Hi... I serve as an IoT engineer
I can build you a Raspiberry Pi python script(Program1) and and Android app(Program2) that can,
-Host a service of a piconet(A network of connected Bluettooth devices.. Android devices in your case) - Program1
-The script running on the pi is going to shuffle the cards and distribute 2 cards to every connected android device. - Program1
-A button connected to your RaspberryPi's GPIO pins by clicking on which, RaspPi runs this program1(Optionally can be connect to your mouse as well)
-Android app that can be installed easily on any android device using a local .apk file that will be given to you.-Program2
-Opening / Running this android app will automatically connect with RaspPi and receive its 2 hole cards.-Program2