How can I show or hide a block based on if the contact is a client or not ?

Hi @Hugo N. 

I don't believe it's possible to do this with display logic without some preparation (see below, though I'm happy to be proved wrong!)

If this is for a campaign, I'd create a segment of purchasers and non-purchasers and tailor your campaign to each audience.

If this is for a flow, you could add a conditional split: 'placed order zero times' over all time with YES branch for your discount offer emails.

Alternatively, to use display logic for a block, I suggest this:

• Create a placed order event flow with a profile filter of 'placed order equals 1 over all time’ so only new customers enter it.
• Add a first step that updates a custom property. Let's call this 'customer' and configure so it sets to boolean true (i.e on their first order).
• This flow will flag new customers after the flow is live i.e customer = true
• For historical customers, create a segment: 'purchased at least once over all time' and export as a csv. Add to the csv a customer column and set all profiles to the value: true
• Import your csv into a temporary single opt-in list. During the import ensure you do not update profiles' subscription status.
• Once the import is complete, you can delete the temporary list (profiles won’t be deleted, just the list). All historical customers will now have customer = true
• To only display a block to non-purchasers, use this display logic: not person|lookup:'customer' - if the 'customer' property does not exist for a profile, is empty, or is the boolean value false it won't display (which will be the case for non-customers).
• Test the above process with your test profiles first!

Hope that helps!

Andy