In backgammon, a player's luck is calculated (when a match is analyzed after its completion by computer) by comparing the player's equity before he throws the dice with what his equity would be if he made the best move after throwing.
The game ends, of course, with one player reaching an equity of zero; there's a nice tidy theorem that says the final result of the game = (luck of player 1) - (luck of player 2) - (cost of mistakes by player 1) + (cost of mistakes by player 2).
The same definition could be applied to poker, after computers have some idea of how to estimate the equity of a position in the middle of a multiplayer hand, which is pretty far beyond Poki. If you are looking at a series of events with some payoff table associated with different sequences of events, you might find the same definition useful.
For further details on the backgammon definition of luck, see the article at
http://www.math.columbia.edu/~zare/luckequity.html