How to minimize the expected value of the resulting sum in this dice & number game?
$begingroup$
The game is as follows: I place nine tiles numbered 1-9 inclusive lying on the table face up. I then roll two standard, six-sided dice and note their outcomes. I now have two options:
- Flip over the tiles corresponding to the results of each die (e.g. if I roll a 3 and a 4, I flip the two tiles with 3 and 4 on them to be face down).
- Take the sum of the two die and flip over that singular tile (e.g if I roll a 3 and a 4, I flip over the tile with a 7 on it to be face down).
Now some additional rules: If I ever roll two die such that their sum is a 10, 11 or 12, I discard that outcome and re-roll (since we only have tiles labeled 1-9). If I roll an outcome and one (or both) of the tiles for that outcome are already flipped, I am forced to take the other option (e.g. if I roll a 3 and a 4 but the tile labeled 4 is flipped, I must flip the 7 tile instead). If both moves are unavailable (e.g. I roll a 3 and a 4 but the tiles labeled 4 and 7 are already flipped), the game ends.
The question is: what is the best strategy to minimize the sum of the numbers on the remaining tiles once the game ends?
probability game-theory dice expected-value
asked Dec 9 '18 at 22:01
cashwickcashwick
161
$endgroup$
add a comment |
$begingroup$
The game is as follows: I place nine tiles numbered 1-9 inclusive lying on the table face up. I then roll two standard, six-sided dice and note their outcomes. I now have two options:
- Flip over the tiles corresponding to the results of each die (e.g. if I roll a 3 and a 4, I flip the two tiles with 3 and 4 on them to be face down).
- Take the sum of the two die and flip over that singular tile (e.g if I roll a 3 and a 4, I flip over the tile with a 7 on it to be face down).
Now some additional rules: If I ever roll two die such that their sum is a 10, 11 or 12, I discard that outcome and re-roll (since we only have tiles labeled 1-9). If I roll an outcome and one (or both) of the tiles for that outcome are already flipped, I am forced to take the other option (e.g. if I roll a 3 and a 4 but the tile labeled 4 is flipped, I must flip the 7 tile instead). If both moves are unavailable (e.g. I roll a 3 and a 4 but the tiles labeled 4 and 7 are already flipped), the game ends.
The question is: what is the best strategy to minimize the sum of the numbers on the remaining tiles once the game ends?
probability game-theory dice expected-value
asked Dec 9 '18 at 22:01
cashwickcashwick
161
$endgroup$
add a comment |
$begingroup$
The game is as follows: I place nine tiles numbered 1-9 inclusive lying on the table face up. I then roll two standard, six-sided dice and note their outcomes. I now have two options:
- Flip over the tiles corresponding to the results of each die (e.g. if I roll a 3 and a 4, I flip the two tiles with 3 and 4 on them to be face down).
- Take the sum of the two die and flip over that singular tile (e.g if I roll a 3 and a 4, I flip over the tile with a 7 on it to be face down).
Now some additional rules: If I ever roll two die such that their sum is a 10, 11 or 12, I discard that outcome and re-roll (since we only have tiles labeled 1-9). If I roll an outcome and one (or both) of the tiles for that outcome are already flipped, I am forced to take the other option (e.g. if I roll a 3 and a 4 but the tile labeled 4 is flipped, I must flip the 7 tile instead). If both moves are unavailable (e.g. I roll a 3 and a 4 but the tiles labeled 4 and 7 are already flipped), the game ends.
The question is: what is the best strategy to minimize the sum of the numbers on the remaining tiles once the game ends?
probability game-theory dice expected-value
asked Dec 9 '18 at 22:01
cashwickcashwick
161
$endgroup$
The game is as follows: I place nine tiles numbered 1-9 inclusive lying on the table face up. I then roll two standard, six-sided dice and note their outcomes. I now have two options:
- Flip over the tiles corresponding to the results of each die (e.g. if I roll a 3 and a 4, I flip the two tiles with 3 and 4 on them to be face down).
- Take the sum of the two die and flip over that singular tile (e.g if I roll a 3 and a 4, I flip over the tile with a 7 on it to be face down).
Now some additional rules: If I ever roll two die such that their sum is a 10, 11 or 12, I discard that outcome and re-roll (since we only have tiles labeled 1-9). If I roll an outcome and one (or both) of the tiles for that outcome are already flipped, I am forced to take the other option (e.g. if I roll a 3 and a 4 but the tile labeled 4 is flipped, I must flip the 7 tile instead). If both moves are unavailable (e.g. I roll a 3 and a 4 but the tiles labeled 4 and 7 are already flipped), the game ends.
The question is: what is the best strategy to minimize the sum of the numbers on the remaining tiles once the game ends?
probability game-theory dice expected-value
probability game-theory dice expected-value
asked Dec 9 '18 at 22:01
cashwickcashwick
161
asked Dec 9 '18 at 22:01
cashwickcashwick
161
asked Dec 9 '18 at 22:01
cashwickcashwick
161
asked Dec 9 '18 at 22:01
cashwickcashwick
161
asked Dec 9 '18 at 22:01
cashwickcashwick
161
161
add a comment |
add a comment |
1 Answer
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$begingroup$
Nice question. These just some thoughts, nothing to back it up.
The question might be better phrased as: "What is the best strategy that maximizes the sum of the numbers on the flipped tiles?" I think the best way to maximize that is to make the game last as long as possible. And to do that, by minimizing the number of flipped tiles, hence always flipping over the sum rather than the two (or one in the case of a double) lesser tiles.
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
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1 Answer
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1 Answer
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$begingroup$
Nice question. These just some thoughts, nothing to back it up.
The question might be better phrased as: "What is the best strategy that maximizes the sum of the numbers on the flipped tiles?" I think the best way to maximize that is to make the game last as long as possible. And to do that, by minimizing the number of flipped tiles, hence always flipping over the sum rather than the two (or one in the case of a double) lesser tiles.
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
$endgroup$
add a comment |
$begingroup$
Nice question. These just some thoughts, nothing to back it up.
The question might be better phrased as: "What is the best strategy that maximizes the sum of the numbers on the flipped tiles?" I think the best way to maximize that is to make the game last as long as possible. And to do that, by minimizing the number of flipped tiles, hence always flipping over the sum rather than the two (or one in the case of a double) lesser tiles.
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
$endgroup$
add a comment |
$begingroup$
Nice question. These just some thoughts, nothing to back it up.
The question might be better phrased as: "What is the best strategy that maximizes the sum of the numbers on the flipped tiles?" I think the best way to maximize that is to make the game last as long as possible. And to do that, by minimizing the number of flipped tiles, hence always flipping over the sum rather than the two (or one in the case of a double) lesser tiles.
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
$endgroup$
Nice question. These just some thoughts, nothing to back it up.
The question might be better phrased as: "What is the best strategy that maximizes the sum of the numbers on the flipped tiles?" I think the best way to maximize that is to make the game last as long as possible. And to do that, by minimizing the number of flipped tiles, hence always flipping over the sum rather than the two (or one in the case of a double) lesser tiles.
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
answered Dec 10 '18 at 9:43
palmpopalmpo
4061213
4061213
add a comment |
add a comment |
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