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Good one.
If we assume the Dragon is sporting enough to not roast the knight before Melee begins, and the knight has only the most basic equipment (plate armour, regular shield, and +1 sword, as an unenchanted weapon will not penetrate the dragon's skin), then the probability of victory after 100,000 battles becomes 5.4% only once the knight reaches rank 21(!). At rank 22 the knight's chance is 25% and it jumps to 84% at rank 23; this jump is because the average HP of a 23rd rank knight is 33, which lets the knight survive an additional round of combat (the dragon does 8hp per hit).
A perhaps more realistic scenario gives the Knight Expert Parry and Sword Master, and typical equipment for someone of high rank: +1 plate armour, +2 sword, regular shield. We will give him a potion of strength and a potion of dexterity to enhance his Attack, Defence, AB, Damage, and initiative. Conversely, let's say the dragon blasts him at the beginning of the battle for 12hp damage (after armour). Now the knight wins about 3% of the battles at rank 18 and 25% at rank 19. The equipment and skills of the mighty more than offset the scorching.
Cheers,
-Kyle
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