First, the option to fight death has a 20% chance of success, providing you're neither sick nor hurt (in which case you automatically fail and die). And on success you will get either Wounded, Mangled, One-eyed, or One-handed. Each of those has an equal 25% chance to trigger. That basically means that fighting Death has a 80% chance to kill you, 5% chance to give you Wounded, 5% chance to give you Mangled, 5% chance to give you One-eyed, and 5% chance to give you One-handed. That boils down to a 15% chance to be more or less okay.
The way chess with Death works is that the game keeps track of a score. During the course of the chess game you'll be able to make three moves. Your moves can increase or decrease the score and by the end of the match your score needs to be 5 in order for you to win. In the tooltips "great move" means +2 score, "good move" means +1 score, "neutral move" means unchanged score, "bad move" means -1 score, and "terrible move" means -2 score.
You can start the game with a score of 2 already if you talked to death and either offered it to stay with you or paid it to stay at an inn (+1) and if you choose to play as black (+1). In the rest of the post I'm going to assume that you always do both of those. This means you'll need to collect 3 more points during the chess match itself.
The following traits will give you an option to automatically get +2 points during the first move: Gamer, Genius.
The following traits will give you an option to automatically get +1 points during the first move: Deceitful, Master Schemer, Strategist, Quick, Shrewd.
The following traits will give you an option to automatically get +2 points during the second move: Drunkard, Hedonist, Master Seducer/Seductress, Impaler
The following traits will give you an option to automatically get +1 points during the second move: Gamer
In the first move you'll also have options to "play it safe" (25% good, 55% neutral, 20% bad) and "play it risky" (20% great, 40% good, 40% terrible) but they will on average give you 0 score, so both of them are bad and special options unlocked by traits are preferable. If you have no trait that unlocks a special option, but you do have a trait that will allow you to get +2 score in the second move I would advise playing it safe, otherwise I would advise playing it risky (it's your best chance to get enough points by the end of the game).
Note that if you play risky and make a terrible move you'll get -2 score and it will be impossible to win. If you play it safe and get a bad move you'll get -1 score and you'll only be able to win if you can get +2 on your second move from a trait.
In the second move you'll have the option to cheat. This option is not affected by traits and will work 2 times out of 3 and give you +1 score. If it fails Death will become angry and you die. If you instead focus on the game you'll have a 25% chance to get +1 score. This is essentially playing it safe and risky once again and the same reasoning applies. Special options are always preferable and if none of those are available it depends on how you did in the first round. If you did well in the first move just focus on the game and if you did poorly you'd best take the risk.
For the last move you get the option to offer a random child, lover, friend, or spouse (picked by the game in that order if nobody of the previous category is available). If you're neither a Gamer nor smart (Genius, Quick, or Shrewd) this will notably improve your chances of surviving and as long as the person chosen isn't too valuable I would recommend choosing it.
Trusting your skill depends on whether you actually have any skill. If you're smart or a Gamer you'll get 20% chance of a great move, 30% chance to make a good move, 30% chance to make a neutral move, and 20% chance to make a bad move. Otherwise you'll have a 20% chance to make a good move, 50% chance to make a neutral one, and a 30% chance to make a bad move.
If you are a Gamer you can get +2 score during your first move and +1 during your second. This means that as long as you can avoid making a bad move in the last move you're good. You have 80% chance to survive if you trust your skill and 85% chance to survive if you offer a sacrifice (child, lover, friend, or spouse; picked by the game in that order).
But the optimal case is when you are a Genius and you have a trait that will allow you to get +2 score in the second round (either that or a Drunkard Gamer). Together with the 2 points you should start with that would give you a guaranteed 6 points by the time you reach the final round, so even if you get a bad move while trusting your skill you still win the game.
If you don't have any helpful traits at all your best option is probably to simply fight death. You have a 15% chance you'll come through hurt, but functional which is better than your odds of surviving chess without any of the special options unlocked by traits.