spicy binom_test gives the same answer for alternative greater or less I'm seeing something very unexpected with the binomial test function in spicy (python).
from spicy.stats import binom, binom_test
binom_test(5,10,.5,alternative="greater")

This gives me: 0.6230468749999999
But then when I change the alternative:
binom_test(5,10,.5,alternative="less")

I again get: 0.6230468749999999.
Shouldn't the p-values from the two kinds of tests sum to $1$? How can it not matter what your alternative is. Can someone confirm this is incorrect behavior or am I missing something?
The spicy version I'm running (this is a Mac): 1.6.2.

As often happens, the answer occurred to me right after I posted the question (even though it hadn't for the past few hours).
The p-value is the probability of observing something "as or more extreme" than the observed test statistic. Here, it happens to be sum of the PMF's of the Binomial distribution at 5, 6, 7, 8, 9 and 10. This just happens to be the same as the PMF's at 0, 1, 2, 3, 4, 5 from symmetry (because I took $p=0.5$). I'm leaving the question in instead of deleting it for future reference.
