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The definition of zero-sum, means that when you add up the losses and the profits you get 0, ie the negative fgure of the losses cancels out the positive figure, allow me to demonstrate,
So you see, as above in principle somebody has to make a loss if you make a profit.
So yes mathematically it is a zero-sum game, the answer will always be 0, but the notion that if somebody makes a profit the other person has to make a loss is debated only because of the varied use of the word 'loss'.
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A simple example; George trades the monthly chart only, for a few thousand pips. Ralph trades the hourly chart for 50 to 100 pips. George wins a trade for 1500 pips after 3 months. In between, Ralph has won 2000 pips from the shorter term trades, even though at times, he bet against George.
In the meantime, brokers have made money off both their trades (not the definition of zero-sum) and jobs were created.
Various Countries gained or lost a trade advantage because their currency appreciated/depreciated in value. And so it goes....
So actually, someone DOES NOT have to lose just because I win a trade. If I take 100 pips out of George's trade he still wins and so have I. The brokers have made money from both our trades and given a large enough swing, a Country has gained/lost a little trading edge.
When the Joker is in the deck.. fear not and play it well