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I would like to give a new customer a specified amount of “virtual” cash to spend in my shop. When they add products to their cart OR their wishlist I would like to have a check if they have enough credit to purchase the product.
You have plans to add store credit functionality to Magento. At this time, this feature will not make it into the first stable release of Magento. Although this will not exactly function as you describe, I think this future feature could be customized to your needs.