This question caused a massive fight in a number theory class I was in a few years ago. Class was split, and no one changed their opinion. Curious if it is obvious to outsiders, or if anyone can offer any proof.
Course was split with most poker and blackjack players arguing these are dependent events, with most others claiming they were independent and you could simulate relevant events with an infinite deck.
Take a standard deck with no jokers. 52 cards. Four aces, four deuces, four threes, and so on. Shuffle the deck. Draw cards until you spot a match, ie, a card with the same numerical value as the last card drawn. Does drawing such a match affect the odds of drawing a subsequent match later in the deck?
Clarifying note: I call a match a "pair" in the title, but "match" is more precise. Drawing three in a row counts as two matches, but most people would not call that two pairs.
Best Answer
Obviously, since you are drawing cards in a sequence, the probability of a second match is dependent on whether a match was drawn beforehand, especially since the three-in-a row scenario can happen immediately after a match.
Suppose the first two cards form a match of two aces. Then the third card could well be an ace, forming a second match that could not have occurred if the first two cards were different. Thus the probability that the second match happens on the third card depends on whether a match was made at the second card.