I understand that independent events (such as a fair coin flip) should not be viewed in succession. For example, if you flip heads 10 times in a row, the odds of flipping the next coin heads is still 50%.
However, there is another way of looking at the coin flips.
What is the probability of flipping 11 heads in a row And I already know that to be
0.5^11 ~= 0.1%
So if you were making a bet on coin flips and 10 heads came up, would you still base a bet on the 50% fact, or on the odds of getting heads 11 times in a row (.1%) fact? If you consider the 50% fact or 0.1% fact, please explain why?