User:TetsutaroOokami/Collection Strategy

tl;dr The strategy most efficient on stamina is:

• Play only Mild (10 stamina) outside of Chance Boss
• Play only Super Spicy (50 stamina) for Chance Boss

Detailed Calculations

Chance Boss Expectancy

Chance Boss Expectancy gauge shows the chance in which a Chance Boss will appear after the next event quest:

• default chance 10%
• +10% for every event quest that did not result in Chance Boss appearance, regardless of difficulty played
• reverts to default chance (10%) after Chance Boss appearance

• n = number of normal event quests needed before Chance Boss appears
• p(n) = chance for a Chance Boss to appear after n normal event quests

n	p(n)		np(n)
1	10%	= 10%	0.1
2	90% × 20%	= 18%	0.36
3	90% × 80% × 30%	= 21.6%	0.648
4	90% × 80% × 70% × 40%	= 20.1%	0.806
5	90% × 80% × 70% × 60% × 50%	= 15.1%	0.756
6	90% × 80% × 70% × 60% × 50% × 60%	= 9.07%	0.544
7	90% × 80% × 70% × 60% × 50% × 40% × 70%	= 4.23%	0.296
8	90% × 80% × 70% × 60% × 50% × 40% × 30% × 80%	= 1.45%	0.116
9	90% × 80% × 70% × 60% × 50% × 40% × 30% × 20% × 90%	= 0.32%	0.029
10	90% × 80% × 70% × 60% × 50% × 40% × 30% × 20% × 10% × 100%	= 0.03%	0.003
Average number of normal event quests needed before Chance Boss			3.66 → 4

Typical Drops per Quest

• s = total Special Skill Effect for Mild difficulty

Difficulty		Mild 甘口	Medium 中辛	Hot 辛口	Spicy 激辛	Super Spicy 超激辛
Stamina		10	15	20	30	50
Normal Quest
No. of Stages		3	4	5	5	5
Collection Item Drops	Normal Stages	4/6/8 (avg. 6)	6/8 (avg. 7)	8/10/12 (avg. 10)	5/10/15 (avg. 10)	10/15/20 (avg. 15)
	Boss Stage	5/10/20/30 (avg. 16)	5/10/20/30/50 (avg. 23)	20/30/50/70 (avg. 42)	50/70/100/140 (avg. 90)	100/180/200/250 (avg. 182)
	SS Effect	s	2s	3s	6s	12s
Typical Drops		2×6+16+s =28+s	3×7+23+2s =44+2s	4×10+42+3s =82+3s	4×10+90+6s =130+6s	4×15+182+12s =242+12s
Chance Boss
Collection Item Drops	Basic	50	75	140	250	500
	SS Effect	3s	6s	9s	18s	36s
Typical Drops		50+3s	75+6s	140+9s	250+18s	500+36s

Stamina Strategy Efficiency

• Assume each cycle has 4 normal event quests with one Super Spicy (50) Chance Boss

Diff. for normal quest	Typical Drops per cycle		Stamina per cycle	Average Drop per Stamina
Mild (10)	(28+s)×4 + 500+36s	= 40s+612	90	0.444s + 6.8
Medium (15)	(44+2s)×4 + 500+36s	= 44s+676	110	0.4s + 6.145
Hot (20)	(82+3s)×4 + 500+36s	= 48s+828	130	0.369s + 6.369
Spicy (30)	(130+6s)×4 + 500+36s	= 60s+1020	170	0.352s + 6
Super Spicy (50)	(242+12s)×4 + 500+36s	= 64s+1468	250	0.336s + 5.872

Diff. for normal quest	s
	0	50	100	150	200	250	300	350
Mild (10)	6.800	29.022	51.244	73.467	95.689	117.911	140.133	162.356
Medium (15)	6.145	26.145	46.145	66.145	86.145	106.145	126.145	146.145
Hot (20)	6.369	24.831	43.292	61.754	80.215	98.677	117.138	135.600
Spicy (30)	6.000	23.647	41.294	58.941	76.588	94.235	111.882	129.529
Super Spicy (50)	5.872	22.672	39.472	56.272	73.072	89.872	106.672	123.472