(1). The person who starts wins in the following sequences (with the probability of occurring given in brackets)
Therefore total probability of winning
= (256 + 64 + 16 + 4 + 1)/512
(2) The chance of a draw is in the sequence
Since the starter's chance of a win + starter's chance of a draw + starter's chance of a defeat = 1,
341/512 + 1/1024 + starter's chance of a defeat = 1
or 683/1024 + starter's chance of a defeat = 1
=> starter's chance of a defeat = 341/1024
The odds of defeat of the starter is therefore, 341 to 683.
Hope that helps.
P.S. theArch, now I see your "reasoning" (I wasn't logged in when I saw your post). Phew !! Did you use AutoCad to draw that one??
Who says elephants can't dance?