1) Depends on the amount of people in the group and the knowledge of the bettor about the people in my social group.
2) The problem of finding the minimum size of a group to have a probability of at least 50% of finding two people with the same birthday is a classic problem in probability known as the birthday problem or the birthday paradox.To solve the problem, we need to calculate the probability of two people not having the same birthday in a group of n people, and then set this probability to be less than 50%. The probability of two people not having the same birthday in a group of n people can be calculated as follows:

P(n) = (365/365) * (364/365) * (363/365) * … * ((365 – n + 1)/365)

where (365/365) is the probability that the first person has a unique birthday, (364/365) is the probability that the second person has a different birthday than the first person, and so on, until ((365 – n + 1)/365) is the probability that the nth person has a different birthday than the first n – 1 people.

To find the smallest value of n for which P(n) is less than 0.5, we can use trial and error, or we can use a formula derived from the above expression, known as the approximate formula:

n ≈ √(2 * 365 * ln(1/(1 – 0.5)))

Using this formula, we can calculate that the minimum size of a group to have a probability of at least 50% of finding two people with the same birthday is approximately 23. This means that in a group of 23 people, there is a 50-50 chance that at least two of them share the same birthday.