Meaning of "no odds against success affected me"

How about undaunted? From Lexico:

undaunted: Not intimidated or discouraged by difficulty, danger, or disappointment; ‘they were undaunted by the huge amount of work needed’

"Failure being almost certain, no odds against success affected me" means that you were undaunted by the challenges ahead of you, regardless of what others considered your low probability of success.

If you are considering taking a risky course of action you normally assess the risk that you might fail, usually informally and very often just in your head.

The chance of success of any course of action can be expressed in terms of 'betting odds': if you were a reasonably fit person and you intended to jump over a 50cm ditch with concrete sides the chance of success would be at least 1000:1, that is out of 1001 attempts you would expect 1000 to succeed. However if you were a normally fit person (as opposed to a serious athlete who has trained in the standing long jump) and you were intending to jump over a 2 metre ditch with soft sides the odds of success would be much lower, more like 1:1000 which means that out of 1001 attempts you would expect only 1 to succeed. That can also be expressed as the the odds against success being 1000:1.

If, instead of a ditch you were thinking about whether to jump over a 2 metre wide, 30metre deep crevasse in a glacier the odds against success would probably be very similar to jumping over the 2 metre ditch but the consequence of failure would be much greater. If you failed to jump the ditch you would get wet, possibly get filthy and might injure yourself. But if you failed to jump the crevasse you would die. The odds against success would probably convince you not to try.

The writer was obviously in very dire straits or in the mood to take great risks. He was considering doing something with huge odds against success, possibly 10,000:1. However he, for whatever reason, was about to make the attempt anyway. He knew that the odds against success were enormous because he was almost certain to fail but had determined to try anyway.

The meaning of "no odds against success affected me" is that no matter what the odds against success were they had no effect on his decision-making processes or, by extension, on his mood and confidence. He was ignoring the fact that he was almost bound to fail.