Mixing
If shuffling distributes cards, can it also ‘undistribute’ them?
1
$begingroup$
Assuming you have six decks of cards which have been used in a canasta game. If wildcards are randomly placed throughout the six decks before shuffling, what are the odds that there will be $7$ wildcards together after shuffling the cards $10$ times?
combinatorics
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
$endgroup$
add a comment |
1
$begingroup$
Assuming you have six decks of cards which have been used in a canasta game. If wildcards are randomly placed throughout the six decks before shuffling, what are the odds that there will be $7$ wildcards together after shuffling the cards $10$ times?
combinatorics
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
$endgroup$
$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31
add a comment |
1
1
1
$begingroup$
Assuming you have six decks of cards which have been used in a canasta game. If wildcards are randomly placed throughout the six decks before shuffling, what are the odds that there will be $7$ wildcards together after shuffling the cards $10$ times?
combinatorics
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
$endgroup$
Assuming you have six decks of cards which have been used in a canasta game. If wildcards are randomly placed throughout the six decks before shuffling, what are the odds that there will be $7$ wildcards together after shuffling the cards $10$ times?
combinatorics
combinatorics
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
edited Jan 19 at 10:46
N. F. Taussig
44.5k103357
44.5k103357
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
asked Jan 19 at 7:14
Philena FarmerPhilena Farmer
62
62
$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31
add a comment |
$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31
$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31
add a comment |
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$begingroup$
What have you tried? How many wild cards are there? How large are the decks of cards (I know pinochle uses different decks than bridge for instance)? If you believe the shuffle count is important, then so too is the shuffling mechanism (because the mathematical version of shuffling is a true random permutation and you can't tell the difference between doing it once and doing it twice); what is the mechanism, and is there a mathematical model of that shuffling technique?
$endgroup$
– Dan Uznanski
Jan 19 at 10:56
$begingroup$
My premise is that if, after the game, the wildcards are not distributed before shuffling begins then the wild cards will end up being more widely distributed after shuffling than if the wild cards had been scattered throughout the decks before shuffling. In other words, if they are randomly distributed to begin with does shuffling have a greater chance of keeping them evenly distributed, a less chance of them being evenly distributed, or doesn’t matter?
$endgroup$
– Philena Farmer
Jan 19 at 19:29
$begingroup$
There are 54 cards in each deck - a regular deck plus two jokers. Shuffling is done mechanically.
$endgroup$
– Philena Farmer
Jan 19 at 19:31