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+# Selection of the Notary Set Size
+
+As mention in our consensus algorithm, we follow the hypergeometric distribution to decide the size of notary set.
+
+Given a node set of size N, the ratio R of Byzantine nodes, and the notary set of size n, then, the probability that more than 1/3 of notary set is Byzantine nodes is
+
+<p align="center">
+  <img src="https://imgur.com/wszheq8.png" width="250">
+</p>
+
+We set the probability to be 10^-8; that is, there is less than one fault during 10000 years in expectation (notary set is re-selected every hour).
+Assume R=1/5. We can derive the proper size of the notary set according to the equation and the result is shown in the following figure.
+
+
+<p align="center">
+  <img src="https://i.imgur.com/ylQP4Qu.png">
+</p>
+
+For convenience, we give two curves to approximate the data points.
+The first one is y = 70.5 ln(x) - 264, which is the purple dash line and the second one is y = 74 ln(x) - 264, which is the green dash line.
+The following table is the resilience ratio to the Byzantine given the size of notary set and probability 10^-8.
+
+
+
+| node set size | notary set size | resilience | notary set size | resilience |
+| -------- | -------- | -------- | --- | --- |
+| 200 | 110 | 0.199 | 123 | 0.220 |
+| 400 | 159 | 0.197 | 174 | 0.207 |
+| 600 | 187 | 0.194 | 203 | 0.202 |
+| 800 | 208 | 0.197 | 224 | 0.202 |
+| 1000 | 223 | 0.197 | 252 | 0.202 |
+| 1500 | 252 | 0.199 | 270 | 0.204 |
+| 2000 | 272 | 0.199 | 291 | 0.207 |
+| 4000 | 321 | 0.207 | 342 | 0.209 |
+
+
+Tangerine mainnet will use y = 70.5 ln(x) - 264 to decide the size of the notary set under different sizes of the node set.