I wouldn't blame you for thinking that the outcome of the games available at the inns are based on chance or luck, but like almost everything else in Crowntakers, the results of these games are 100% scripted. While the available game itself is random, all you need to do to win every single time is to make sure you have the right mercenary in your party. There is no RNG to these games. If you have the right merc, you win. If you don't, you lose. Some of them are pretty obvious to their character, others only make sense if you know their backstories.
Without further ado, here's the list of who's will win each game:
Arm Wrestling - Darion Card Game - Melic Chess - Erus Darts - Jeda Divination - Malda Drinking - Theogal Insult Match - Halfarus Juggling - Velena Poetry - Meledar Singing - Zoe
HOW DOES THIS HELP THE SPEEDRUN? This should be obvious, but since the results are guaranteed and you're probably opening the Tavern menu anyway, it's always good to check the game. If you have the right merc, it's a free 2gp for 1 or 2 seconds of your time - this is especially good since 5gp can save you minutes by bribing enemies.