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Message: <blockquote data-quote="Brother MacLaren" data-source="post: 2715621" data-attributes="member: 15999">Well, consider the possibility that they fight foes of equal CR.  To make it simple, start with NPC opponents: your NPC Fighter takes on other Fighters in 1-on-1 combat, with a 50% chance of winning and, if successful, about 4/13 of the XP needed to advance a level.  (That is, a party of 4 would need 13 encounters equal to their average level to advance; he's going solo so he gets 4x).  Give him a little bonus - he'll need it and it makes the math simpler.  He now needs 3 wins to advance, with a 50% chance of winning each time.So that would be a 1/8 chance of advancing to the next level without being defeated.  If he can survive some defeats by running away, surrendering, or stabilizing while unconscious,  his chances of eventually making the next level will be better.  Let's say that his actual chance of reaching the next level is doubled because of that, to 1/4. Assuming that he always fought other NPCs of his level, he'd have a 1 in 256 chance of going up 4 levels to level 5, a 1 in 262,144 chance of getting to 10, and a roughly 1 in 275 billion chance of getting to level 20 -- although long before that point he'd have run out of equal-CR NPC opponents to face and so would be taking on monsters and giants.Clearly, advantages that boost your odds of winning above that 50% without boosting your ECL are most useful.  Higher ability scores, good equipment, max starting HP, etc.  A safer course is to routinely fight lower-CR opponents, but even a 40-hp Ftr4 taking on an orc Bbn1 (CR 1) could be dropped by a single critical hit.</blockquote>

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