Dislikeda coin toss is a bit unfair to use - tossing a coin either goes heads or tails with an evens chance of heads or tails, however choosing long or short does not unless you are betting on the next tick. stop sizes mean that the choice 'long' can go short to begin with and still win if it turns around.
a coin cannot change it's side once fallen as a trade can hence the anaolgy is not the same. Your zero expectancy does not fit in when using a coin to choose direction only.
Also, your zero expectancy supposes that you have a perfect coin in windless conditions. Coins are not balanced 100% and external forces can affect the coin.
Money management in trading is the same as having an imperfect coin - it is weighted one way or another.
ps, roulette wheels are rarely perfect too - trust me I know this
pps, waiting for someone to talk about Shannon and his random walk money management.Ignored
A great trader could flip the coin, go long or short, and if it isn't a good trade, close it for the spread; if good, let it go. But that wouldn't really be flipping a coin, it would be that trader using his system.
I think that's maybe where you were coming from.
Most of us probably went through a stage where we preferred not to have to decide, or be responsible for the trade. Indicators, EA's, signals from elsewhere, or flip a coin, anything but having to decide ourselves what to do and risk being wrong!