Strengthen

You strengthen cards by choosing a card to strengthen and then sacrificing up to eight cards which will be lost while the selected card is increased in level.  Each sacrificed card adds XP value which is then applied to the target card.  The XP value of the sacrificed card depends upon its rarity (# of stars), its level and its evolved generation. Strengthening is key to getting maximum value from cards and cards should be maxed out before evolving them.  The ratio of value increase is constant for every card.

If X is the level 1 card strength for a given card, then the following ratios appear to hold (with a tiny margin of rounding error).

• Level 20: X * 1.57
• Level 40: X * 2.33
• Level 80: X * 3.45
• Level 160: X * 4.93

The amount of XP and number of coins required for each level up increases.  Thus, strengthening from 1 to 20 is quite fast and requires ~160 XP while strengthening in the higher levels multiple sacrifice cards for a single level.

The amount of XP that a card will give when you sacrifice it, is its base XP (the amount it will give when it's level 1 - which depends on its rarity), plus 1/2 the XP you've put into that card. Thus if you've strengthened a 2-star card up to level 13 by sacrificing eight 1-star level 1 cards (80 XP), then that 2-star level 13 card can be sacrificed to give 80/2 + 14 = 54 XP to another card.

Base XP (to give)
Rarity	XP
1-star	10
2-star	14
3-star	25
4-star	40

Rounded to the nearest coin, the number of coins required to strengthen a card is $coins=20*\sqrt{Level}$. This is the level of the card being strengthened, and is not dependent upon the card being sacrificed.

XP required to level
Level	XP	Formula
2	4	$XP = \text{round} \left( \frac{1}{8} \cdot Lv^2 + 5 \cdot Lv - 7 \frac{1}{8} \right)$
3	9
4	15
5	21
6	27
7	34
8	41
9	48
10	55
11	63
12	71
13	79
14	88	$XP = \text{round} \left( \frac{1}{2} \cdot Lv^2 - 5 \frac{1}{2} \cdot Lv + 67 \right)$
15	97
16	107
17	118
18	130
19	143
20	157
21	170	$XP = \text{round} \left( \frac{1}{4} \cdot Lv^2 + 4 \cdot Lv - 24 \frac{1}{8} \right)$
22	185
23	200
24	216
25	232
26	249
27	266
28	284
29	302
30	321
31	340
32	360
33	380
34	401
35	422
36	444
37	466
38	489
39	512
40	536
41	560
42	585
43	610
44	636
45	662
46	689
47	716
48	744
49	772
50	801
51	830
52	860
53	890
54	921
55	952
56	984
57	1016
58	1049
59	1082
60	1116
61	1150
62	1185
63	1220
64	1256
65	1292
66	1329
67	1366
68	1404
69	1442
70	1481
71	1520
72	1560
73	1600
74	1641
75	1682
76	1724
77	1766
78	1809
79	1852
80	1896