Is it possible define position advantage on table on terms of correction to odds? Namely, is it possible to quantify the effect of position on a players equity?
This chart shows how position effects expected value, which is what I think you are interested in from reading your question.
Position has no effect on odds, which are determined by relative hand strength and is the same regardless of position.
Theoretically speaking, equity is impacted by position but it would be impossible to define as it would be different for every player, and also different for every player against every opponent and further still different for every player against every opponent with every possible hand combination. The only way to know for sure what the true equity would be for each of those would be to have a massive sample size of hands for all possibilities, which could never happen.
If you are seeking to define it in general terms for all players, I suggest you just toss the idea. If you are seeking to define it for one player and you have access to a very large sample of hands for that one player, then you may be able to accomplish something.
Say you have a huge sample of hands for this one player playing 6-max NLHE at low stakes, on the same online poker site, where we can assume the competition is relatively similar, on average, over the entire sample. All you would need to do is examine the expected value of each hand and how it varies by position. For example: how much was won or lost, on average, with AA from UTG, UTG+1, UTG+2, Button, SB and BB. You now know how the equity of having AA varies by position. Do that for every hand combination.
Yes, the later your position, the greater the probability that you have the best hand.
Not sure what you mean by equity though.
But in terms of probability:
Suppose the probability that a random hand is better than yours is p.
if you have one player to act, the probability that you have the best had is 1-p.
if you have n players to act, that probability is approximately (1-p)^n.