j****i
发帖数: 305 | 1 Roll a dice, sum up all cumulative outcomes. The first time it is over 15,
what is most likely results (out of 16,17,18,19,20,21)? | h**6
发帖数: 4160 | 2 应该是16。
设得到不超过15的最大的结果是x，则 x 在[10, 15]范围内
若x=10，只能得到16
若x=11，可得16, 17
若x=12，可得16, 17, 18
若x=13，可得16, 17, 18, 19
若x=14，可得16, 17, 18, 19, 20
若x=15，可得16, 17, 18, 19, 20, 21
当然，有闲心的话，也可以把概率算出来，验证我的结论。 | p********7
发帖数: 549 | 3 I couldn't catch the meaning of your description. Do you mean you roll for
several times, and sum up all results?
【在 j****i 的大作中提到】
: Roll a dice, sum up all cumulative outcomes. The first time it is over 15,
: what is most likely results (out of 16,17,18,19,20,21)?
| j****i
发帖数: 305 | 4 Roll the die and keep track of the accumulative sum.
【在 p********7 的大作中提到】
: I couldn't catch the meaning of your description. Do you mean you roll for
: several times, and sum up all results?
| k*p
发帖数: 1526 | 5 程序模拟1000次结果
16 278
17 256
18 181
19 152
20 92
21 41
验证了这个想法
应该是16。
设得到不超过15的最大的结果是x，则 x 在[10, 15]范围内
若x=10，只能得到16
若x=11，可得16, 17
若x=12，可得16, 17, 18
若x=13，可得16, 17, 18, 19
若x=14，可得16, 17, 18, 19, 20
若x=15，可得16, 17, 18, 19, 20, 21
当然，有闲心的话，也可以把概率算出来，验证我的结论。
【在 h**6 的大作中提到】
: 应该是16。
: 设得到不超过15的最大的结果是x，则 x 在[10, 15]范围内
: 若x=10，只能得到16
: 若x=11，可得16, 17
: 若x=12，可得16, 17, 18
: 若x=13，可得16, 17, 18, 19
: 若x=14，可得16, 17, 18, 19, 20
: 若x=15，可得16, 17, 18, 19, 20, 21
: 当然，有闲心的话，也可以把概率算出来，验证我的结论。
| j****i
发帖数: 305 | 6 My explaination is that the sum follows a diffusion equation, and drifts
away from origin. This means that
the left most number (16) gets the most flux. But after the peak of the
distribution passes 15, the numbers
16, 17 ... will get more probability. So I'm not sure how to show that the
game is more likely to have stopped
before the peak passed 15, though it may look obvious.
What if we stop when the sum is above 12? My feeling is that the answer may
not be 13.
Can you check?
s
【在 k*p 的大作中提到】
: 程序模拟1000次结果
: 16 278
: 17 256
: 18 181
: 19 152
: 20 92
: 21 41
: 验证了这个想法
:
: 应该是16。
| k*p
发帖数: 1526 | 7 Unfortunately, it is 13. I guess the closest number always gets higher
chance. That's the result of the game rule.
13 284
14 256
15 175
16 151
17 95
18 39
My explaination is that the sum follows a diffusion equation, and drifts
away from origin. This means that
the left most number (16) gets the most flux. But after the peak of the
distribution passes 15, the numbers
16, 17 ... will get more probability. So I'm not sure how to show that the
game is more likely to h
【在 j****i 的大作中提到】
: My explaination is that the sum follows a diffusion equation, and drifts
: away from origin. This means that
: the left most number (16) gets the most flux. But after the peak of the
: distribution passes 15, the numbers
: 16, 17 ... will get more probability. So I'm not sure how to show that the
: game is more likely to have stopped
: before the peak passed 15, though it may look obvious.
: What if we stop when the sum is above 12? My feeling is that the answer may
: not be 13.
: Can you check?
| j****i
发帖数: 305 | 8 Fair enough. :)
【在 k*p 的大作中提到】
: Unfortunately, it is 13. I guess the closest number always gets higher
: chance. That's the result of the game rule.
: 13 284
: 14 256
: 15 175
: 16 151
: 17 95
: 18 39
:
: My explaination is that the sum follows a diffusion equation, and drifts
|
|
