Which has a higher probability rate in a 52 card deck: being dealt 4 of a kind in succession or alternation?

Question

Their is an arbitrary shuffle. Successive is as it implies: being dealt four cards in a row. Alternating means one down, and then one to you. If it eases results, we are referring to the first four cards to be dealt in the Successive dealing and the first 8 in Alternating. I've been pondering this question assuming a simple answer but I haven't reached a conclusion to date. If you are going to answer it for points please write something ridiculous to make me laugh. I'd prefer humor over the words "Succession" or "Alternation."

Answer 1

Think of the probability of picking 4 cards from somewhere in the deck and finding them all the same... it would be something like (52/52 x 3/51 x 2/50 x 1/49). But whatever it is, it doesn't matter. Just call this probability p. Now does it matter where you draw the cards from? If I were to pick the first 4 cards, the last 4 cards, a random collection of cards, alternating cards, etc. will the results be any different? No, the probability is always the same probability p.

It's the same with the lottery. While the sequence 1,2,3,4,5 might seem less likely to occur than something like 13, 17, 26, 37, 42, they actually have the same probability.

However, you may notice that dealers always deal one card to each player, then repeat. They don't deal 5 cards to one, then 5 cards to another, etc. The reason has nothing to do with probability and everything to do with preventing cheating. It's much easier to perhaps keep a set of cards together while shuffling (with false shuffles, palming, etc.) and then make sure they get placed at the top of the deck. Then if you dealt them to one person, they'd get all the desirable cards. However, if you have to alternate, then it is near impossible to arrange the cards so that one person gets the desirable cards.

Answer 2

Maybe I'm wrong here, but you seem to only be asking the probablilty between being dealt the four successive cards, or the four alternating cards. If you are dealt the cards either way, the probability is the same. 100%, you've got the cards. If you mean, drawing four of a kind, or some other four-carded hand, then the probability is still the same, because either way you are only receiving four cards at random. The likelihood of getting four of the same cards right next to each other is just as low as getting four of the same cards seperated by one card each.

Ultimately, it doesn't matter stastically, unless you have some other parameters that must be satisfied. Then your answer might be different.

:)

Answer 3

Assuming all else is equal the probability of each will be the same.