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In that case, go with my previous post: The Shadowbard would still be performing Inspire Courage. Rinaldo casts Virtuoso Performance (standard action) and starts both Inspire Greatness on Tuwo and Flint (move action), plus Bladethirst (swift action) to add an additional +3 enhancement bonus on either Tuwo's or Flint's bow, whichever it would be most beneficial to.

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Using the intensified rod she pulled earlier, Messa calls on Desna's brilliance to smite the witch.
Casting Intensified Burst of Radiance, targeting the yellow star on the map. DC 19 saving throw vs blindness.
ioun stone caster level boost: 1d4 - 1 ⇒ (4) - 1 = 3
SR check, dwoemer's essence: 1d20 + 20 + 5 ⇒ (10) + 20 + 5 = 35
Damage (no saving throw, good and light): 10d4 ⇒ (1, 3, 3, 1, 2, 1, 2, 1, 3, 1) = 18

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No one fully answered my question. A lot of buffs got tossed off that I had never heard of. Let me double check. Still going: Good Hope, Inspire Courage, Discordant Voice, Flint can have Bladethirst, Haste, Blessing of Fervor, Particulate Form, (Order of the Dragon Challenge ended when Rinaldo went unconscious), Hunter's Blessing. Freebooter's Bane.
"Not cool."
Tuwo takes a 5ft fly closer and fires a cluster of shots.
attack #1 using perfect strike: 3d20 + 42 ⇒ (16, 16, 12) + 42 = 86
dmg: 1d8 + 30 ⇒ (2) + 30 = 32
holy?: 2d6 ⇒ (2, 6) = 8
sonic: 1d6 ⇒ 3
attack #2: 1d20 + 42 ⇒ (1) + 42 = 43
dmg: 1d8 + 30 ⇒ (6) + 30 = 36
holy?: 2d6 ⇒ (5, 2) = 7
sonic: 1d6 ⇒ 2
attack #3: 1d20 + 42 - 5 ⇒ (16) + 42 - 5 = 53
dmg: 1d8 + 30 ⇒ (3) + 30 = 33
holy?: 2d6 ⇒ (3, 1) = 4
sonic: 1d6 ⇒ 4
attack #4: 1d20 + 42 - 5 ⇒ (1) + 42 - 5 = 38
dmg: 1d8 + 30 ⇒ (8) + 30 = 38
holy?: 2d6 ⇒ (1, 1) = 2
sonic: 1d6 ⇒ 6
attack #5: 1d20 + 42 - 10 ⇒ (18) + 42 - 10 = 50
dmg: 1d8 + 30 ⇒ (8) + 30 = 38
holy?: 2d6 ⇒ (4, 2) = 6
sonic: 1d6 ⇒ 6
haste attack: 1d20 + 42 ⇒ (16) + 42 = 58
dmg: 1d8 + 30 ⇒ (3) + 30 = 33
holy?: 2d6 ⇒ (5, 1) = 6
sonic: 1d6 ⇒ 3
ki strike: 1d20 + 42 ⇒ (1) + 42 = 43
dmg: 1d8 + 30 ⇒ (6) + 30 = 36
holy?: 2d6 ⇒ (5, 3) = 8
sonic: 1d6 ⇒ 2
Better all those 1s are on attacks then saves.

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Fire away Tuwo
Did Messa's spell have any notable effect? If she overcame the SR, there's a 1 in 20 chance Baba Yaga nat 1'd the save vs blindness. ;-)

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Messa discovers there is no SR when she casts her spell.
reflex save: 1d20 + 27 ⇒ (8) + 27 = 35

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Sorry, closing in on the end of my grad school semester while still teaching in this new environment.
Three of Tuwo's arrows sink into Baba Yaga once again, she is definitely feeling the weight of the wounds being inflicted on her. Some of them heal once again, but she is still heavily injured.
This is probably the point at which she would retreat and bide her time, but that's not very fun for this inconsequential fight.
Baba Yaga begins chanting while her hands glow. You hear demonic whispering as shadowy energy pools around her, then forms a pentagram on the floor. "This was fun and all, but its time to call in a favor." she cackles as a stone archway rises from the pentagram. The stone archway grows to a huge size before a lightning bolt shaped sword stabs out of hit held by a red, scaly hand. The hand is quickly followed by hooves feat, then a flaming whip. The hooved feet take a step from the gate to reveal a horned head with four glowing eyes. It smiles wickedly at you before its wings spread out from its form and the gate receeds into the floor once again.
The Balor roars back at Baba Yaga, "YOU CALL ME FOR THESE MORTALS? WHAT A WASTE OF YOUR FAVOR WITCH. I SHALL FINISH THEM QUICKLY." he says before turning to you, "KNOW YOU FACE ALGANOTH, PRINCE OF SIN, BALOR OF THE ABYSS."
He then begins swinging his weapons at Rinaldo and Tuwo, a terrible smile on his face for the carnage to come.
sword vs Tuwo: 1d20 + 31 ⇒ (10) + 31 = 41
sword vs Tuwo: 1d20 + 26 ⇒ (8) + 26 = 34
sword vs Tuwo: 1d20 + 21 ⇒ (9) + 21 = 30
sword vs Tuwo: 1d20 + 16 ⇒ (15) + 16 = 31
Tuwo dodges the sword with ease thanks to his monastic training, greatly frustrating the Balor.
whip at Rinaldo: 1d20 + 30 ⇒ (5) + 30 = 35
whip at Rinaldo: 1d20 + 25 ⇒ (17) + 25 = 42
whip at Rinaldo: 1d20 + 20 ⇒ (2) + 20 = 22
Rinaldo is not as equally skilled in the art of dodging as Tuwo and gets brutally whipped twice by the Balor's large flaming whip.
damage: 1d4 + 7 ⇒ (4) + 7 = 11 physical 1d6 ⇒ 2 fire
damage: 1d4 + 7 ⇒ (3) + 7 = 10 physical 1d6 ⇒ 4 fire
free grapple checks with the whip: 1d20 + 33 ⇒ (8) + 33 = 41
free grapple checks with the whip: 1d20 + 33 ⇒ (13) + 33 = 46
I'm pretty sure you have freedom of movement up so no grapple?
Initiative Order, Bold May Go!
Map Slide
Baba Yaga, -401
Flint
Rinaldo, -28hp (6 fire?)
Tuwo
Messa

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Yes on FoM; and Rinaldo does take Fire damage if there's no save involved. Will post a full round when I'm not slammed at work, but for Flint and Tuwo's benefit, assume all three performances are still going (Inspire Courage, Inspire Greatness, and Bladethirst).

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Does Messa have a Bit O Luck left? Good time to use it on Flint.

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She does, and unless anyone needs healing or a different spell, that is often her default action. I'll ask her to confirm after work.

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Sure, Flint would be happy with a touch of luck this round.

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Messa's home-office is five feet from mine, so I just checked in with her. Bit of Luck on Flint it is!
Messa touches Flint on the shoulder, saying, "Desna smiles on you!"
Rinaldo, still standing over his fallen companion, and his shadowy double continue chanting to aid the remaining pathfinders. Rinaldo draws his sword and steps over to the witch-queen. "Your friend can't change what is going to happen! You are going down!"
5' step, draw sword, swift action to Challenge her again, standard to attack.
Attack: 1d20 + 24 ⇒ (14) + 24 = 38 damage : 1d6 + 14 ⇒ (1) + 14 = 15 Sonic: 1d6 ⇒ 5
Inspire Courage - All allies who perceive my performance gain +3 morale bonus on saving throws against charm and fear effects and a +3 competence bonus on attack and weapon damage rolls.
Discordant Voice - If you are within 30' of me and affected by my current performance, do an additional 1d6 sonic damage on each attack. If using a ranged attack, the target must also be within 30' of me.
Bladethirst - The targeted weapon (or 50 pieces of ammuniction) gains up to +3 worth of additional enhancement bonus
Order of the Dragon Challenge - All allies gain +2 circumstance bonus to attack the target of my challenge while I threaten them

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Tuwo continues to make his point.
Clustered Shots at the witch including Good Hope, Inspire Courage, Discordant Voice, Haste, Blessing of Fervor, Particulate Form, Hunter's Blessing. Freebooter's Bane. Order of the Dragon Challenge, Point Blank shot.
attack #1 Perfect Strike: 3d20 + 42 ⇒ (7, 1, 15) + 42 = 65
dmg: 1d8 + 29 ⇒ (5) + 29 = 34
holy?: 2d6 ⇒ (4, 6) = 10
sonic: 1d6 ⇒ 4
attack #2: 1d20 + 42 ⇒ (9) + 42 = 51
dmg: 1d8 + 29 ⇒ (6) + 29 = 35
holy?: 2d6 ⇒ (6, 4) = 10
sonic: 1d6 ⇒ 5
Haste attack: 1d20 + 42 ⇒ (8) + 42 = 50
dmg: 1d8 + 29 ⇒ (2) + 29 = 31
holy?: 2d6 ⇒ (6, 4) = 10
sonic: 1d6 ⇒ 5
attack #3: 1d20 + 42 - 5 ⇒ (2) + 42 - 5 = 39
dmg: 1d8 + 29 ⇒ (1) + 29 = 30
holy?: 2d6 ⇒ (5, 2) = 7
sonic: 1d6 ⇒ 6
attack #4: 1d20 + 42 - 5 ⇒ (16) + 42 - 5 = 53
dmg: 1d8 + 29 ⇒ (3) + 29 = 32
holy?: 2d6 ⇒ (5, 4) = 9
sonic: 1d6 ⇒ 5
attack #5: 1d20 + 42 - 10 ⇒ (2) + 42 - 10 = 34
dmg: 1d8 + 29 ⇒ (2) + 29 = 31
holy?: 2d6 ⇒ (4, 3) = 7
sonic: 1d6 ⇒ 6
ki strike: 1d20 + 42 ⇒ (3) + 42 = 45
dmg: 1d8 + 29 ⇒ (5) + 29 = 34
holy?: 2d6 ⇒ (5, 2) = 7
sonic: 1d6 ⇒ 2

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Flint focuses fire on the crone's nose.
Attack 1, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (19, 13) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 72
Take the better of the two rolls - To hit 59 and threatens a crit.
Confirm Crit, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (16, 9) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 65
Confirms Crit with a 56.
damage(crit),Gravity Bow, Good Hope, Divine Favor, Bard Song, Bane, Freebooter Bane, Hunter's Blessing: 6d6 + 36 + 6 + 9 + 9 + 2d6 + 6 + 3 + 6 + 1d6 ⇒ (3, 3, 5, 6, 4, 4) + 36 + 6 + 9 + 9 + (4, 4) + 6 + 3 + 6 + (2) = 110
Attack 2, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (6, 8) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 54 (Miss)
Attack 3, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (18, 6) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 64
Hits AC 58 - Hit
damage,Gravity Bow, Good Hope, Divine Favor, Bard Song, Bane, Freebooter Bane, Hunter's Blessing: 2d6 + 12 + 2 + 3 + 3 + 2d6 + 2 + 1 + 2 + 1d6 ⇒ (3, 2) + 12 + 2 + 3 + 3 + (6, 4) + 2 + 1 + 2 + (3) = 43
Burn a KI point - Extra attack
Attack 4, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (20, 18) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 78
To hit 60 - Threatens a crit
Confirm Crit, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (20, 20) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 80
Yup that confirms like crazy!
damage(crit),Gravity Bow, Good Hope, Divine Favor, Bard Song, Bane, Freebooter Bane, Hunter's Blessing: 6d6 + 36 + 6 + 9 + 9 + 2d6 + 6 + 3 + 6 + 1d6 ⇒ (2, 3, 1, 1, 4, 5) + 36 + 6 + 9 + 9 + (3, 5) + 6 + 3 + 6 + (2) = 101
Attack 5, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 24 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (9, 14) + 24 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 58 (Miss)
Attack 6, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (19, 1) + 29 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 60
Sorry this should only be +24 but still hits AC 54 so hits and it might even crit confirm!
crit confirm, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 24 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (16, 20) + 24 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 71
Hits AC 55 and crits confirms
damage(crit),Gravity Bow, Good Hope, Divine Favor, Bard Song, Bane, Freebooter Bane, Hunter's Blessing: 6d6 + 36 + 6 + 9 + 9 + 2d6 + 6 + 3 + 6 + 1d6 ⇒ (2, 3, 6, 5, 5, 3) + 36 + 6 + 9 + 9 + (3, 6) + 6 + 3 + 6 + (5) = 113
Last Attack!
Attack 7, Good hope,Divine Favor, Blessing of Fervor, Bard Song, Order,Bane,Freebooter Bane, Hunter's Blessing, Penalties,Touch of Good Luck: 2d20 + 19 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 ⇒ (12, 8) + 19 + 2 + 3 + 2 + 3 + 2 + 2 + 1 + 2 - 6 = 50 (Miss)
Any overflow arrows would target the Demon of course.

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Arrows fly out from the two zen archers, ignoring the Balor and aiming straight for Baba Yaga. The Balor tries to intercept some with its quick reflexes, but amazingly, the arrows, infused with the ki of the archers, bend and curve out of the way of the Balor. Many of them imbed themselves into Baba Yaga in rapid succession, each one causing her to stumble and hunch over until finally, the last arrow from Tuwo penetrates her exposed head. She collapses to the ground, but even know, you see your arrows being pushed out from her wounds as they miraculously heal themselves.
The Balor laughs, "HAH! THE WITCH FALLS! CONSIDER MY FAVOR REPAID WEAKLING." it says as it disappears in a puff of teleportation magic, its laughter slowly fading away, leaving the cavern in silence.
You have defeated Baba Yaga, a level 20 mythic witch! While you cannot kill her due to her unsurpassable regeneration, you can consider yourselves victorious!