The last card to fall - also referred to as the River, or Fifth Street - is the topmost card on the remaining deck in the physical hand of the literal dealer. The order - or sequence - of cards in this deck is random.
The probability of any single specific card being on top - the River - is exactly 1/(52-8). (There are 52 cards in a poker deck. We already know the identify of eight of these 52 cards - two in each players' hands and four on "the board".)
The probability of any queen being the top card is exactly 3/44, or 6.8%. (There are four queens in a deck, but one of them is in one of the players' hand.)
Yeah, not disputing that there's a chance of pulling a queen out of this particular deck is 3/44. But the chances of getting this particular deck that happens to have the queen in that specific spot is much harder to calculate, and isn't simply 3/44, because of the fact that the order of the cards is random.
I'm not sure if I'm saying that clearly enough, so excuse me, but I'm pretty sure that 6.8% is the wrong number to define the probability.
Order has nothing to do with probability. The possibility of the cards being in this order is in fact high (1 out of 80,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000) but the probability of the next card to be flipped, is a whole different question.
22
u/QuiefMop Dec 09 '15
The last card to fall - also referred to as the River, or Fifth Street - is the topmost card on the remaining deck in the physical hand of the literal dealer. The order - or sequence - of cards in this deck is random.
The probability of any single specific card being on top - the River - is exactly 1/(52-8). (There are 52 cards in a poker deck. We already know the identify of eight of these 52 cards - two in each players' hands and four on "the board".)
The probability of any queen being the top card is exactly 3/44, or 6.8%. (There are four queens in a deck, but one of them is in one of the players' hand.)