatever happened is somewhere there.
(...and if it makes you feel any better, I'm in a Ph.D. program based around cognitive modelling, specifically of estimating conditional probabilities (i.e. "If I do X, then how likely is it that Y will happen?" and how learning and experience changes that estimate). This is a lot fresher to me.)
These are NOT all my creations! The lead authors are identified as follows: [TS] Tempest Stormwind, [AR] Andarious Rosethorn, [RT] Radical Taoist, [SN] Sionnis, [DH] DisposableHero_, [SH] Seishi.
[TS] The Pinball Brothers: Large And In Charge (Melee, Lockdown, Charge, Juggling) [TS] Ashardalon Reborn: I Will Swallow Your Soul (Melee, Fear, Negative Levels, AoE, Theme) [AR] "A"-Game Paladin: Play That Funky Music, Knight Boy! (Team Support, Melee, Theme, Single-Class) [RT] Uncanny Trapsmith: Get in, make it look like an accident, get out. (Skillmonkey, Stealth/Scout/Infiltration, Unorthodox Methods, Theme) [AR] Wizsassin: *Everything* is permitted. (Spellcaster, Support, Sneak Attack, Utility) [TS] Phantom Rush: General Gish Gouda. (Gish, Theme, Setting-Specific(Eberron), Early-Entry PrC) [TS] Storm Knight: Another kind of gish. (Melee/"Gish", Theme, Setting-Specific(Eberron), Unorthodox Methods) [TS] Inevitable Nightmare: The weapon you only have to fire once. (Melee, "Unorthodox" Methods (no charging), Reliability) [AR] Captain Constitution: The number one threat to America. (Melee, TOUGHTOUGHTOUGH, Defense, Theme) [AR] Nuker: I casts the spells that makes the peoples fall down! (Spellcaster, damage, blasting, damage) [TS] Dread Lord of the Dead: Let the Reaping Begin! (NPC-only, Variable (combat/casting/leadership), Iconic Villain, Theme) [AR] Heavy Crusader: No Rest. No Mercy. No Matter What. (Melee, Damage (No charging), Variable, Theme). [TS] Gun Fu: It's bullet time (Ranged, THEORETICAL, Twin weapons, Theme) [RT] Face First: We should talk. (Psionic, social, mind-control, info-management) [SN] Chaingun Porcupine: Never Enuff Dakka. (Ranged, Skirmishing, Spike Damage, Incarnum) [RT] Always On Edge: The Mortal Draw deals death. (Melee, Generalist, Dungeoneering, Stunt) [AR] Feral Druid: Real feral taste. Zero druid calories. (Melee, offense, damage, murder) [RT] Rusty!: Man's Best Friend (Sentry, Support, Backup, Rearguard) [RT] The T3 (Tashalatora Triple Threat): My Kung Fu is More Powerful (Hybrid, Flex-Function, Melee, Caster) [RT] The #1 Snoipah: Boom. 'Eadshot. (Caster, Theme, Spike, Trapscout) [AR] Dreamblade: Rest in Pieces. (Melee, Damage, Single-Class, Combo/Momentum) [AR] Evasion Tank: “When fighting angry blind men, is best to stay out of the way.” (Melee, Tank, Unorthodox Methods (attack negation), Theme) [DH] Psycarnum Warrior: ↑↑↓↓←→←→BA Start (Melee, Tank, Psionics, Incarnum, 1337 h4x) [AR] Heavy Weapons Elf: WHO TOUCHED MY BOW? (Ranged, Cohort, Damage, Unorthodox Methods (ranged ToB)) [RT] Gnowhere Gnome: A little man who wasn't there (Caster, Stealth, Single-Class, Elusive) [AR] Uberflank: I got your back. (Melee, support, stunt, teamwork) [TS] Flip the Bird: Everyday I'm shuffling (Ranged, harrier, unorthodox methods (ranged ToB / off-turn movement), support) [DH] Eat Sleep Gank: Real Ultimate Power (Stealth, Assassination, Spike, Magic Versatility) [AR] Slash and Burn: Mind, Body, Blade, Flame / Aspects of a greater whole / which delivers death. (Melee, Theme (flex-style), Damage, Stunt) [RT] Edge of the Light: Cut, Fade to Black (Melee, Defense/Offense, Momentum, Tactical) [RT] Quiet Murder: Cut throats, not corners. (Melee, Stealth, Harrier, Tactical) [TS] Wand Overdrive: Say Hello to my little friends. (Caster, support/artillery/variable, wand specialist) [RT] God Hand: What did the five fingers say to the face? (Melee/Gish, Unarmed, SAD, Theme) [AR] Zero Buff Time Gish: Try to keep up! (Gish, Speed, Movement, Opportunity) [TS] Robo Tackle: I Am Iron Man. (Melee, setting-specific (Eberron), positioning, theme, stunt)
But 2 LF effects stacking like that sounds pretty good. Nearly a 50% chance to avoid taking critical damage just from combining a class ability and a fairly cheap (I think?) enchantment.
This is just probability arithmetic, not really a comprehensive view of "math". Nor is it really a good view of probability (but now I'm letting my inner Bayesian show).
(Nothing personal, but it really bugs me when people conflate doing sums, algebra (including linear algebra, though that's quite different from the fundamental stuff you cover in grade school), calculus, discrete mathematics (including group theory, graph theory, and number theory) and geometry all under the same label. They're quite different, and people can excel in different areas while being weak in others. (It's usually just a matter of expressing the concepts in terms people "get". I find physics is a good place for this, particularly if you stick within a Newtonian framework: showing people how those annoying formulas they had to memorize in science class for position, velocity, and acceleration are all "really" connected is a surprisingly good example for getting "AHA!" moments.)
But 2 LF effects stacking like that sounds pretty good. Nearly a 50% chance to avoid taking critical damage just from combining a class ability and a fairly cheap (I think?) enchantment.
The Light Fortification enhancement is a +1 bonus for 25% immunity. Any armor needs to be at least +1 to start, so the minimum cost for this is 4000gp and the marginal cost (that is, the cost over and above the initial +1) is 3000gp. Hypothetically you could double up on this on a normal character by wearing a suit of Light Fortification armor and a Light Fortification shield or bracers of armor, giving you 44% for 6000gp (and inflating the cost of both pieces for further enhancement, which is the main reason you'd not want to do this in the long run).
The Moderate Fortification enhancement is +3 for 75% immunity. The minimum cost of a Medium Fortification suit of armor is 16,000gp, with a marginal cost of 15,000gp. The Heavy Fortification enhancement is +5 for 100% immunity; this costs 36,000gp (or 35000 marginal). Given the situational nature of this ability, though, I'm not sure it's worth it unless you either have money to spare or have an artificer on the team (who can temporarily infuse your armor with this ability whenever you need it).
It looks like a good deal, particularly at the low levels, provided you're facing enough precision-damage-based opponents. HOWEVER, this doesn't scale well, since you get diminishing returns - a Moderate + a Light protects 81.25% for a marginal cost of 19,000 (or +4000gp for +6.25% fortification), and two Moderates costs more and protects less than one Heavy. Similarly, if you managed to stack five Light Fortification armors/shields/bracers/etc. on yourself somehow (chain shirt + chahar-aina + dastana + shield + bracers, let's say), and did nothing else to them, you'd have a 76.25% fortification level - but it'd cost around 20,000gp, which is more expensive than the 75% Medium fortification effect.
Given a reasonable level of precision damage, I'd only expect to see multiple fortification effects if I was playing something naturally fortified (say, a warforged) and we had fortification gear readily available through loot (say, fighting several humanoid NPCs). I wouldn't go out of my way to do this unless you were A) at a relatively low level, before the costs start climbing that high, AND B) you're fighting a lot of precision-damage foes, being aware that only critical hit specialists are likely to show up on the DM's side with any frequency (and critical hit specialists only get crits some of the time, while Fortification won't save you from their base damage).
EDIT:
If it matters, this is also the same stunt you can use with miss-chance effects to become virtually unhittable from any attack roll made without True Seeing or a related piercing effect. Separate miss chances, provided they stem from different sources (i.e. concealment from darkness and displacement stack, but two different concealments don't), provide a cumulative miss chance in exactly the same way as I've illustrated here. The reason that's usually a better deal is that it doesn't cost you gold to get those buffs up (a 20% miss chance from shadows, a 50% miss chance from Displacement, and a Mirror Image spell (read: 8/9ths miss chance) works out to a 0.4% chance of being hit, while an infinite Armor Class is still hit on a natural 20 (read: 5% of the time)).
These are NOT all my creations! The lead authors are identified as follows: [TS] Tempest Stormwind, [AR] Andarious Rosethorn, [RT] Radical Taoist, [SN] Sionnis, [DH] DisposableHero_, [SH] Seishi.
[TS] The Pinball Brothers: Large And In Charge (Melee, Lockdown, Charge, Juggling) [TS] Ashardalon Reborn: I Will Swallow Your Soul (Melee, Fear, Negative Levels, AoE, Theme) [AR] "A"-Game Paladin: Play That Funky Music, Knight Boy! (Team Support, Melee, Theme, Single-Class) [RT] Uncanny Trapsmith: Get in, make it look like an accident, get out. (Skillmonkey, Stealth/Scout/Infiltration, Unorthodox Methods, Theme) [AR] Wizsassin: *Everything* is permitted. (Spellcaster, Support, Sneak Attack, Utility) [TS] Phantom Rush: General Gish Gouda. (Gish, Theme, Setting-Specific(Eberron), Early-Entry PrC) [TS] Storm Knight: Another kind of gish. (Melee/"Gish", Theme, Setting-Specific(Eberron), Unorthodox Methods) [TS] Inevitable Nightmare: The weapon you only have to fire once. (Melee, "Unorthodox" Methods (no charging), Reliability) [AR] Captain Constitution: The number one threat to America. (Melee, TOUGHTOUGHTOUGH, Defense, Theme) [AR] Nuker: I casts the spells that makes the peoples fall down! (Spellcaster, damage, blasting, damage) [TS] Dread Lord of the Dead: Let the Reaping Begin! (NPC-only, Variable (combat/casting/leadership), Iconic Villain, Theme) [AR] Heavy Crusader: No Rest. No Mercy. No Matter What. (Melee, Damage (No charging), Variable, Theme). [TS] Gun Fu: It's bullet time (Ranged, THEORETICAL, Twin weapons, Theme) [RT] Face First: We should talk. (Psionic, social, mind-control, info-management) [SN] Chaingun Porcupine: Never Enuff Dakka. (Ranged, Skirmishing, Spike Damage, Incarnum) [RT] Always On Edge: The Mortal Draw deals death. (Melee, Generalist, Dungeoneering, Stunt) [AR] Feral Druid: Real feral taste. Zero druid calories. (Melee, offense, damage, murder) [RT] Rusty!: Man's Best Friend (Sentry, Support, Backup, Rearguard) [RT] The T3 (Tashalatora Triple Threat): My Kung Fu is More Powerful (Hybrid, Flex-Function, Melee, Caster) [RT] The #1 Snoipah: Boom. 'Eadshot. (Caster, Theme, Spike, Trapscout) [AR] Dreamblade: Rest in Pieces. (Melee, Damage, Single-Class, Combo/Momentum) [AR] Evasion Tank: “When fighting angry blind men, is best to stay out of the way.” (Melee, Tank, Unorthodox Methods (attack negation), Theme) [DH] Psycarnum Warrior: ↑↑↓↓←→←→BA Start (Melee, Tank, Psionics, Incarnum, 1337 h4x) [AR] Heavy Weapons Elf: WHO TOUCHED MY BOW? (Ranged, Cohort, Damage, Unorthodox Methods (ranged ToB)) [RT] Gnowhere Gnome: A little man who wasn't there (Caster, Stealth, Single-Class, Elusive) [AR] Uberflank: I got your back. (Melee, support, stunt, teamwork) [TS] Flip the Bird: Everyday I'm shuffling (Ranged, harrier, unorthodox methods (ranged ToB / off-turn movement), support) [DH] Eat Sleep Gank: Real Ultimate Power (Stealth, Assassination, Spike, Magic Versatility) [AR] Slash and Burn: Mind, Body, Blade, Flame / Aspects of a greater whole / which delivers death. (Melee, Theme (flex-style), Damage, Stunt) [RT] Edge of the Light: Cut, Fade to Black (Melee, Defense/Offense, Momentum, Tactical) [RT] Quiet Murder: Cut throats, not corners. (Melee, Stealth, Harrier, Tactical) [TS] Wand Overdrive: Say Hello to my little friends. (Caster, support/artillery/variable, wand specialist) [RT] God Hand: What did the five fingers say to the face? (Melee/Gish, Unarmed, SAD, Theme) [AR] Zero Buff Time Gish: Try to keep up! (Gish, Speed, Movement, Opportunity) [TS] Robo Tackle: I Am Iron Man. (Melee, setting-specific (Eberron), positioning, theme, stunt)
If it matters, this is also the same stunt you can use with miss-chance effects to become virtually unhittable from any attack roll made without True Seeing or a related piercing effect. Separate miss chances, provided they stem from different sources (i.e. concealment from darkness and displacement stack, but two different concealments don't), provide a cumulative miss chance in exactly the same way as I've illustrated here. The reason that's usually a better deal is that it doesn't cost you gold to get those buffs up (a 20% miss chance from shadows, a 50% miss chance from Displacement, and a Mirror Image spell (read: 8/9ths miss chance) works out to a 0.4% chance of being hit, while an infinite Armor Class is still hit on a natural 20 (read: 5% of the time)).
It certainly makes seeking a desirable enchantment for would-be mage slayers.
The kraken stirs. And ten billion sushi dinners cry out for vengeance. - Good Omens
= My most popular campaign item; for all your adventuring convenience.Show
Zauber's Mutable Rod: This rod has a number of useful functions that make it easier to live in the wilderness. It is made of polished wood, with five studlike buttons on one end. Each button produces a different effect when pressed. Unless otherwise noted, the rod’s functions have no limit on the number of times they can be employed. • When button 1 is pressed, one end of the rod produces a small flame, equivalent to a candle. • When button 2 is pressed, the rod unfolds into a two-person tent, complete with bedrolls and warm blankets. • When button 3 is pressed, the rod becomes a one-handed hammer, suitable for pounding pitons into a wall. • When button 4 is pressed, the rod becomes a sturdy iron spade. • When button 5 is pressed, the rod becomes a wooden bucket able to hold 2 gallons of liquid. Once per day, it can be commanded to fill with fresh water. If the rod is seriously damaged or broken in any of its alternate forms (button 2, 3, 4, or 5), it reverts to its basic rod form and cannot be activated for 24 hours. Moderate conjuration; CL 9th; Craft Rod, minor creation; Price 375 gp; Weight 2 lb.
