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When Acquisitions Expert enters the battlefield, target opponent reveals a number of cards from their hand equal to the number of creatures in your party. You choose one of those cards. That player discards that card. (Your party consists of up to one each of Cleric, Rogue, Warrior, and Wizard.)
An ability referring to the number of creatures in your party gets a number from zero to four. Such abilities never ask which creatures are in your party, and you never have to designate specific creatures as being in your party. You can't choose to exclude creatures from this count to lower the number.
If a creature has more than one party creature type, and there are multiple ways to count that creature that could result in a different number of creatures in your party, the highest such number is used. For example, if you control a Cleric and a Cleric Wizard, the number of creatures in your party is two. You can't choose to have it be just one by counting the Cleric Wizard first as a Cleric.
If an ability of a creature counts the number of creatures in your party, that number is counted as the ability resolves. If that creature is still on the battlefield when the ability resolves, it'll be counted if appropriate.
If there are no creatures in your party as Acquisitions Expert's ability resolves, the target opponent reveals no cards and you choose no card.
To determine "the number of creatures in your party," check whether you control a Cleric, whether you control a Rogue, whether you control a Warrior, and whether you control a Wizard. The number is the total number of those checks to which you answered yes. Each creature you control can be counted for only one of those checks.
