I know that Good-Turing smoothing helps us to trim a bit of probability from some more frequent events and give it to the events we've never seen. Thus it keeps our model from assigning zero probabilities to unobserved events. But while dealing with a dataset, I encountered an interesting result. Here is the data I observed about national teams that win a yearly competition:
9 USA, 3 China, 2 France, 1 Japan, 1 Russia = 16 teams.
When I use Good-Turing smoothing to estimate how likely that next winner is Russia it gives the same result with MLE.
$C^*(Russia)=2*\dfrac{1}{2}=1\;\;,\quad P^*_{GT}(Russia)=\dfrac{1}{16}$
I just couldn't understand how it is possible to get the same result even if carrying some probability for unseen events. Thanks in advance.
