Math Problem
September 21st, 2011 at 3:01:16 PM
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1. Single deck game of blackjack
2. You cannot see your cards or the dealers
3. You are told what each player has, including whether or not it is a "soft" number
4. Normal BJ rules of any double, splits unlimited, double after split, no re-hit aces, no surrender, dealer stays on soft 17.
5. No cut card, final hand is a push if it cannot be completed.
The Math question is what are the odds a player can know with absolute certainity the final two cards in the deck?
Assume the player is a genius who can keep the numbers clear in his head like it were a spreadsheet, or even that he has a computer program in front of him to deduce what hand had played when.
The question behind the question I suppose is after 50 cards are dealt from a deck of cards in a blackjack format, how certain can you be what the final two cards are if you were blind and only were told the total of your hand and the dealers?
2. You cannot see your cards or the dealers
3. You are told what each player has, including whether or not it is a "soft" number
4. Normal BJ rules of any double, splits unlimited, double after split, no re-hit aces, no surrender, dealer stays on soft 17.
5. No cut card, final hand is a push if it cannot be completed.
The Math question is what are the odds a player can know with absolute certainity the final two cards in the deck?
Assume the player is a genius who can keep the numbers clear in his head like it were a spreadsheet, or even that he has a computer program in front of him to deduce what hand had played when.
The question behind the question I suppose is after 50 cards are dealt from a deck of cards in a blackjack format, how certain can you be what the final two cards are if you were blind and only were told the total of your hand and the dealers?
Statistics don't lie, they deceive.
September 21st, 2011 at 3:26:33 PM
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You will know the total of the last 2 cards with certainty. You will also know every time an Ace comes out (either a soft hand, BJ, or if hitting, an increase in 1), so will know if there is an Ace left or not.
You couldn't tell what, say, a 19 was made of, because you can't tell between T,J,Q,K. Ignoring suits (the odds would be 0 if you had to know the suits with certainty), you could only know for sure if the last 2 cards contained an Ace and no 10 card. Otherwise, there would be too many options to make any other total.
So, 4/52 * 36/51 + 32/52*4/51 = 10.1% (ace first + 2-9 first)
You couldn't tell what, say, a 19 was made of, because you can't tell between T,J,Q,K. Ignoring suits (the odds would be 0 if you had to know the suits with certainty), you could only know for sure if the last 2 cards contained an Ace and no 10 card. Otherwise, there would be too many options to make any other total.
So, 4/52 * 36/51 + 32/52*4/51 = 10.1% (ace first + 2-9 first)
Wisdom is the quality that keeps you out of situations where you would otherwise need it
