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Cash can be very helpful for the new couple to get their life started. While there is no set rule on an amount that parents can give as a gift, it can be marked for a particular purpose such as paying for a honeymoon or a down payment for a new house.
There really is no average for a gift from parents as budgets for everyone is different. You can consider some amounts such as a cash gift for the rehearsal dinner (800.00 on average) to a nice cash gift of a few thousand.