The chances of you existing:

If you go back 10 generations (250 years) the chance of you being born at all is at most 1 divided by 6 x 10100 or
1 in 60000000000000000000000000000000000 00000000000000000000000000 000000000000000000000000000000000000.
In gambling, even a chance of 1 to 100 is not worth a gamble.
Are you ever lucky to be alive!!

If you go back 1 million years or 40 000 generations (each generation is considered 25 years), your chance of being born is at most 1 in 1.8 x 10403167 or
18 with 403,166 zeros after the 1.

In other words your chances of existing is essentially zilch, even if we were considering this possibility only a short 250 years ago.
Right now you do exist, so the actual chance is 100%, but the predicted likelihood in the past of you being born would be essentially zero.

The calculations of these numbers (calculations shown below) tend to overestimate your chances of being.
They only include numbers based on your father's contribution, his father's contribution, his father contribution, and so on. In other words the calculations are based only on the direct male line.
They do NOT include the following factors that would make the chances of your existence even less:
- your mother's contribution
- the men and women that died in war, famine, disease without or with fewer offspring-- in some generations 50% of humanity.
- the men and women that died from natural causes.
- children that died before reaching the age of reproduction.
- fetuses and fertilized eggs that died and were naturally aborted.

You are the result of many generations of survivors. One of the people that died prematurely could have been your Dad or your Dad's Dad and so on. Somehow, none of your forefathers died before passing on his genes to the next man in your lineage. Because of the deaths mentioned most human lineages died out, while luckily yours survived. Lo and behold, here you are!
Because of these deaths, your odds of existing were actually much less than the odds given below.