I recently saw the coin toss spiel and it got me thinking. They were saying a share can eventually go up or down so the probability is 50:50 and if your reward/risk is 1:1 then you will break even in the long run (ignoring costs), so the way to become profitable is to change your reward/risk to 2:1. 50% of the trades will make 2 units profit and 50% will lose 1 unit so overall you will be profitable - so they say.
The problem I have with this is that they failed to mention that the probability of a 1 unit move is different to the probablity of a 2 unit move, so its more complex than what they were saying. The bigger the reward, the less chance of hitting it. So a 2:1 system could still have a low expectancy.
So this got me thinking about trying to find an optimal reward/risk relationship but its been a long time since I did probability at school so the maths has got me stumped.
Can anyone help with the formula for working this out. As I see it the higher the reward/risk ratio, the smaller the chance of a successfull trade. There must be a mathematically optimal value for reward/risk which would lead to an optimal target/stop criteria.