I'm trying to calculate the probability of being dealt a winning hand from the start in the card game "Sevens" while playing as 4 players.
By being 4 players you get 13 cards each, so using the formula for combinations: C(n,r) = n! / r!(n-r)! where n = 52 and r = 13 I get a total of 635.013.559.600,00 different combinations of hands.
To win from the very start I could be dealt an entire suit, which gives me 4 different possibilites of a winning hand. So that alone should give me 1 in a roughly 159 billion chance to win right away.
I could also be given all the 7s, 8s, 9s and one of the 10s to win. So my question is: how do I figure out how many different hands there are that can win the game right away?