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If as I flip a coin, the times I get heads approach the times I get tails then why isn't there a bigger chance to get tails in two coin flips if I first got heads?

mathamatacs
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    Because the behaviour of the coin on average doesn't affect the behaviour of the coin on each individual trial. Mathematically, we say that each trial is independent :) – Thomas Russell May 24 '17 at 15:53
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    It's a 'memoryless' property of a coin toss - the coin doesn't know hat it did in the past, the chances of a head stay at 50% - the perceived 'levelling out' will only tend to occur as a percentage of times there are are heads and tails, not the number of heads and tails. The expectation of the absolute difference in the numbers of heads and tails goes up with each coin toss. but not as quickly as the number of tosses increases – Cato May 24 '17 at 16:38

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