This file contains some example of procedure SeqAsyV
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S is, {-1, 0, 1}
The Asymptotics of a Gambler's Chance of Ending with, 0, Dollars and Never be\
ing in debt after n rolls with a fair die whose faces are, {-1, 0, 1}
By Shalosh B. Ekhad
Consider a gambler who rolls a, 3,
-sided fair die , hence with each side lending with probability, 1/3
If the amount is positive he gets the indicated number of dollars, and if i\
t is negative
he has to pay the absolute value of the number shown.
if it is 0, he gets nothing and pays nothing.
He gets kicked out of the casino as soon as as he is in debt.
The estimated asymptotic expression of his probability of surviving n rolls \
of the die and ending with exactly, 0, dollars
to order , 1, in n is:
3.57290586829
1.46580753571 - -------------
n
-----------------------------
3/2
n
and in Maple input format:
1/n^(3/2)*(1.46580753571-3.57290586829/n)
This took , 10.191, seconds.
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S is, {-2, -1, 0, 1, 2}
The Asymptotics of a Gambler's Chance of Ending with, 0, Dollars and Never be\
ing in debt after n rolls with a fair die whose faces are,
{-2, -1, 0, 1, 2}
By Shalosh B. Ekhad
Consider a gambler who rolls a, 5,
-sided fair die , hence with each side lending with probability, 1/5
If the amount is positive he gets the indicated number of dollars, and if i\
t is negative
he has to pay the absolute value of the number shown.
if it is 0, he gets nothing and pays nothing.
He gets kicked out of the casino as soon as as he is in debt.
The estimated asymptotic expression of his probability of surviving n rolls \
of the die and ending with exactly, 0, dollars
to order , 1, in n is:
0.668958752295
0.538753112041 - --------------
n
-------------------------------
3/2
n
and in Maple input format:
1/n^(3/2)*(.538753112041-.668958752295/n)
This took , 24.337, seconds.
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S is, {-2, -1, 3}
The Asymptotics of a Gambler's Chance of Ending with, 0, Dollars and Never be\
ing in debt after n rolls with a fair die whose faces are, {-2, -1, 3}
By Shalosh B. Ekhad
Consider a gambler who rolls a, 3,
-sided fair die , hence with each side lending with probability, 1/3
If the amount is positive he gets the indicated number of dollars, and if i\
t is negative
he has to pay the absolute value of the number shown.
He gets kicked out of the casino as soon as as he is in debt.
The estimated asymptotic expression of his probability of surviving n rolls \
of the die and ending with exactly, 0, dollars
to order , 1, in n is:
0.289506768582
0.238318446778 - --------------
n
-------------------------------
3/2
n
and in Maple input format:
1/n^(3/2)*(.238318446778-.289506768582/n)
This took , 23.318, seconds.
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S is, {-3, -1, 4}
The Asymptotics of a Gambler's Chance of Ending with, 0, Dollars and Never be\
ing in debt after n rolls with a fair die whose faces are, {-3, -1, 4}
By Shalosh B. Ekhad
Consider a gambler who rolls a, 3,
-sided fair die , hence with each side lending with probability, 1/3
If the amount is positive he gets the indicated number of dollars, and if i\
t is negative
he has to pay the absolute value of the number shown.
He gets kicked out of the casino as soon as as he is in debt.
The estimated asymptotic expression of his probability of surviving n rolls \
of the die and ending with exactly, 0, dollars
to order , 1, in n is:
0.14294189
0.165340019419 - ----------
n
---------------------------
3/2
n
and in Maple input format:
1/n^(3/2)*(.165340019419-.14294189/n)
This took , 32.406, seconds.