The winning trader do take a larger percentage of the profits - because they have different skill sets... like the advantage the large-claw lobsters, a slight edge is all you need to make a profound difference.
As another example, the winning horse in a race may come down to a photo to see which nose was ahead... and yet the first place horse will win far greater prize than the second place horse.
But - that winning traders take half of the profits is hindsight observation of a completed event, and not limiting your future ability to be within the top traders making that bigger profit.
I also like your 'flipping the coin' analogy - many new traders are gambling on blind luck. They don't have a practiced strategy they have prepared - they have not resigned themselves to waiting for the right time to use the strategy.
And so it comes down to information.
Information about how money works, along with the habits to make it work on your behalf - and you will be within the small group of profitable traders.
In other words, you can choose to grow your claws - and take a bigger share!