The odds of coin tossing and winning all six as heads - is the same as having six kids and all 6 are the same gender. So your statement that the chances are 50/50 is only correct when you only consider each toss individually.
In reality it is .5 x .5 x .5 x.5 x .5 x .5 = .0156 o 1.56%
With fractions you can use 1/2 x 1/2 etc. Taking it to 6 times you have 1/64.
I am going to write to Mythbusters and ask them to do this coin-flip thing.
Or is the final episode already in the can?
The past toss means nothing to the next toss.
Childbirth[edit]
Instances of the gambler’s fallacy being applied to childbirth can be traced all the way back to 1796, in Pierre-Simon Laplace’s A Philosophical Essay on Probabilities. Laplace wrote of the ways in which men calculated their probability of having sons: “I have seen men, ardently desirous of having a son, who could learn only with anxiety of the births of boys in the month when they expected to become fathers. Imagining that the ratio of these births to those of girls ought to be the same at the end of each month, they judged that the boys already born would render more probable the births next of girls.” In short, the expectant fathers feared that if more sons were born in the surrounding community, then they themselves would be more likely to have a daughter.[4]
Some expectant parents believe that, after having multiple children of the same sex, they are “due” to have a child of the opposite sex. While the Trivers–Willard hypothesis predicts that birth sex is dependent on living conditions (i.e. more male children are born in “good” living conditions, while more female children are born in poorer living conditions), the probability of having a child of either sex is still generally regarded as near 50%.