For both competitors roll d20 + AB + Lance DMG (d6 if not included in weapon list). The winner of the round is one with higher result. If lance DMG die scores highest possible result roll again for cumulative effect. In addition this second DMG die roll inflicts HP damage. See the table below what happens for the loser:
Difference of results / Effect
1 - 5 = Winner successfully breaks his lance on competitors shield
6 - 8 = Winner successfully breaks his lance on competitors armor (save versus paralyze or fall down*)
9 - 10 = Winner successfully breaks his lance on competitors helmet (save versus paralyze or fall down* +5 to the roll)
11 - 15 = Winner successfully breaks his lance on competitor and knocks him down of a horse*
16 + =Winner successfully breaks his lance on competitor, knocks him down* and deals d6 HP damage
*Knocked Down Of A Horse
If competitor is knocked down of a horse roll d6 and see additional results from the table below.:
d6 / Effect
1 - 3 = Falling down doesn't hurt but is humiliating
4 - 8 = Falling down deals damage**
9 + = Falling down deals damage** and results broken bone***
Normally jousting with lances doesn't deal damage except if the opponent is knocked down from the horse. Roll d6 for HP damage.
If bone breaks during jousting the healing time is 2d4 + 9 weeks during what time 5 penalty is suffered to each roll what affects the injured body part. Randomly determine from a table below what bone is broken:
1d6 / Broken bone
1, 2 - Left arm
3, 4, 5 - Right arm
6, 7 - Left leg
8, 9 - Right leg
10, 11 - Rib
12 - Back****
Broken back is very serious and needs 4d6 + 9 weeks of rest to heal and character is not able to walk or perform complicated physical actions involving full body. Every time character is moved uncautiously add 5% to final roll to determine if character is paralyzed for good.
After the healing period roll d% to see if injure is permanent. Start with 10% and add 5% for every time character was moved irresponsibly.
These rules might seem to be a little complicated but I was just playing with some tables and wanted to create a small mini-game. You can easily strip these rules and just roll d20 + AB versus armor class for both of them and successful attack is a hit. If both hit it's a tie. You might also want to roll for damage but it's up to your decision does damage affect HP directly or does the damage have some other effects.
For example if damage die used is d6 results 1-4 don't deal actual damage but 5-6 might deal or possibly drop the opponent.