Or do we keep throwing until someone has won two out of three? If Inflation is in play, do we need to play four rounds? What happens if there’s a tie in that case?

A: You keep playing games until someone has 2 out of 3 wins. Just re-throw ties: since they don’t result in a player gaining a win, they don’t count towards the number of games played.

If Inflation is in effect, you would indeed need to play 4 games instead of 3. If that turns out 2-2, keep playing until someone gets one more win. Like “sudden death” in an overtime tie situation: whoever scores first wins. Essentially, you’ll have to play until one player gets 3 wins, instead of just 2 as for the non-inflated tournament.

In either of these cases, there is no situation where no-one loses cards (unless, I suppose, someone didn’t have cards to lose in the first place). Perhaps it’s clearer to say: there is no such thing as a tie in this tournament; no situation where there is not a winner and loser.