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The word 勝ち目 means "odds / chance of success". It is made up of two nouns 勝ち and 目.
勝ち obviously means "winning / victory". But what does the kanji 目 mean?
Does 勝ち目 mean something along the lines of "your observation (eye) for success"? E.g. "勝ち目はないよ" meaning "you have no observation for success"?
It's "chance" or "clue" of something.
You can think about 目 in 一番目 or 二番目, it represents a step of doing something.
So 勝ち目がない means that you don't have any "chance", "clue" or "can do anything" for winning.
The phoneme me comes from Old Japanese and just like how mi means fruit(実) and body(身), it had a couple related but not exactly same meanings. For mi, there were straightforward translations in Chinese for the different uses so they were able to select two different characters and nobody is confused about them anymore, but for me they may have had trouble selecting characters for the different uses and for whatever reason decided to keep them all as 目. So my message here is that 勝ち目 might have as much to do with 'eyes' as 我が身 has to do with fruits.
As for the actual answer to your question, I don't really know. I don't think there is a great deal of consensus for the etymology of many words using 目. Your random guess for its etymology might as well be accepted because there is not much evidence for anything else. However, me might have had something to do with spaced markings for counting things (think of its use as an ordinal marker) and my random guess is that the number of marks could be related to a probability.
