Antonym of the word "fault"

It is not your meed that you won the lottery.

It is not by your merit that you won the lottery.

Though archaic, meed fits because meed is deserved or earned reward. Something obtained through fortune rather than through deserving it is not one's meed.

Merriam-Webster:

1 archaic : an earned reward or wage

2 : a fitting return or recompense

Oxford Dictionaries:

archaic : A person's deserved share of praise, honour, etc.

If you don't like using an archaism, try merit, which has similar meanings:

M-W:

1b : the qualities or actions that constitute the basis of one's deserts

Consider

It is not your merit that you won the lottery.

I agree that the proposal

It is not to your credit that you won the lottery.

does not fit well, albeit for another reason. The phrase would fit better with a statement like

It is not to your credit that you are playing the lottery.

The meaning here is that your actions point to an undesirable characteristic of yours, perhaps a character flaw (a gambling nature) or a poor grasp of probabilities (if you believe that you will win).

There are two ways to deal with trying to express an antonym:

• find the word that fills the slot perfectly. Often enough, there is an exact antonym, which matches all the salient criteria. But also there is often a lexical gap, not an exact word to fill the slot, or a candidate doesn't match everything (like register, frequency, or important contextual implications)

  For the noun 'fault', the most important thing is you did it and it was bad. The synonym of fault that seems closest is error, and of its antonyms, the most appropriate seem to be:

  achievement

  or

  success

  Putting either of these into your sentence, the better one seems to be:

  It is not your achievement that you won the lottery.

  It is not perfect, sounds a little stilted, has some implications not found in 'fault', but I think gets most of the way there. In most circumstances, 'achievement' is not a direct antonym of 'fault', but it does seem to work OK here.

• or sometimes it's just better to rewrite the sentence to communicate the same feeling but not necessarily with the same structure. Translators/interpreters have to do this all the time, often with the excuse 'you just don't say it that way, there's no word for word parallel, you just say it this other way'.

  For this, a thesaurus is often misleading because it tries to maintain part of speech, even if a different part of speech is better. I can only suggest:

  It is not through any skill of your own that you won the lottery.

  or

  You didn't win the lottery by any particular skill.

The latter is a total rewrite, and could easily be made better, but captures the opposite of fault in that you did it, but it was good ('skill' implies it was intentional, and 'of your own' or 'You' implies it was caused by you.