Author Topic: Init math and matchups OR helping you find the desired init advantage. (Read 17584 times)

Sunic_Flames · « **on:** June 21, 2008, 11:50:24 PM »

Ok, first off init is an opposed check. So the numbers don't matter in an absolute sense, only in a relative sense. +0 vs +0 is exactly the same as +15 vs +15. Only the difference between your init and your opponents init matters. So that's what I will focus on here.

So here are the numbers for your advantage. If your opponent has the advantage, read them as his chance to win or invert them to get your chance. This should help you decide how much higher to get your init compared to that of your expected opponents.

Also note, ties go to the higher Dex, or if equal reroll.

+0: 47.5% win, 5% tie, 47.5% loss.
+1: 52.5% win, 4.75% tie, 42.75% loss.
+2: 57.25% win, 4.5% tie, 38.25% loss.
+3: 61.75% win, 4.25% tie, 34% loss.
+4: 66% win, 4% tie, 30% loss.
+5: 70% win, 3.75% tie, 26.25% loss.
+6: 73.75% win, 3.5% tie, 22.75% loss.
+7: 77.25% win, 3.25% tie, 19.5% loss.
+8: 80.5% win, 3% tie, 16.5% loss.
+9: 83.5% win, 2.75% tie, 13.75% loss.
+10: 86.25% win, 2.5% tie, 11.25% loss.
+11: 88.75% win, 2.25% tie, 9% loss.
+12: 91% win, 2% tie, 7% loss.
+13: 93% win, 1.75% tie, 5.25% loss.
+14: 94.75% win, 1.5% tie, 3.75% loss.
+15: 96.25% win, 1.25% tie, 2.5% loss.
+16: 97.5% win, 1% tie, 1.5% loss.
+17: 98.5% win, 0.75% tie, 0.75% loss.
+18: 99.25% win, 0.5% tie, 0.25% loss.
+19: 99.75% win, 0.25% tie, 0.00% loss.
+20 or higher: 100% win, 0% tie, 0% loss.

As you can see there is a definitive diminishing returns effect. The greater your init advantage, the less each point gives you and the less the dex tiebreaker matters. Assuming a dex advantage equal init is 50/50. To increase that to 60/40 you need +2. 70/30 requires +4. 80/20 requires +7. 90/10 requires +11. And 100/0 requires +20.

Without a dex advantage those breakpoints are +1, +3, +5, +8, +12, and +20 respectively.

Your individual circumstances cannot be predicted and there are too many variables to try but this should give you all the information to figure it out on your own.

Enjoy this CO resource contribution, courtesy of the resident Kitsune.

SorO_Lost · « **Reply #1 on:** June 22, 2008, 05:50:55 AM »

Some initiative boosters for the edge.

Items
Eager (MiC): +1 weapon, +2 <unnamed> to initiative while welding it to your double weapon for split initiative. j/k, just hold it alright?
Warning (MiC): +1 weapon, +5 insight to initiative while it is held.
Initiative (OA): +20,000gp weapon, +2 luck to initiative while carrying it.
Belt of Battle (MiC): 12,000gp, +2 competence to initiative while worn.
Bracers of Blinding Strike (MiC): 5,000gp, +2 competence to initiative while worn.
Bracers of the Hunter (SoX): 8,500gp, +2 competence to initiative while worn.
Ring of Anticipation (DotU): 6,000gp, roll initiative twice and take the higher number.

Grafts
Flexible Spine (LoM): 91,000gp, +4 racial bonus to initiative. Ouch, grafts are supposed to be cheaper than normal items.
Silthilar Tendons (LOM): 110,000gp, +2 <unnamed> to dexterity. Just buy a tome and w/e else.

Soul Melds
Bluesteel Bracers (MoI): +2 insight to initiative, arm bind to share it with your party.

Spells
Combat Readiness (DotU): bard/sor/wiz 1, precast <1min*cl>, +<cl/3, max 6> insight to initiative.
Neverskitter (SpC): sor/wiz 1, immediate action during init rolls, +5 <unnamed> to initiative.
Primal Instinct (DM): druid 3/sor 3, ran 2, +5 competence bonus to initiative checks for 24 hours, hells yeah.
Sign (SpC): cleric 1, precast <10min*cl>, +4 <unnamed> to your next initiative check.

Classes
Dragon Shamen (PHBII): sense aura, <ds levels/5>+1 <unnamed> bonus to initiative.
Dread Commando 1~5 (HoB): +<dc level> competence to the entire party's initiative.
Darkrunner 3 (LoM): intelligence bonus to initiative while underground.
Exemplar 8 (CAv): intelligence bonus to initiative.
Factotum(DS): intelligence bonus to dexterity checks, aka initiative.
Iajutsu Master 2 (OA): charisma to initiative.
Marshal 1 (online/Mini): charisma bonus to initiative for the entire party.
Swiftblade 2 (online): <arcane casting ability> bonus to initiative.

Feats
Danger Sense (CAd): grants a 1/day initiative reroll, requires Improved Initiative.
Draconic Aura (DM): Up to +4 <unnamed> to initiative.
Guerrilla Scout (HoB, pg97): +1 <unnamed> bonus to initiative.
Improved Initiative (core): +4 <unnamed> to initiative.
Lucky Start (CS): you can use luck to reroll initiative.
Nimble Bones (LM): Undead you create gain +4 <unnamed> to initiative. One word: Necropolition.
Quick Reconnoiter (CAr): +2 <unnamed> to initiative.
Yondalla's Sense (RoW): wisdom bonus to initiative.

Other
Aggressive (trait, UA): +2 <unnamed> to initiative.
Dexterity Boosters (core): up to +6 enchantment & +4 inherent for what could be another +5 to initiative.
Humming Bird Familiar (Dragon #323, pg98): +4 <unnamed?> to initiative, elven wizard sub (RotW) may double this.
Lunatic Insight (HoH): Taint up a +1 moral bonus to initiative.
Moment of Alacrity (ToB): diamond mind 6th, +20 <unnamed> to initiative as a swift action.
Time Domain (SpC): grants Improved Initiative.
White Raven Tactics (ToB): white raven 3rd, set an ally's initiative to one lower than your own.

DavidWL · « **Reply #2 on:** June 22, 2008, 07:07:26 AM »

Using a 20 sided die, we can restate this as:

If you have an initiative advantage of n (for n from 0 to 19), then:

The chance that you win initiative =
(380 + 41n - n^2) / 800

The chance that you tie =
(20 - n) / 400

The chance that you lose =
(20 - n) * (19 - n) / 800

I didn't check all of the probabilities you listed, but when you have no advantage (n=0), then it should read:
47.5% Win / 5% Tie / 47.5% Loss

Best,
David

dobu · « **Reply #3 on:** June 22, 2008, 10:24:08 AM »

you may want to add "Combat Readiness" from Drow of the Underdark to your Spelllist. it's a +1 per 3 CL insight Bonus, for 1min/CL. (DotU p.61)

Sunic_Flames · « **Reply #4 on:** June 22, 2008, 10:44:38 AM »

Isn't Nerveskitter Insight (making it not stack with Warning)?

Chances at +0:

If you roll a 1, a 2 or better beats you. (19)
2 is beaten by 3 or better. (18)
...
...
...
20 isn't beatable, it can only be tied. (0)

Which is 47.5%. My mistake. *fixes*

SixthDeclension · « **Reply #5 on:** June 22, 2008, 11:26:03 AM »

Quote from: DavidWL on June 22, 2008, 07:07:26 AM

Using a 20 sided die, we can restate this as:

If you have an initiative advantage of n (for n from 0 to 19), then:

The chance that you win initiative =
(380 + 41n - n^2) / 800

The chance that you tie =
(20 - n) / 400

The chance that you lose =
(20 - n) * (19 - n) / 800

I didn't check all of the probabilities you listed, but when you have no advantage (n=0), then it should read:
47.5% Win / 5% Tie / 47.5% Loss

Best,
David

I believe you are correct in your formula creating sir.

Sunic_Flames · « **Reply #6 on:** June 22, 2008, 12:25:17 PM »

Yeah, I noticed that algorithm when I was making this post. But I forgot how to express it as a formula and decided I wanted it to be useful to those that failed math as well so I just gave the outputs.

ninjarabbit · « **Reply #7 on:** June 22, 2008, 01:42:02 PM »

The humming bird familiar from Dragon magazine gets you +4 to your initative. And depending on how you interpret the elven wizard racial subsitution from Races of the Wild it could become +8.

There's a feat in Complete Adventurer call Quick Reconacuer or something like that that gives you +2 to your initative and makes spot checks free actions. Nothing great but worth noting for the sake of completeness.

Arcane-surge · « **Reply #8 on:** June 22, 2008, 08:07:37 PM »

The Ring of Anticipation from Drow of the Underdark lets you roll twice and take the highest on any initiative roll.

ninjarabbit · « **Reply #9 on:** June 22, 2008, 10:59:02 PM »

There's also the Lucky Start luck feat in Complete Scoundrel that let's you use one of your rerolls to reroll your initative. It's one of the few luck feats that's almost worthwhile.

RobbyPants · « **Reply #10 on:** June 23, 2008, 12:24:03 PM »

I think the Senses aura for the Dragon Shaman grants a bonus to Initiative, as well as Spot and Listen. The bonus ranges from +1 to +5 depending on the DS class level.

Brainpiercing · « **Reply #11 on:** June 23, 2008, 02:48:19 PM »

There is the "Sign" spell that gives +4 (unnamed) in Mini or SpC. 10 min/lvl only, unfortunately.

Ieniemienie · « **Reply #12 on:** June 23, 2008, 02:51:36 PM »

Quote from: Brainpiercing on June 23, 2008, 02:48:19 PM

There is the "Sign" spell that gives +4 (unnamed) in Mini or SpC. 10 min/lvl only, unfortunately.

And expended after one time use

Brainpiercing · « **Reply #13 on:** June 23, 2008, 03:05:55 PM »

Quote from: Ieniemienie on June 23, 2008, 02:51:36 PM

Quote from: Brainpiercing on June 23, 2008, 02:48:19 PM
There is the "Sign" spell that gives +4 (unnamed) in Mini or SpC. 10 min/lvl only, unfortunately.
And expended after one time use

And it's lvl 1, so you can likely as not keep it up all day without problems. How often per encounter do you roll? Plus it's a cleric spell, which is worth noting because Clerics are notorious for being slow, IMHO.

ChristopherGroves · « **Reply #14 on:** December 01, 2008, 09:08:52 PM »

Wu Jen / watchful spirit gets a boost ... add to that the feats from CM to reroll as well.

woodenbandman · « **Reply #15 on:** December 01, 2008, 09:46:01 PM »

Binders and anima mages get bonuses to initiative. Binders are insight, but Anima Mage gets untyped

Endarire · « **Reply #16 on:** December 01, 2008, 09:48:22 PM »

Nerveskitter from Spell Compendium 146 (Sor/Wiz1, Transmutation) gives +5 <unnamed> initiative as an immediate action for 1 encounter.

Also, one can get up to +5 inherent DEX in core from tomes and manuals and one can increase his DEX by up to 5 from levels/HD.

Akalsaris · « **Reply #17 on:** December 02, 2008, 01:15:50 AM »

Danger Sense from Complete Adventurer grants a 1/day initiative reroll. Unlike Lucky Start, it requires Improved Initiative.

Edit: just noticed the Initiative ability from another thread, +5 untyped bonus to initiative on a weapon of legacy (Menu D, I think it's from ToB)

Echoes · « **Reply #18 on:** December 02, 2008, 03:34:24 AM »

Actually, tiebreakers are determined by comparing the total Initiative modifiers (PHB, pg. 136), not just Dex. Just figured I'd point that out.

Akalsaris · « **Reply #19 on:** December 02, 2008, 03:53:02 AM »

Really? My group's always gone with highest dex, not initiative. I wonder if it's a 2nd ed holdover or one of my long-forgotten house rules...

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Author Topic: Init math and matchups OR helping you find the desired init advantage. (Read 17584 times)