UNO! -- Does this game have a winner every time?

How to proof (or disproof) that in an UNO game of 4 players, there will always be a player who can get rid of all their cards within finite amount of rounds?

Prerequisites :

1. Every player says UNO before being caught.
2. The game obeys the classic rules (see https://www.unorules.com/)
3. Players are NOT omniscient in this game.  Every single decision the players make are the best ones (definition needed) based on the cards in their hands only.

Possible ways to solve this problem :

1. Ignore all the action cards (+4, reverse, etc.) first to make the original problem simpler.
2. Simply this game by decreasing the number of the players and how many cards there are.
3. Make all the positions in the game nodes and construct a graph with them.

Author: MaterialMortgage9474