Catch the Last Success

Five deals appear in sequence. Independently, each deal turns out to be 'live' with probability 0.2 (and 'dead' otherwise); you learn live/dead immediately when the deal appears and must accept or pass irrevocably with no recall. You win precisely if you accept the LAST live deal of the five. Using the odds-algorithm logic for such problems (sum the odds r_i = p_i/(1-p_i) from the end until the running total first reaches 1, and start accepting any live deal from that index onward), find the optimal stopping index and your probability of winning.