Because scottsz asked for it, and I have a new player joining our game, here's an example of what combat looks like with my house rules. Keeping things simple, I'm going to use two 5th-level fighters. Since I have a red d20 and a green d20, our battle will pit the Green Knight against the Red Knight. The Green Knight has a Dexterity of 15 and the Constitution of 13. The Red Knight has a Strength of 13. The Green Knight has 21 hit points and the Red has 28. Both wear chain mail and a helm. The Green Knight wields a sword and shield; the Red Knight wants this over quick and hefts a battle ax.
As the two approach each other, we encounter the first house rule: initiative. The battle ax has an initiative of 8 as does the sword. However, the Green Knight's Dexterity gives him an initiative adjustments of +1 so he goes first. The Red Knight’s armor class is 5; the Green Knight needs to roll 12 or higher to hurt him. Unfortunately, he rolls a 3. The Green Knight's AC is 4 thanks to shield. The Red Knight needs to roll a 13 or better. He rolls an 18!
Because the battle ax is a two handed weapon, it does 2d4 damage. The Red Knight rolls very well and does the max possible: 9 points.
Pressed hard by the Red Knight's aggressive opening, the Green Knight attempts to rally. He succeeds with a roll of 19. The one-handed sword does 1D6 damage; the Green Knight rolls a 1. The Green Knight’s rally has stolen the Red Knight’s momentum; the Red Knight rolls an 11.
The next round sees our two combatants exchanging blows to no real effect. The Red Knight, however, remains undaunted and rolls a 15. He rolls a 4 and a 1 for a total of 6 (4+1+1 for STR) damage thanks to his high-strength. The Green Knight is clearly struggling. Another blow like that could take them out of the fight.
He's not down yet, however. In the next round he rolls a 13. The roll for damage is a 5. The Green Knight is growing desperate and his fancy sword-work is simply being power through by the stronger Red Knight. The two knights continue their clash, with the Green Knight wearing away another two of the Red Knight’s hit points. The Red Knight barely seems to notice and lands another telling blow on the Green Knight.
With only six hit points remaining, the Green Knight knows he's in trouble. In a desperate bid for survival, the Green Knight throws shield up between his fragile body and the Red Knight's cruel ax. The heavy blade shatters wood and steel, but the Green Knight emerges still on his feet. His left arm is bruised but not broken. He draws his dagger with his left hand as a companion for his sword.
The Green Knight still rolls only one die for his attacks and his next roll is a 14. For damage, he rolls a 3 and a 1. Since he's using two weapons he chooses the best of those rolls; so the Red Knight takes three points of damage.
Both knights are now feeling the strain of the combat. They circle one another warily, testing each other with feints and sudden attacks. The Green Knight breaks through first and drives his foe back, dealing four points of damage. He presses his momentary advantage, doing another three points of damage. But the Red Knight is having none of it. He shrugs off the Green Knight’s attacks, and lets his foe walk straight into his ax for another four points of damage. The Green Knight unleashes a furious rain of blows, doing six points of damage and reducing the Red Knight to just four points. But the Green Knight has only two hit points, and the Red Knight’s response does seven points of damage.
That reduces the Green Knight zero hit points. He must now roll on the Table of Death & Dismemberment. The 2d6 turns up 7: knocked out for 2d6 rounds, unless wearing a helm. Luckily for the Green Knight, he is wearing a helm and is only stunned for one round. Even luckier, the Red Knight is so shocked by his success that he fails to follow up on it by rolling a 3.
The Green Knight recovers from his stupor and swings at the Red Knight. He rolls a19, and then a 1 and a 5 for damage! That brings the Red Knight to zero hit points, and he rolls a 9 on the Table of Death & Dismemberment. As he's also wearing helm, the ringing blow to his noggin only knocks him down. He forgoes his next attack to get back on his feet; otherwise, he'd be at -2 to attack and the Green Knight would be a +2 to attack.
But no sooner has the Red Knight regained his feet but the Green Knight thwacks him again! There is no need to roll for damage; the Red Knight can never have fewer than zero hit points. So we go straight to the Table of Death & Dismemberment. The roll is a 3: fatal wound. Die in 1d6 turns.
The Red Knight is in no shape to continue the struggle. Under some circumstances, I might let a PC fight on if there is a compelling reason to believe they would struggle on in spite of this grievous wound. The Red Knight, however, is done for. The Green Knight takes mercy on his foe and uses his dagger to provide a coup de grace, ending his agony.
Art by Frank William Warwick Topham and Gustave Courbet.