Gamblers' Logic

I toss a coin and heads turns up five times in a row. 
Which side is more likely to turn up the next time?

• Heads? Five heads in a row is a pattern - the trend is likely to continue.
  
• Tails? Six heads in a row is unusual so tails is more likely.

The above answers are examples of gambler's logic — the perception of patterns in random data.

So which is the correct answer?
Neither - every coin toss has an even chance of turning up heads or tails. It never varies.