Simple one-on-one example
Here’s our thief Alex (HP 19, Melee +4 for 1d10+3, AC 15) sneaking up on an Orc wearing studded leather and wielding a falchion (HP 1d8+1=3, Melee +1 for 2d4+4, AC 13).

Alex tries to sneak up to the Orc: Roll 1d20+sub+DEX. 1+5+2 = 8. Not good. The Orc has to beat only 8 to spot him. He rolls 1d20+sub+MIND (1 from his 1 HD, 0 for MIND bonus) for 11+1 = 12, easily noticing Alex’s attempt to be a shadow.

But what do you expect when you roll a natural 1…

The Orc hits Alex: 1d20 (19) + 1 = 20 which is bigger than AC 15. Damage is 2d4 (3) + 4 = 7. Alex is now down to 12 HP.

Time for initiative rolls! Alex has 1d20 (10) + 2 = 12, the orc has 1d20 (5). Alex is first and attacks with 1d20 (9) + 4 = 14 which is higher than 13. He hits for 1d10 (7) + 3 = 10 points of damage. This kills the orc.

Four against an Ogre
Ok, while eating breakfast this morning I tried the following Ogre fight against my players. These are real player characters, except for Yasu Odong, because I don’t have his character sheet here, and I had to advance Yonkyu and Yasu Odong from 2nd level to 3rd.

Kyoshi, Fighter-3, 29hp, STR 16, DEX 12, MIND 8, AC 16, Masterwork Katana+8/+3 (1d10+7)
Myung, Rogue-3, 21hp, STR 12, DEX 18, MIND 9, AC 14, Wakizashi+7/+2 (1d6+1)
Yonkyu, Cleric-3, 23hp, STR 9, DEX 18, MIND 11, AC 14, Takujo+3 (1d6), Kyuu+7/+2 (1d8), Magic+3 (“The Archer”)
Yasu Odong, Mage-3, 18hp, STR 5, DEX 11, MIND 14, Tanto+1 (1d4-2), Magic+5

vs.

Ogre, 29hp, AC 16, club+8 (2d8+7).

We’re assuming no surprise, no ranged combat, no ambush, and thus I rule that attacks go in order of attack bonus. Since both the ogre and Kyoshi have +8, I rule that the Ogre goes first, then the exact order of players doesn’t matter for the rest of the round.

Ogre rolls 10+8, does 12 damage to Kyoshi – down to 17.
Kyoshi rolls 17+8, does 10 damage to Ogre – down to 19.
Kyoshi rolls 2+3, misses.
Myung tries to hide, rolls 4 + sub (7) + DEX bonus (4) = 15
Ogre tries to spot, rolls 3 + HD (4) = 7, fails.
Yonkyu casts Bull’s Strength on Kyoshi (giving him STR 20), uses 5hp – down to 18.
Yasu Odong casts Sleep on Ogre, rolls 10 + Magic Attack Bonus (5) = 15, uses 3hp – down to 15
Ogre tries to resist, rolls 15 + HD (4) = 19, succeeds.
Ogre rolls 8+8, does 17 damage to Kyoshi – down to 0!
Myung attacks from the shadows, rolls 12+7, does 5+7 damage – down to 7.
(In an alternate universe the sneak failed and he rolled 12 and 15, doing 5 and 6 damage, bringing the ogre down to 8.)
Yonkyu sees that the ogre is badly hurt and rolls 18, does 3 damage – down to 4.
Yasu Odong casts Sleep on Ogre, rolls 9 + Magic Attack Bonus (5) = 14, uses 3hp – down to 12
Ogre tries to resist, rolls 6 + HD (4) = 10, fails, and will fall asleep next round!
Ogre rolls 15+8, does 20 damage to Myung – down to 1!
Myung rolls 9+7, does 5 damage to ogre – killing it before sleep takes effect.

Party wins!

Yonkyu casts Cure Light Wounds twice on Kyoshi & Myung, costing him 12 hp total, healing 2d8+6 for each: 15 for Kyoshi and 14 for Myung.

Status:
Kyoshi @ 15/29hp
Myung @ 15/21hp
Yonkyu @ 11/23hp
Yasu Odong @ 12/18hp
58% of max.

Conclusion:
1. Not a point landing with the party ending at 58% instead of 75%.
2. Combat was interesting I think.
3. The ogre having the initiative did not decide the fight.