The other answers may be correct about Player 001's overall mindset, but they miss the point that in this particular game, he knew he was almost guaranteed to win - and he says this to his team at the time.
At first glance, this game looks like it would be extremely dangerous even for someone who was able to prepare and knew what to expect, even for someone who had organised the games himself. The deaths of the players on each losing team are clear, visible, and unavoidable. In the first two games, if Player 001 had lost, his death could have been faked by a guard firing a blank, as actually happened in the fourth game. In the third game, the very act of losing causes the losers to die, without the guards doing anything.
But you're forgetting how our heroes' team actually wins, even with three women and an old man against a team of stronger men. It's all a matter of strategy, and that strategy comes from Player 001. As he says in the episode itself:
Tug-of-War needs more than just raw strength. All you need is a good strategy in Tug-of-War and combined with good teamwork, you’ll be able to win when you are against stronger teams.
Okay, when I was young, we always like[d] Tug-of-War. It’s a game I know well. And back then, I would always win, even if there was a wrestler on the other team, and it seemed the odds were stuck against us. Listen closely, and I’ll tell you how my team and I were able to win even when it seemed impossible.
First off, having a good leader is very important. The person is at the front and keeps an eye on how the other team is performing. And the rest of the team focuses on the back of their leader’s head and follows their lead. If the leader seems weak or looks like their spirit is beginning to falter, then the game is already over.
And then at the end of the rope, you’ll need to have someone strong and dependable like the anchor of a ship. After that, it’s all about how you arrange the rest of your team. If one player is on the right side of the rope, then the next one should be on the left, all the way down the rope. Both of your feet should be facing straight forward, and then, hold the rope in your armpits. That way, everyone can put in all of their strength.
Finally, and this is absolutely the most important thing. Once the game begins, for the first ten seconds … you have to hold your ground. You should lean back, practically lie down. Push your lower abdomen up to the sky, as hard as you can. And throw your head back to the point where you can almost see the groin of the person behind you. If you do that, the other team won’t be able to pull us to their side. Just hold like this for ten seconds. Then the opposing team will start to get frustrated because they are thinking, “Why won’t they budge?” Because they believed that they were much stronger. If you can hold out for that long, you will be able to catch a moment in your opponents’ hold, and their rhythm breaks.
Even without revealing that he's the mastermind behind all the games, he's stating openly that he feels sure of winning this game, that his team always won Tug-of-War even against physically much stronger opponents. It's his strategy and his confidence that enables the whole team to survive. Even without knowing who he really is, it makes sense that his age, although a disadvantage in terms of brute strength, comes with experience which can help him win games. That's also how he could so easily beat Gi-Hun at marbles, even in a game that seemed to be pure chance: it's all about strategy and understanding people.
So he would've known from the start that the first four games weren't a big risk for him. The fifth one would have been - or at least, even if he was told the right way to step, everyone behind him would have survived too, which would've ruined half the point of the game - and that's probably why he eliminated himself in the fourth game rather than earlier or later.