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Waiting for Rescue

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''For Dungeon Level 1, formula is simple: 16/100 chance per day to get rescued. Now for the really messy problem. Chance for being rescued on Dungeon Levels below 1: You have (17-DunLvl) / 10000 chance of being rescued per day for the first Int(100 * LN(DunLvl)^2 + 22) days. After that, you have (17-DunLvl) / 1000 chance of being rescued per day.''
''For Dungeon Level 1, formula is simple: 16/100 chance per day to get rescued. Now for the really messy problem. Chance for being rescued on Dungeon Levels below 1: You have (17-DunLvl) / 10000 chance of being rescued per day for the first Int(100 * LN(DunLvl)^2 + 22) days. After that, you have (17-DunLvl) / 1000 chance of being rescued per day.''
-
If x = Int(100*ln(Dunlvl)^2+22), p=(17-DunLvl)^2/10000, and P=10*p,
+
If x = Int(100*ln(Dunlvl)^2+22), p=(17-DunLvl)^2/10000, and P=10*p,
your cumulative chance of being rescued any day up to day n is:
your cumulative chance of being rescued any day up to day n is:
<br>
<br>
-
1-(1-p)^n, if n < x
+
1-(1-p)^n, if n < x
<br>
<br>
-
1-(1-p)^x*(1-P)^(n-x), if n > x
+
1-(1-p)^x*(1-P)^(n-x), if n > x
Those formulae can be inverted to get the number of days to wait to have a particular decile or any other percentage chance of rescue:
Those formulae can be inverted to get the number of days to wait to have a particular decile or any other percentage chance of rescue:

Revision as of 11:57, 13 April 2006

In GaiaCat's own words: For Dungeon Level 1, formula is simple: 16/100 chance per day to get rescued. Now for the really messy problem. Chance for being rescued on Dungeon Levels below 1: You have (17-DunLvl) / 10000 chance of being rescued per day for the first Int(100 * LN(DunLvl)^2 + 22) days. After that, you have (17-DunLvl) / 1000 chance of being rescued per day.

If x = Int(100*ln(Dunlvl)^2+22), p=(17-DunLvl)^2/10000, and P=10*p,

your cumulative chance of being rescued any day up to day n is:

1-(1-p)^n, if n < x


1-(1-p)^x*(1-P)^(n-x), if n > x

Those formulae can be inverted to get the number of days to wait to have a particular decile or any other percentage chance of rescue:
n=x+(ln(1-decile)-x*ln(1-p))/ln(1-P), if n > x, the other formula is easy enough to invert.

For convenience I have done the calculations for three quartiles, 90% and 99%:

Level 25% 50% 75% 90% 99%
2 82,1 108,9 154,8 215,4 367,8
3 148,3 177,1 226,2 291,2 454,5
4 214,7 245,7 298,7 368,7 544,7
5 276,9 310,5 367,9 443,8 634,5
6 334,9 371,5 434,2 517,0 725,2
7 388,8 429,1 498,1 589,3 818,4
8 440,6 485,5 562,1 663,5 918,2
9 489,6 540,1 626,4 740,5 1027,1
10 537,9 595,6 694,3 824,8 1152,6
11 584,4 651,7 766,9 919,2 1301,8
12 632,6 713,5 851,8 1034,6 1494,0
13 683,0 784,2 957,1 1185,7 1760,2
14 742,0 877,0 1107,7 1412,7 2179,0
15 823,3 1025,8 1372,0 1829,7 2979,8

So if you die on level 15, you have a 99% chance of being rescued before the 3000-th day. Better not to think of the remaining 1%.

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