Pincers Versus Pyro [M4★]

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Conditions:: Hunt a Shogun Ceanataur and a Rathian
Failure Conditions:: Reward hits 0, or time expires

High-Strung Researcher: The Rathian's fiery breath, or the Shogun Ceanataur's pincers. Which is more perilous? I can't stop thinking about it... I can't even sleep at night! Please, could you go figure this out for me?

Done

Monster	HP	Attack	Parts	Ailment
Rathian	21,150 HP	10	7.6	2.4
Rathian	28,553 HP	10	15.2	4.8
Rathian	35,955 HP	10	22.8	7.2
Rathian	42,300 HP	10	30.4	9.6
Rathalos	33,320 HP	9.25	7.6	2.4
Rathalos	44,982 HP	9.25	15.2	4.8
Rathalos	56,644 HP	9.25	22.8	7.2
Rathalos	66,640 HP	9.25	30.4	9.6
Khezu	24,480 HP	9.75	7.6	2.4
Khezu	33,048 HP	9.75	15.2	4.8
Khezu	41,616 HP	9.75	22.8	7.2
Khezu	48,960 HP	9.75	30.4	9.6
Magnamalo	30,600 HP	9.25	7.6	2.4
Magnamalo	41,310 HP	9.25	15.2	4.8
Magnamalo	52,020 HP	9.25	22.8	7.2
Magnamalo	61,200 HP	9.25	30.4	9.6
Rakna-Kadaki	36,400 HP	9.75	7.6	2.4
Rakna-Kadaki	49,140 HP	9.75	15.2	4.8
Rakna-Kadaki	61,880 HP	9.75	22.8	7.2
Rakna-Kadaki	72,800 HP	9.75	30.4	9.6
Shogun Ceanataur	17,200 HP	9.5	7.6	2.4
Shogun Ceanataur	23,220 HP	9.5	15.2	4.8
Shogun Ceanataur	29,240 HP	9.5	22.8	7.2
Shogun Ceanataur	34,400 HP	9.5	30.4	9.6

Rewards:

Item	Amount	Rate
Heavy Armor Sphere	x2	28%
Adamant Jewel	x1	32%
Lazurite Jewel	x2	18%
Melding Honey	x2	12%
Golden Egg	x1	10%