Given a deck of cards and N players, once I have drawn a card, how can I determine my odds of having the highest card?
I want to know what the formula is for calculating a players odds of having the highest card among players once they have each drawn a card but each player only knows the card he has drawn, the number of other players, and the cards that were in the deck before he drew his card.
For example, lets assume a fresh deck and 4 players. If I draw a 7. What are the odds that I will have the highest card among all players?
I intend to use this in some code I am writing as a demonstration, and I just want to make sure my logic is correct.
So far I figure that I need the total number of cards in the deck minus 1 (for the card I drew), lets call it C (so for a fresh deck that would be 52, but its still a variable)
Then I need to determine how many cards in the deck are lower than my card, lets call it L.
- So for the first other player I need to do L / C
- And for the second other player I need to do L - 1 / C - 1
- And for the third other player I need to do L - 2 / C - 2
And I need to multiply those results together (L / C) x (L - 1 / C - 1) x (L - 2 / C - 2) to get the odds.
Am I right? Also, I am sure there is probably a better way to do this if it is right.