Are chest drops random or is there a pattern that they are received in?

In general, chests received are not random. There is a long repeated pattern in which you receive chests. You may have noticed that early on, chest 12 to be precise, you received a Magic Chest. Everyone else did too.

As mentioned in this answer there are more modern ways of reviewing your chest cycle than manually counting. For more information on the cycle, see below. However, if you'd just like to view where you are in your current cycle then I recommend you enter your player tag into https://statsroyale.com/

Old Way:

A user Asdamp on Reddit decrypted the CSV files that contain the data for this pattern and posted it.

All players start their cycles at different places, so to keep track of your own cycle you'll need to pay attention to the magical and giant chests that you receive.

The following is the order in which chests are received:

1. Silver
2. Silver
3. Silver
4. Gold
5. Silver
6. Silver
7. Gold
8. Silver
9. Silver
10. Silver
11. Silver
12. Magic
13. Silver
14. Silver
15. Gold
16. Silver
17. Silver
18. Silver
19. Gold
20. Silver
21. Silver
22. Silver
23. Silver
24. Gold
25. Silver
26. Gold
27. Silver
28. Silver
29. Silver
30. Silver
31. Gold
32. Silver
33. Silver
34. Silver
35. Silver
36. Gold
37. Silver
38. Silver
39. Gold
40. Silver
41. Silver
42. Silver
43. Silver
44. Gold
45. Silver
46. Silver
47. Gold
48. Silver
49. Silver
50. Silver
51. Silver
52. Giant
53. Silver
54. Silver
55. Gold
56. Silver
57. Silver
58. Silver
59. Gold
60. Silver
61. Silver
62. Silver
63. Silver
64. Gold
65. Silver
66. Gold
67. Silver
68. Silver
69. Silver
70. Silver
71. Gold
72. Silver
73. Silver
74. Silver
75. Silver
76. Gold
77. Silver
78. Silver
79. Gold
80. Silver
81. Silver
82. Silver
83. Silver
84. Magic
85. Silver
86. Silver
87. Gold
88. Silver
89. Silver
90. Silver
91. Silver
92. Gold
93. Silver
94. Silver
95. Gold
96. Silver
97. Silver
98. Silver
99. Gold
100. Silver
101. Silver
102. Silver
103. Silver
104. Gold
105. Silver
106. Gold
107. Silver
108. Silver
109. Silver
110. Silver
111. Gold
112. Silver
113. Silver
114. Silver
115. Silver
116. Gold
117. Silver
118. Silver
119. Gold
120. Silver
121. Silver
122. Silver
123. Silver
124. Gold
125. Silver
126. Silver
127. Gold
128. Silver
129. Silver
130. Silver
131. Silver
132. Magic
133. Silver
134. Silver
135. Gold
136. Silver
137. Silver
138. Silver
139. Gold
140. Silver
141. Silver
142. Silver
143. Silver
144. Gold
145. Silver
146. Gold
147. Silver
148. Silver
149. Silver
150. Silver
151. Gold
152. Silver
153. Silver
154. Silver
155. Silver
156. Gold
157. Silver
158. Silver
159. Giant
160. Silver
161. Silver
162. Silver
163. Silver
164. Gold
165. Silver
166. Silver
167. Gold
168. Silver
169. Silver
170. Silver
171. Silver
172. Gold
173. Silver
174. Silver
175. Gold
176. Silver
177. Silver
178. Silver
179. Gold
180. Silver
181. Silver
182. Silver
183. Silver
184. Gold
185. Silver
186. Gold
187. Silver
188. Silver
189. Silver
190. Silver
191. Giant
192. Silver
193. Silver
194. Silver
195. Silver
196. Gold
197. Silver
198. Silver
199. Gold
200. Silver
201. Silver
202. Silver
203. Silver
204. Magic
205. Silver
206. Silver
207. Gold
208. Silver
209. Silver
210. Silver
211. Silver
212. Gold
213. Silver
214. Silver
215. Gold
216. Silver
217. Silver
218. Silver
219. Gold
220. Silver
221. Silver
222. Silver
223. Silver
224. Gold
225. Silver
226. Gold
227. Silver
228. Silver
229. Silver
230. Silver
231. Giant
232. Silver
233. Silver
234. Silver
235. Silver
236. Gold
237. Silver
238. Silver
239. Gold
240. Silver

After you make a complete cycle through this list, you start back at the top at 0, and the cycle repeats. It is worth mentioning that only chests received increment the cycle, so feel free to battle while you have 4 chests without worrying about missing that Magic Chest.

As a final note, if you're quite lucky, you may receive a Super Magical Chest. These chests are awarded randomly, and can happen anywhere within a cycle, or not at all. Receiving Super Magical Chests will not affect your cycle, your next chest will be in the order you expect.