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Is there software to buy and sell stocks in real time on very small moves in price? 
I'm answering in a perspective of an End-User within the United Kingdom. Most stockbrokers won't provide Real-time information without 'Level 2' access, however this comes free for most who trade over a certain threshold. If you're like me, who trade within their ISA Holding each year, you need to look elsewhere.  I personally use IG.com. They've recently began a stockbroking service, whereas this comes with realtime information etc with a paid account without any 'threshold'. Additionally, you may want to look into CFDs/Spreadbets as these, won't include the heavy 'fees' and tax liabilities that trading with stocks may bring.