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Usually, they will request an authorisation on your card for the amount you would have to pay if you donβt show up without cancelling before the free cancellation deadline.
That is usually the cost of the first night, though details may vary. it can sometimes be for 2 or 3 nights or a different fixed amount. In very rare cases it would be for the full cost of he stay, but generally in those cases it would be a pre-payment instead.
Note that some hotels will request the authorisation as soon as they process the booking, while others will do it only the day you arrive or the day before that (thatβs their way of having a guarantee in case of no show). Some will do it only if the hotel is somewhat full (very rare), most will do it in all cases.
Check the term for cancellation fees and/or guarantee amount, that should give you an idea. If you really want to know exactly, call the hotel.