Are the games predetermined ahead of time, or do they change as the competition goes along?

My theory is that it's the latter. The Front Man draws up a series of games, but changes them so that an "appropriate" number of participants reach a certain round.

In Season 2, RLGL was also the first game but far more players survived due to Gi Hun's advice. And the six-legged pentathlon also had a high survival rate, probably because they miscalculated and hadn't used it in the games before. So then Mingle may have been included because you can control the number of players advancing by adjusting the number of rounds you want to play and the players per room in each round. And this is exactly what they did, they made it so exactly 100 people would survive to participate in the fourth game.

Also, the games on the wall in Season 3 didn't reflect what was actually played. There was something that looked like monkey bars or players swinging on a rope, and a depiction of what looked like checkers. Neither of these games featured in the end. There was a rope game, but it involved jumping over the rope rather than swinging on it, and checkers was entirely absent. I suspect these games were initially planned, but later switched out for the games we actually saw.