I volunteered there for two weeks last August. We were only full one day. Your chances of getting beds are very good. And they even have a little side room that they will give families (if available).
A good predictor could be albergue vacancy rate in key starting towns (St Jean, Astorga, Sarria). This could be a good indicator of +X days to arrival in SdC. The Wise Pilgrim app has just added a voluntary feature where albs can self-report.
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