I have a random pulling of cards probability question....

Ok, I was playing a drinking game with friends where you are supposed to guess which card is going to be randomly drawn next. The first three cards drawn were the 9, 8 and then 7 of hearts. A friend then told the person guessing to choose a 6. I objected saying that the probability the next card is going to be a 6 is extremely low because of the 3 cards that were drawn and their order. They claim it is just as likely that a 6 of hearts will be drawn next as any other card in the deck at this point because it's a 1 in 49 chance regardless.

Well if they forgot to shuffle the deck the next card would be the 6 of hearts.

Drinking game? hmmm...then the answer relies on a number of things. How drunk were you? Are you sure that the deck was shuffled? Was it truly random?
How drunk were you? Did you remember to remove the jokers? There were definitely only 52 cards total, right?

If a 52 card deck is randomized, then each card is equally likely to be drawn. Once 3 are removed, each of the remaining cards (including the 6 of hearts) has a 1/49 chance of being drawn.

So, what was the next card drawn?

My money for the next card drawn is the rules card or the advertisement card. ;)

Quote: S6I6X

Ok, I was playing a drinking game with friends where you are supposed to guess which card is going to be randomly drawn next. The first three cards drawn were the 9, 8 and then 7 of hearts. A friend then told the person guessing to choose a 6. I objected saying that the probability the next card is going to be a 6 is extremely low because of the 3 cards that were drawn and their order. They claim it is just as likely that a 6 of hearts will be drawn next as any other card in the deck at this point because it's a 1 in 49 chance regardless.

Your friends are right, you are wrong. End of story. As another poster suggested, I'd put some money on it being a 6 of hearts, as the shuffle was probably bad.

I think you were behind in the drinking game.

Your friends are right. You don't know the next card, and it's just as likely that the 6 of hearts gets drawn as any of the other remaining cards.

Just like in a lottery, if the first 3 numbers are drawn and they are 1-2-3, the next number being 4 is just as likely as any other number.

I've played a drinking game like that before. One person is drawing the cards, the others around the circle guess. The first person guesses a card. Either they're right, or the dealer says higher/lower(only rank, no suits). That person then makes a second guess. If they get it right on the first or second guess, the dealer drinks. If the player gets it wrong they drink. Three players in a row must be stumped before the dealer can pass the cards. So you don't wanna be the dealer when there's only say 10-12 cards left cause you'll probably keep drinking.

Under these rules, I don't think you'd want to pick the 6 cause you wanna give yourself the best chance at your second guess. So if the first few cards are all low, I'd imagine you'd want to pick nine or ten. If it's lower, you'd probably steer clear of the other low ones already picked.

Quote: ewjones080

I've played a drinking game like that before. One person is drawing the cards, the others around the circle guess. The first person guesses a card. Either they're right, or the dealer says higher/lower(only rank, no suits). That person then makes a second guess. If they get it right on the first or second guess, the dealer drinks. If the player gets it wrong they drink. Three players in a row must be stumped before the dealer can pass the cards. So you don't wanna be the dealer when there's only say 10-12 cards left cause you'll probably keep drinking.

Under these rules, I don't think you'd want to pick the 6 cause you wanna give yourself the best chance at your second guess. So if the first few cards are all low, I'd imagine you'd want to pick nine or ten. If it's lower, you'd probably steer clear of the other low ones already picked.

Yep, we played then when I was in college too! I believe it's called Fuck the dealer.

It should be pointed out, that although every card that is left in the deck, if you are solely guessing cards based on their face value, then it would be foolish to guess a 7, 8, or 9.

A 6 would have been a fine choice (and likely worth some excitement if the 6 of hearts came)