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Think grid.
Theory: with a spread of 0 (and tradecost of 0), if we trade at diverse levels (i.e. think two grids intermixed, or think numerous orders permitted), with diverse lot sizes, and hedging is allowed, then it's never possible to make sure a profit - however small - provided the amount of trades are limited/is finite (i.e. rules out mGrid/Williama).
True or false?
With 100% confidence now: for non-varied levels, the announcement is true. One can achieve a great win rate , but the huge losses found (less often) will offset the huge winners (more often) if sufficient trades are made. The end result consistently churns towards 0.
Hum. Perhaps it is possible.
So, it is wise not to exchange... Right?
With near 100% confidence: for non-varied amounts, the announcement is true. An individual can attain a 75%, even a 81.25% success rate, but the big losses will cancel the winners if enough trades are made.
How about varied amounts?