Pursuit of the Sun 1.2

The mechanics of the mounted tournament.
1. Initiative.
Initiative equals the horse's SPD + 1/2 of the character's initiative. The one who wins the initiative receives a 20% bonus to accuracy and a +5% chance to unseat the opponent.
2. Clash
The character can aim at the opponent's shield or helmet.
If aiming at the shield, accuracy equals the character's accuracy + the horse's SPD + 5 accuracy for each level of the polearm skill - 5 for each level of the shield skill of the opponent. The chance to unseat the opponent is (attacker's strength + horse's strength - defender's resistance - 5 for a knight's saddle) * 5%.
If neither is unseated, the clash is won by the one who wins the accuracy roll.
If aiming at the helmet, accuracy equals the character's accuracy + 5 accuracy for each level of the polearm skill, evasion equals 10 + the horse's SPD * 2.
The chance to unseat the opponent is (attacker's strength + horse's strength * 2 + DEX/5 - defender's resistance - 5 for a knight's saddle) * 5%.
If one hits the shield and the other hits the helmet, the one who hit the helmet wins.
If both hit the helmet, the one who rolled higher accuracy wins.
If both are unseated, it is declared a draw.

Added 1 minute ago

I thought at least you could buy some gear...

It could have been possible with a different quest solution... To replenish the ranks, either sleep or look for a powder (not the one that affects sanity).

Added 48 seconds ago

And what does "two battles" mean? I'm starting to feel uneasy...

The tournament and your own. Although the latter may not even exist...