We could resolve the "physical" problem.
For example, a poker table could be the size of an olympic stadium. Cards are stone blocks and the player on the button is required to carry them to the players and place the board cards in the center of the stadium.
If a player makes certain number of donkish moves, they can be issued a donkey to help them carry the cards.
There can be other exemptions as well. For example, in the case of Vanessa Rousso or Isabel "No Mercy" Mercier, there could be an exemption from carrying the cards provided they wear skimpy swimming suits.
If you have any other ideas, let's hear them.