diff --git a/docs/index.rst b/docs/index.rst
index 78cf263..11148ab 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -60,7 +60,7 @@ real skill of player is between :math:`\mu \pm 2\sigma` with 95% confidence. ::
    trueskill.Rating(mu=25.000, sigma=8.333)
 
 If some player's rating is higher :math:`\beta` than another player's, the
-player may have about 80% of chance to beat the other player. The default value
+player may have about a 76% (specifically :math:`\Phi(\frac {1}{\sqrt{2}})`) chance to beat the other player. The default value
 of :math:`\beta` is :math:`\frac{ 25 }{ 6 }`.
 
 Ratings will approach real skills through few times of the TrueSkill's Bayesian
diff --git a/trueskill/__init__.py b/trueskill/__init__.py
index b28fb9c..98a2db9 100644
--- a/trueskill/__init__.py
+++ b/trueskill/__init__.py
@@ -39,7 +39,7 @@
 MU = 25.
 #: Default initial standard deviation of ratings.
 SIGMA = MU / 3
-#: Default distance that guarantees about 75.6% chance of winning.
+#: Default distance that guarantees about 76% chance of winning.
 BETA = SIGMA / 2
 #: Default dynamic factor.
 TAU = SIGMA / 100
@@ -153,7 +153,7 @@ class TrueSkill(object):
     :param mu: the initial mean of ratings.
     :param sigma: the initial standard deviation of ratings. The recommended
                   value is a third of ``mu``.
-    :param beta: the distance which guarantees about 75.6% chance of winning.
+    :param beta: the distance which guarantees about 76% chance of winning.
                  The recommended value is a half of ``sigma``.
     :param tau: the dynamic factor which restrains a fixation of rating. The
                 recommended value is ``sigma`` per cent.