Hello,
A player in my saga does not really care about his magus gaining warping points. He has already comprehend a twilight and does not fear doing it again.
To set my mind on that matter I'd like to see some figures, for instance the probabilities to enter long or eternal twilight depending on the warping score. Are there such maths somewhere on this forum?
Thanks!
This is based on the die roll for most part and characteristics of the character... so no stats ^^.
My criamon magus has gone 5 times in twilight in 3 adventures, but with his 8+2 enigmatic wisdom, he also managed to comprend 5 times for a big gain of a major focus and a big spell of crvi (which is the one i use to go in twilight now) (yes, i'm going voluntary in twilight... who said that a +6 twilight points CrVi personnal spell was not wonderful? 
There's so much more involved than just the Warping Score; it's hard to answer your question without many pages. (I'm really tired right now, so hopefully these are right.) First you have to have a big enough botch. This depends on the number of botch dice but never exceeds 10%.
1 die -- 0%
2 dice -- 0.1% w/ 2 points
3 dice -- 0.27% w/ 2 points and 0.01% w/ 3 points
4 dice -- 0.486% w/ 2 points, 0.036% w/ 3 points, and 0.001% w/ 4 points
5 dice -- 0.729% w/ 2 points, 0.081% w/ 3 points, 0.0045% w/ 4 points, and 0.0001% w/ 5 points
6 dice -- 0.91854% w/ 2 points, 0.1458% w/ 3 points, 0.01215% w/ 4 points, 0.00054% w/ 5 points, and 0.00001% w/ 6 points
etc.
Second you have the probability of entering Twilight which is based on the number of Warping Points gained as well as many other factors. There are way too many factors, so I'm writing these by the total of the magus's stuff minus the total of the storyguide's stuff (rolls not included). Remember that the tie favors the magus and that the storyguide cannot botch. I'm not going to work most of these out perfectly.
10 -- around 2%
9 --
8 --
7 --
6 --
5 --
4 --
3 --
2 --
1 --
0 -- 45.1%
-1 --
-2 --
-3 --
-4 --
-5 --
-6 --
-7 --
-8 --
-9 --
-10 -- around 99%
(I'll finish later.)
Third you have the probability of controlling it well enough or not. This depends on Intelligence, Warping Score, and the Warping Points gained. Comprehension itself, though related, is irrelevant.
(I'll edit this later.)
In three adventures you managed a greater than 10-die botch and another 6-die botch? Wow. Or is your storyguide generous? Or are you using the extra 1d10 Warping Points (which included in ArM5 accidentally) and including those points for the effects (which isn't supposed to happen)?
Chris
Twilight is actually beneficial to young magi, especially Criamon ones. However, as your magus gains Warping Points it becomes less and less beneficial - so just let him go through his Twilights, don't sweat it. It's a self-correcting problem. Sooner than he thinks, he'll end up stuck in Twilight for a few years while everyone else adventures, or ends up having a bad twilight episode.
The real down-side to accumulating warping points is that it cuts your life - it's warping, not aging, that usually limits magi age. However, even this is not true if you allow the magus to pursue immortality. So really, warping isn't that big of a cost.
I recommend not to sweat it. It's a nice little feature of the rules, and if the player likes it - fine.
If it bothers you, you could engineer environments and situations that are likely to increase his Twilight and make it bad. Have him inadvertantly use Infernally tainted raw vis, or have him enter the Magic Realm to effectively go through twilight as an adventure (where you control the "bad things" much more).
I can't help you with the actual math, I'm afraid.
Being stuck in twilight is the best thing a criamon magus can expect
I'm not sure it was accidentally included - certainly the errata mentions it to further explain an example, not to contradict it, and without that (or making Warping vastly more common and easy to acquire), Twilight would be barely worth mentioning - yes, wizards would fade away briefly and perhaps acquire a minor Twilight scar but the acquition of knowledge and understanding that beneficial Twilight grants would effectively be impossible - no new Virtues or wisdom would appear, and House Criamon would just be a group of weirdos who vanish more often and come back slightly faster without the insight they claim.
In an attempt to answer the OP's questions, here is a table of simulated experiments.
Int 0 - Warping 0 - Botch Dice 1
[98982, 1018, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 0 - Botch Dice 2
[98121, 1879, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 0 - Botch Dice 3
[97315, 2685, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 0 - Botch Dice 4
[96602, 3398, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 1 - Botch Dice 1
[37562, 61446, 992, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 1 - Botch Dice 2
[37408, 60651, 1941, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 1 - Botch Dice 3
[37429, 59913, 2658, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 1 - Botch Dice 4
[37505, 59115, 3380, 0, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 2 - Botch Dice 1
[23094, 6564, 69326, 1016, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 2 - Botch Dice 2
[23632, 6388, 68197, 1783, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 2 - Botch Dice 3
[23274, 6463, 67461, 2802, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 2 - Botch Dice 4
[23400, 6568, 66591, 3441, 0, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 3 - Botch Dice 1
[13126, 4569, 5460, 75836, 1009, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 3 - Botch Dice 2
[13218, 4550, 5507, 74784, 1941, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 3 - Botch Dice 3
[13231, 4543, 5538, 73975, 2713, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 3 - Botch Dice 4
[13213, 4688, 5657, 72921, 3521, 0, 0, 0, 0, 0, 0]
Int 0 - Warping 4 - Botch Dice 1
[7311, 2385, 3579, 4461, 81236, 1028, 0, 0, 0, 0, 0]
Int 0 - Warping 4 - Botch Dice 2
[7205, 2450, 3630, 4481, 80451, 1783, 0, 0, 0, 0, 0]
Int 0 - Warping 4 - Botch Dice 3
[7313, 2472, 3573, 4418, 79535, 2689, 0, 0, 0, 0, 0]
Int 0 - Warping 4 - Botch Dice 4
[7279, 2474, 3556, 4372, 78975, 3344, 0, 0, 0, 0, 0]
Int 0 - Warping 5 - Botch Dice 1
[4368, 1468, 1575, 2421, 3356, 85835, 977, 0, 0, 0, 0]
Int 0 - Warping 5 - Botch Dice 2
[4376, 1363, 1614, 2459, 3394, 84935, 1859, 0, 0, 0, 0]
Int 0 - Warping 5 - Botch Dice 3
[4310, 1455, 1536, 2467, 3556, 83954, 2722, 0, 0, 0, 0]
Int 0 - Warping 5 - Botch Dice 4
[4387, 1407, 1587, 2432, 3541, 83224, 3422, 0, 0, 0, 0]
Int 0 - Warping 6 - Botch Dice 1
[3342, 532, 629, 1379, 1574, 2328, 89267, 949, 0, 0, 0]
Int 0 - Warping 6 - Botch Dice 2
[3270, 522, 652, 1449, 1530, 2349, 88305, 1923, 0, 0, 0]
Int 0 - Warping 6 - Botch Dice 3
[3150, 514, 644, 1384, 1544, 2309, 87725, 2730, 0, 0, 0]
Int 0 - Warping 6 - Botch Dice 4
[3334, 517, 618, 1453, 1561, 2332, 86993, 3192, 0, 0, 0]
Int 0 - Warping 7 - Botch Dice 1
[2248, 421, 661, 540, 663, 1471, 1426, 91589, 981, 0, 0]
Int 0 - Warping 7 - Botch Dice 2
[2317, 414, 646, 533, 661, 1375, 1442, 90729, 1883, 0, 0]
Int 0 - Warping 7 - Botch Dice 3
[2255, 445, 681, 514, 619, 1421, 1456, 89921, 2688, 0, 0]
Int 0 - Warping 7 - Botch Dice 4
[2312, 391, 644, 530, 618, 1463, 1388, 89126, 3528, 0, 0]
Int 0 - Warping 8 - Botch Dice 1
[1500, 315, 510, 406, 655, 494, 671, 1315, 93120, 1014, 0]
Int 0 - Warping 8 - Botch Dice 2
[1647, 304, 518, 431, 689, 517, 676, 1278, 92047, 1893, 0]
Int 0 - Warping 8 - Botch Dice 3
[1568, 324, 527, 414, 681, 507, 597, 1334, 91403, 2645, 0]
Int 0 - Warping 8 - Botch Dice 4
[1500, 322, 567, 413, 666, 526, 678, 1303, 90572, 3453, 0]
Int 0 - Warping 9 - Botch Dice 1
[992, 211, 418, 316, 530, 414, 628, 502, 525, 94449, 1015]
Int 0 - Warping 9 - Botch Dice 2
[1055, 196, 422, 341, 512, 423, 613, 502, 564, 93491, 1881]
Int 0 - Warping 9 - Botch Dice 3
[1007, 226, 445, 383, 517, 430, 643, 540, 542, 92563, 2704]
Int 0 - Warping 9 - Botch Dice 4
[1031, 250, 396, 345, 542, 450, 678, 539, 585, 91743, 3441]
Int 0 - Warping 10 - Botch Dice 1
[650, 121, 331, 225, 449, 317, 549, 414, 678, 433, 95833]
Int 0 - Warping 10 - Botch Dice 2
[647, 105, 325, 207, 430, 309, 593, 397, 651, 413, 95923]
Int 0 - Warping 10 - Botch Dice 3
[717, 105, 312, 225, 417, 329, 534, 447, 669, 405, 95840]
Int 0 - Warping 10 - Botch Dice 4
[651, 129, 304, 230, 437, 367, 581, 396, 652, 439, 95814]
Int 1 - Warping 0 - Botch Dice 1
[98995, 1005, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 0 - Botch Dice 2
[98121, 1879, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 0 - Botch Dice 3
[97360, 2640, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 0 - Botch Dice 4
[96602, 3398, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 1 - Botch Dice 1
[45178, 53828, 994, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 1 - Botch Dice 2
[45230, 52915, 1855, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 1 - Botch Dice 3
[45237, 52001, 2762, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 1 - Botch Dice 4
[45139, 51415, 3446, 0, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 2 - Botch Dice 1
[29932, 7685, 61392, 991, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 2 - Botch Dice 2
[29747, 7610, 60830, 1813, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 2 - Botch Dice 3
[30019, 7681, 59635, 2665, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 2 - Botch Dice 4
[29939, 7682, 58950, 3429, 0, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 3 - Botch Dice 1
[17940, 5457, 6538, 69085, 980, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 3 - Botch Dice 2
[17759, 5698, 6550, 68134, 1859, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 3 - Botch Dice 3
[17806, 5513, 6521, 67474, 2686, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 3 - Botch Dice 4
[17623, 5605, 6589, 66737, 3446, 0, 0, 0, 0, 0, 0]
Int 1 - Warping 4 - Botch Dice 1
[9600, 3488, 4377, 5682, 75851, 1002, 0, 0, 0, 0, 0]
Int 1 - Warping 4 - Botch Dice 2
[9632, 3620, 4423, 5669, 74724, 1932, 0, 0, 0, 0, 0]
Int 1 - Warping 4 - Botch Dice 3
[9671, 3607, 4408, 5677, 73979, 2658, 0, 0, 0, 0, 0]
Int 1 - Warping 4 - Botch Dice 4
[9796, 3579, 4377, 5599, 73268, 3381, 0, 0, 0, 0, 0]
Int 1 - Warping 5 - Botch Dice 1
[5770, 1535, 2400, 3490, 4474, 81292, 1039, 0, 0, 0, 0]
Int 1 - Warping 5 - Botch Dice 2
[5777, 1506, 2431, 3448, 4471, 80414, 1953, 0, 0, 0, 0]
Int 1 - Warping 5 - Botch Dice 3
[5702, 1596, 2443, 3490, 4542, 79583, 2644, 0, 0, 0, 0]
Int 1 - Warping 5 - Botch Dice 4
[5811, 1587, 2343, 3455, 4482, 78969, 3353, 0, 0, 0, 0]
Int 1 - Warping 6 - Botch Dice 1
[3868, 659, 1349, 1557, 2249, 3613, 85713, 992, 0, 0, 0]
Int 1 - Warping 6 - Botch Dice 2
[4042, 678, 1460, 1629, 2347, 3503, 84457, 1884, 0, 0, 0]
Int 1 - Warping 6 - Botch Dice 3
[3851, 701, 1506, 1617, 2345, 3553, 83744, 2683, 0, 0, 0]
Int 1 - Warping 6 - Botch Dice 4
[3907, 655, 1346, 1593, 2319, 3566, 83307, 3307, 0, 0, 0]
Int 1 - Warping 7 - Botch Dice 1
[2794, 644, 552, 660, 1430, 1435, 2400, 89099, 986, 0, 0]
Int 1 - Warping 7 - Botch Dice 2
[2780, 663, 514, 634, 1398, 1500, 2510, 88174, 1827, 0, 0]
Int 1 - Warping 7 - Botch Dice 3
[2753, 642, 513, 639, 1484, 1478, 2357, 87472, 2662, 0, 0]
Int 1 - Warping 7 - Botch Dice 4
[2727, 656, 511, 614, 1328, 1474, 2371, 86939, 3380, 0, 0]
Int 1 - Warping 8 - Botch Dice 1
[1859, 520, 388, 681, 528, 628, 1288, 1547, 91518, 1043, 0]
Int 1 - Warping 8 - Botch Dice 2
[1901, 536, 426, 662, 507, 672, 1286, 1607, 90524, 1879, 0]
Int 1 - Warping 8 - Botch Dice 3
[1918, 533, 414, 600, 548, 663, 1304, 1607, 89757, 2656, 0]
Int 1 - Warping 8 - Botch Dice 4
[1820, 545, 391, 708, 534, 634, 1284, 1562, 89017, 3505, 0]
Int 1 - Warping 9 - Botch Dice 1
[1172, 460, 334, 544, 420, 628, 523, 495, 1388, 93044, 992]
Int 1 - Warping 9 - Botch Dice 2
[1251, 429, 347, 562, 431, 659, 507, 626, 1389, 91907, 1892]
Int 1 - Warping 9 - Botch Dice 3
[1247, 434, 310, 537, 422, 644, 482, 573, 1455, 91186, 2710]
Int 1 - Warping 9 - Botch Dice 4
[1242, 455, 331, 543, 472, 626, 529, 541, 1332, 90453, 3476]
Int 1 - Warping 10 - Botch Dice 1
[767, 324, 208, 465, 323, 521, 430, 649, 426, 668, 95219]
Int 1 - Warping 10 - Botch Dice 2
[803, 334, 216, 458, 313, 573, 435, 652, 406, 642, 95168]
Int 1 - Warping 10 - Botch Dice 3
[727, 314, 211, 459, 308, 518, 387, 680, 410, 656, 95330]
Int 1 - Warping 10 - Botch Dice 4
[803, 334, 221, 468, 305, 532, 439, 628, 440, 595, 95235]
Int 2 - Warping 0 - Botch Dice 1
[99002, 998, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 0 - Botch Dice 2
[98131, 1869, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 0 - Botch Dice 3
[97400, 2600, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 0 - Botch Dice 4
[96454, 3546, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 1 - Botch Dice 1
[55076, 43900, 1024, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 1 - Botch Dice 2
[54635, 43482, 1883, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 1 - Botch Dice 3
[54243, 43003, 2754, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 1 - Botch Dice 4
[54413, 42178, 3409, 0, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 2 - Botch Dice 1
[37774, 7693, 53549, 984, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 2 - Botch Dice 2
[37625, 7666, 52936, 1773, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 2 - Botch Dice 3
[37564, 7699, 52031, 2706, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 2 - Botch Dice 4
[37327, 7865, 51453, 3355, 0, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 3 - Botch Dice 1
[22983, 6667, 7578, 61751, 1021, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 3 - Botch Dice 2
[23348, 6566, 7625, 60642, 1819, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 3 - Botch Dice 3
[23104, 6640, 7644, 59900, 2712, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 3 - Botch Dice 4
[23214, 6643, 7639, 59113, 3391, 0, 0, 0, 0, 0, 0]
Int 2 - Warping 4 - Botch Dice 1
[13527, 4400, 5662, 6647, 68762, 1002, 0, 0, 0, 0, 0]
Int 2 - Warping 4 - Botch Dice 2
[13222, 4454, 5753, 6609, 68075, 1887, 0, 0, 0, 0, 0]
Int 2 - Warping 4 - Botch Dice 3
[13421, 4497, 5608, 6532, 67235, 2707, 0, 0, 0, 0, 0]
Int 2 - Warping 4 - Botch Dice 4
[13196, 4275, 5572, 6405, 67098, 3454, 0, 0, 0, 0, 0]
Int 2 - Warping 5 - Botch Dice 1
[7345, 2511, 3436, 4517, 5509, 75665, 1017, 0, 0, 0, 0]
Int 2 - Warping 5 - Botch Dice 2
[7309, 2356, 3418, 4581, 5589, 74942, 1805, 0, 0, 0, 0]
Int 2 - Warping 5 - Botch Dice 3
[7550, 2473, 3498, 4495, 5594, 73697, 2693, 0, 0, 0, 0]
Int 2 - Warping 5 - Botch Dice 4
[7408, 2423, 3506, 4288, 5636, 73353, 3386, 0, 0, 0, 0]
Int 2 - Warping 6 - Botch Dice 1
[4518, 1369, 1585, 2305, 3575, 4519, 81129, 1000, 0, 0, 0]
Int 2 - Warping 6 - Botch Dice 2
[4394, 1410, 1673, 2327, 3572, 4503, 80268, 1853, 0, 0, 0]
Int 2 - Warping 6 - Botch Dice 3
[4476, 1447, 1583, 2361, 3490, 4379, 79511, 2753, 0, 0, 0]
Int 2 - Warping 6 - Botch Dice 4
[4426, 1363, 1523, 2356, 3393, 4436, 79050, 3453, 0, 0, 0]
Int 2 - Warping 7 - Botch Dice 1
[3370, 498, 675, 1400, 1504, 2408, 3491, 85656, 998, 0, 0]
Int 2 - Warping 7 - Botch Dice 2
[3322, 519, 666, 1449, 1415, 2404, 3417, 84887, 1921, 0, 0]
Int 2 - Warping 7 - Botch Dice 3
[3323, 529, 678, 1469, 1450, 2389, 3455, 83929, 2778, 0, 0]
Int 2 - Warping 7 - Botch Dice 4
[3329, 532, 662, 1433, 1457, 2402, 3419, 83419, 3347, 0, 0]
Int 2 - Warping 8 - Botch Dice 1
[2513, 420, 664, 519, 646, 1304, 1585, 2326, 89049, 974, 0]
Int 2 - Warping 8 - Botch Dice 2
[2429, 393, 655, 492, 626, 1373, 1603, 2362, 88140, 1927, 0]
Int 2 - Warping 8 - Botch Dice 3
[2469, 434, 706, 509, 648, 1317, 1605, 2343, 87273, 2696, 0]
Int 2 - Warping 8 - Botch Dice 4
[2333, 398, 704, 518, 648, 1314, 1582, 2227, 86834, 3442, 0]
Int 2 - Warping 9 - Botch Dice 1
[1678, 320, 529, 429, 670, 501, 551, 1408, 1490, 91402, 1022]
Int 2 - Warping 9 - Botch Dice 2
[1672, 322, 523, 453, 624, 508, 577, 1445, 1532, 90377, 1967]
Int 2 - Warping 9 - Botch Dice 3
[1634, 353, 522, 406, 654, 502, 559, 1353, 1493, 89659, 2865]
Int 2 - Warping 9 - Botch Dice 4
[1708, 330, 569, 447, 646, 474, 520, 1387, 1394, 89026, 3499]
Int 2 - Warping 10 - Botch Dice 1
[1058, 219, 446, 344, 548, 385, 657, 429, 664, 1327, 93923]
Int 2 - Warping 10 - Botch Dice 2
[1095, 195, 460, 281, 534, 409, 634, 430, 630, 1301, 94031]
Int 2 - Warping 10 - Botch Dice 3
[1126, 224, 453, 315, 528, 394, 659, 412, 674, 1308, 93907]
Int 2 - Warping 10 - Botch Dice 4
[1098, 206, 463, 316, 516, 434, 674, 417, 596, 1395, 93885]
Int 3 - Warping 0 - Botch Dice 1
[98964, 1036, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 0 - Botch Dice 2
[98087, 1913, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 0 - Botch Dice 3
[97353, 2647, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 0 - Botch Dice 4
[96511, 3489, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 1 - Botch Dice 1
[62503, 36476, 1021, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 1 - Botch Dice 2
[62519, 35606, 1875, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 1 - Botch Dice 3
[62437, 34925, 2638, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 1 - Botch Dice 4
[62157, 34391, 3452, 0, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 2 - Botch Dice 1
[45428, 9310, 44247, 1015, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 2 - Botch Dice 2
[45163, 9467, 43471, 1899, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 2 - Botch Dice 3
[45261, 9341, 42668, 2730, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 2 - Botch Dice 4
[45028, 9486, 41993, 3493, 0, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 3 - Botch Dice 1
[29985, 7531, 7556, 53907, 1021, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 3 - Botch Dice 2
[29792, 7647, 7654, 53028, 1879, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 3 - Botch Dice 3
[29927, 7561, 7772, 52037, 2703, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 3 - Botch Dice 4
[29972, 7654, 7837, 51191, 3346, 0, 0, 0, 0, 0, 0]
Int 3 - Warping 4 - Botch Dice 1
[17653, 5710, 6522, 7591, 61529, 995, 0, 0, 0, 0, 0]
Int 3 - Warping 4 - Botch Dice 2
[17754, 5669, 6487, 7492, 60709, 1889, 0, 0, 0, 0, 0]
Int 3 - Warping 4 - Botch Dice 3
[17747, 5699, 6486, 7653, 59725, 2690, 0, 0, 0, 0, 0]
Int 3 - Warping 4 - Botch Dice 4
[17765, 5616, 6604, 7512, 59029, 3474, 0, 0, 0, 0, 0]
Int 3 - Warping 5 - Botch Dice 1
[9890, 3497, 4507, 5578, 6539, 68939, 1050, 0, 0, 0, 0]
Int 3 - Warping 5 - Botch Dice 2
[9932, 3451, 4516, 5659, 6464, 68069, 1909, 0, 0, 0, 0]
Int 3 - Warping 5 - Botch Dice 3
[9979, 3388, 4474, 5503, 6561, 67445, 2650, 0, 0, 0, 0]
Int 3 - Warping 5 - Botch Dice 4
[9698, 3586, 4452, 5526, 6488, 66844, 3406, 0, 0, 0, 0]
Int 3 - Warping 6 - Botch Dice 1
[5784, 1591, 2338, 3564, 4441, 5631, 75670, 981, 0, 0, 0]
Int 3 - Warping 6 - Botch Dice 2
[5905, 1603, 2359, 3476, 4434, 5595, 74703, 1925, 0, 0, 0]
Int 3 - Warping 6 - Botch Dice 3
[5999, 1632, 2383, 3585, 4412, 5606, 73709, 2674, 0, 0, 0]
Int 3 - Warping 6 - Botch Dice 4
[5908, 1565, 2397, 3595, 4334, 5572, 73259, 3370, 0, 0, 0]
Int 3 - Warping 7 - Botch Dice 1
[3861, 601, 1393, 1465, 2374, 3336, 4348, 81596, 1026, 0, 0]
Int 3 - Warping 7 - Botch Dice 2
[4005, 658, 1418, 1475, 2435, 3400, 4388, 80371, 1850, 0, 0]
Int 3 - Warping 7 - Botch Dice 3
[3852, 670, 1407, 1471, 2425, 3618, 4456, 79446, 2655, 0, 0]
Int 3 - Warping 7 - Botch Dice 4
[4014, 705, 1454, 1548, 2455, 3495, 4295, 78652, 3382, 0, 0]
Int 3 - Warping 8 - Botch Dice 1
[2885, 676, 516, 647, 1366, 1596, 2309, 3514, 85502, 989, 0]
Int 3 - Warping 8 - Botch Dice 2
[2843, 649, 530, 647, 1302, 1504, 2342, 3348, 84865, 1970, 0]
Int 3 - Warping 8 - Botch Dice 3
[2920, 716, 514, 644, 1355, 1503, 2294, 3443, 83775, 2836, 0]
Int 3 - Warping 8 - Botch Dice 4
[2870, 628, 515, 631, 1341, 1597, 2271, 3458, 83226, 3463, 0]
Int 3 - Warping 9 - Botch Dice 1
[1981, 542, 447, 634, 515, 578, 1404, 1506, 2286, 89078, 1029]
Int 3 - Warping 9 - Botch Dice 2
[1993, 557, 415, 719, 498, 585, 1402, 1492, 2397, 88029, 1913]
Int 3 - Warping 9 - Botch Dice 3
[1931, 575, 411, 690, 475, 536, 1431, 1482, 2291, 87447, 2731]
Int 3 - Warping 9 - Botch Dice 4
[1977, 521, 432, 655, 502, 542, 1421, 1447, 2323, 86763, 3417]
Int 3 - Warping 10 - Botch Dice 1
[1349, 417, 304, 518, 399, 659, 435, 614, 1303, 1446, 92556]
Int 3 - Warping 10 - Botch Dice 2
[1361, 435, 307, 520, 419, 679, 417, 642, 1336, 1413, 92471]
Int 3 - Warping 10 - Botch Dice 3
[1365, 453, 331, 533, 417, 658, 458, 659, 1339, 1479, 92308]
Int 3 - Warping 10 - Botch Dice 4
[1288, 458, 306, 537, 412, 626, 386, 605, 1337, 1474, 92571]
Int 4 - Warping 0 - Botch Dice 1
[99005, 995, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 0 - Botch Dice 2
[98072, 1928, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 0 - Botch Dice 3
[97361, 2639, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 0 - Botch Dice 4
[96574, 3426, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 1 - Botch Dice 1
[69738, 29231, 1031, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 1 - Botch Dice 2
[70205, 27871, 1924, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 1 - Botch Dice 3
[69842, 27444, 2714, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 1 - Botch Dice 4
[69536, 26978, 3486, 0, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 2 - Botch Dice 1
[54982, 7790, 36200, 1028, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 2 - Botch Dice 2
[54659, 7809, 35607, 1925, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 2 - Botch Dice 3
[54434, 7724, 35210, 2632, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 2 - Botch Dice 4
[54512, 7676, 34350, 3462, 0, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 3 - Botch Dice 1
[37294, 7752, 9441, 44472, 1041, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 3 - Botch Dice 2
[37397, 7744, 9277, 43633, 1949, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 3 - Botch Dice 3
[37454, 7800, 9254, 42723, 2769, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 3 - Botch Dice 4
[37443, 7685, 9289, 42164, 3419, 0, 0, 0, 0, 0, 0]
Int 4 - Warping 4 - Botch Dice 1
[23422, 6429, 7571, 7733, 53882, 963, 0, 0, 0, 0, 0]
Int 4 - Warping 4 - Botch Dice 2
[23549, 6512, 7609, 7734, 52701, 1895, 0, 0, 0, 0, 0]
Int 4 - Warping 4 - Botch Dice 3
[23361, 6662, 7448, 7829, 52002, 2698, 0, 0, 0, 0, 0]
Int 4 - Warping 4 - Botch Dice 4
[23331, 6461, 7474, 7819, 51478, 3437, 0, 0, 0, 0, 0]
Int 4 - Warping 5 - Botch Dice 1
[13350, 4433, 5600, 6454, 7454, 61738, 971, 0, 0, 0, 0]
Int 4 - Warping 5 - Botch Dice 2
[13215, 4485, 5601, 6490, 7628, 60714, 1867, 0, 0, 0, 0]
Int 4 - Warping 5 - Botch Dice 3
[13208, 4538, 5497, 6634, 7649, 59851, 2623, 0, 0, 0, 0]
Int 4 - Warping 5 - Botch Dice 4
[13211, 4480, 5505, 6662, 7521, 59232, 3389, 0, 0, 0, 0]
Int 4 - Warping 6 - Botch Dice 1
[7553, 2302, 3627, 4386, 5592, 6468, 69050, 1022, 0, 0, 0]
Int 4 - Warping 6 - Botch Dice 2
[7540, 2309, 3596, 4351, 5551, 6565, 68163, 1925, 0, 0, 0]
Int 4 - Warping 6 - Botch Dice 3
[7645, 2317, 3459, 4406, 5497, 6512, 67504, 2660, 0, 0, 0]
Int 4 - Warping 6 - Botch Dice 4
[7377, 2379, 3646, 4371, 5527, 6607, 66647, 3446, 0, 0, 0]
Int 4 - Warping 7 - Botch Dice 1
[4643, 1398, 1460, 2407, 3482, 4408, 5543, 75645, 1014, 0, 0]
Int 4 - Warping 7 - Botch Dice 2
[4498, 1322, 1495, 2492, 3401, 4509, 5529, 74893, 1861, 0, 0]
Int 4 - Warping 7 - Botch Dice 3
[4689, 1480, 1428, 2316, 3464, 4373, 5608, 73903, 2739, 0, 0]
Int 4 - Warping 7 - Botch Dice 4
[4570, 1421, 1513, 2382, 3484, 4389, 5608, 73175, 3458, 0, 0]
Int 4 - Warping 8 - Botch Dice 1
[3530, 500, 592, 1339, 1559, 2275, 3476, 4473, 81213, 1043, 0]
Int 4 - Warping 8 - Botch Dice 2
[3546, 547, 680, 1334, 1571, 2287, 3439, 4401, 80258, 1937, 0]
Int 4 - Warping 8 - Botch Dice 3
[3522, 550, 635, 1374, 1620, 2323, 3585, 4428, 79279, 2684, 0]
Int 4 - Warping 8 - Botch Dice 4
[3464, 513, 609, 1315, 1538, 2338, 3485, 4300, 79059, 3379, 0]
Int 4 - Warping 9 - Botch Dice 1
[2554, 435, 666, 515, 575, 1388, 1471, 2297, 3459, 85658, 982]
Int 4 - Warping 9 - Botch Dice 2
[2453, 475, 706, 504, 514, 1398, 1507, 2254, 3520, 84760, 1909]
Int 4 - Warping 9 - Botch Dice 3
[2529, 419, 674, 551, 542, 1435, 1464, 2295, 3417, 83986, 2688]
Int 4 - Warping 9 - Botch Dice 4
[2483, 417, 593, 538, 532, 1393, 1521, 2379, 3528, 83132, 3484]
Int 4 - Warping 10 - Botch Dice 1
[1857, 355, 528, 402, 661, 424, 605, 1370, 1480, 2367, 89951]
Int 4 - Warping 10 - Botch Dice 2
[1778, 334, 547, 445, 675, 458, 628, 1391, 1491, 2377, 89876]
Int 4 - Warping 10 - Botch Dice 3
[1844, 307, 574, 439, 671, 402, 592, 1245, 1496, 2341, 90089]
Int 4 - Warping 10 - Botch Dice 4
[1848, 309, 536, 436, 642, 406, 631, 1282, 1501, 2355, 90054]
Int 5 - Warping 0 - Botch Dice 1
[99022, 978, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 0 - Botch Dice 2
[98156, 1844, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 0 - Botch Dice 3
[97250, 2750, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 0 - Botch Dice 4
[96502, 3498, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 1 - Botch Dice 1
[76445, 22544, 1011, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 1 - Botch Dice 2
[76552, 21487, 1961, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 1 - Botch Dice 3
[75997, 21325, 2678, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 1 - Botch Dice 4
[75804, 20725, 3471, 0, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 2 - Botch Dice 1
[62412, 7576, 29005, 1007, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 2 - Botch Dice 2
[62244, 7328, 28455, 1973, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 2 - Botch Dice 3
[62244, 7385, 27602, 2769, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 2 - Botch Dice 4
[62178, 7322, 27069, 3431, 0, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 3 - Botch Dice 1
[45024, 9519, 7768, 36716, 973, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 3 - Botch Dice 2
[45186, 9628, 7709, 35555, 1922, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 3 - Botch Dice 3
[45064, 9361, 7775, 35087, 2713, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 3 - Botch Dice 4
[45280, 9362, 7615, 34205, 3538, 0, 0, 0, 0, 0, 0]
Int 5 - Warping 4 - Botch Dice 1
[29777, 7659, 7595, 9703, 44264, 1002, 0, 0, 0, 0, 0]
Int 5 - Warping 4 - Botch Dice 2
[29906, 7580, 7799, 9436, 43346, 1933, 0, 0, 0, 0, 0]
Int 5 - Warping 4 - Botch Dice 3
[30024, 7678, 7637, 9497, 42486, 2678, 0, 0, 0, 0, 0]
Int 5 - Warping 4 - Botch Dice 4
[29783, 7622, 7770, 9237, 42229, 3359, 0, 0, 0, 0, 0]
Int 5 - Warping 5 - Botch Dice 1
[17823, 5615, 6598, 7483, 7785, 53700, 996, 0, 0, 0, 0]
Int 5 - Warping 5 - Botch Dice 2
[17955, 5536, 6545, 7644, 7732, 52734, 1854, 0, 0, 0, 0]
Int 5 - Warping 5 - Botch Dice 3
[17803, 5567, 6532, 7409, 7722, 52295, 2672, 0, 0, 0, 0]
Int 5 - Warping 5 - Botch Dice 4
[17921, 5545, 6599, 7441, 7837, 51265, 3392, 0, 0, 0, 0]
Int 5 - Warping 6 - Botch Dice 1
[9780, 3685, 4435, 5563, 6427, 7333, 61668, 1109, 0, 0, 0]
Int 5 - Warping 6 - Botch Dice 2
[9931, 3542, 4399, 5689, 6532, 7586, 60525, 1796, 0, 0, 0]
Int 5 - Warping 6 - Botch Dice 3
[9814, 3554, 4420, 5537, 6559, 7575, 59803, 2738, 0, 0, 0]
Int 5 - Warping 6 - Botch Dice 4
[9805, 3600, 4390, 5617, 6625, 7710, 58849, 3404, 0, 0, 0]
Int 5 - Warping 7 - Botch Dice 1
[5982, 1498, 2446, 3558, 4342, 5542, 6588, 69074, 970, 0, 0]
Int 5 - Warping 7 - Botch Dice 2
[6029, 1485, 2399, 3439, 4279, 5546, 6459, 68478, 1886, 0, 0]
Int 5 - Warping 7 - Botch Dice 3
[6063, 1477, 2457, 3493, 4582, 5521, 6540, 67139, 2728, 0, 0]
Int 5 - Warping 7 - Botch Dice 4
[5933, 1502, 2400, 3574, 4379, 5572, 6427, 66790, 3423, 0, 0]
Int 5 - Warping 8 - Botch Dice 1
[3976, 622, 1205, 1541, 2385, 3452, 4401, 5612, 75756, 1050, 0]
Int 5 - Warping 8 - Botch Dice 2
[4028, 631, 1385, 1611, 2277, 3396, 4463, 5607, 74751, 1851, 0]
Int 5 - Warping 8 - Botch Dice 3
[4188, 681, 1314, 1624, 2338, 3411, 4471, 5589, 73726, 2658, 0]
Int 5 - Warping 8 - Botch Dice 4
[4066, 660, 1329, 1493, 2283, 3438, 4437, 5647, 73212, 3435, 0]
Int 5 - Warping 9 - Botch Dice 1
[3042, 672, 504, 530, 1425, 1432, 2351, 3408, 4441, 81217, 978]
Int 5 - Warping 9 - Botch Dice 2
[2931, 673, 537, 514, 1463, 1478, 2349, 3403, 4380, 80334, 1938]
Int 5 - Warping 9 - Botch Dice 3
[2948, 676, 523, 562, 1412, 1448, 2346, 3448, 4530, 79427, 2680]
Int 5 - Warping 9 - Botch Dice 4
[2912, 698, 585, 534, 1357, 1517, 2336, 3395, 4377, 78945, 3344]
Int 5 - Warping 10 - Botch Dice 1
[2092, 579, 435, 669, 419, 638, 1341, 1553, 2334, 3488, 86452]
Int 5 - Warping 10 - Botch Dice 2
[2176, 513, 399, 683, 377, 597, 1334, 1489, 2331, 3477, 86624]
Int 5 - Warping 10 - Botch Dice 3
[2151, 537, 390, 580, 418, 669, 1335, 1471, 2250, 3509, 86690]
Int 5 - Warping 10 - Botch Dice 4
[2078, 555, 446, 636, 400, 652, 1287, 1459, 2348, 3396, 86743]Each pair of intelligence vs warping score vs botch dice was tried 100 000 times, using python's mersenne twister.
There is a lot of data in that table. If you can give more information, like the Intelligence score of the magus, and maybe a window on his warping score, this can be reduced to something a little more readable.
Edit: Those lists of numbers are not the most useful converyor of information. The first entry is the frequency (of out 100 000 trials) of breaking out of Twilight instantly. The second entry is the frequency of escaping Twilight in a diameter. This pattern continues, so the sixth entry is the frequency of leaving Twilight after a Moon (entry 5 in the Twilight table on p 88 of the main book).
Edit2: Thanks to Callen, fixed a bug with botch dice and updated the table.
Took a while to find this:
I guess he decided to add the die in the errata. But still, officially the extra die of warping points are not added to the triggering points when determining the twilight effects.
Chris
Somewhat off the topic per se - but still regarding Twillight:
What happens if the Magus' roll for resisting Twillight and the roll for the Twillight Intensity (is that what it's called?) tie? What happens then? Does the Magus resist? Is he sucked in? Or some third option, not quite covered?
page 6: "when a total equals or exceeds the ease factor, the action succeeds" - page 88 does not specifically use the term ease factor but I'd say that the vs. total still only needs to be equaled to avoid twilight, not exceeded.
Wow. That's some impressive self-contradiction there. For myself, I think I'll keep the extra die - I find it makes twilight much more unpredictable, dangerous and scary, and thus fun for my group and I. Without it there, given that you're invulnerable when in Twilight, Twilight becomes little more than enforced and unproductive downtime with the pleasant side effect that you don't age during it - a useful way to skip a dull decade* and see the results of someone else's research but not much more.
*Yes, this is an exaggeration, but I liked the feel of the sentence.
Good job, but something doesn't look right. It looks like the chance of a twilight comprehension botch extending the twilight episode were not included. For example, let's look at the second entry. In that case there is a 1% chance of receiving 2 warping points from the original botch. Not knowing what was used for everything else, let's estimate a 50% chance of avoiding the twilight episode. Once inside there are 3 botch dice for comprehension. There's a 10% chance of rolling a 0 followed by a 27.1% chance of botching (which could be a multiple botch); that's a 2.71% of increasing the duration by at least one level. Overall, that's around 0.0135% chance of an increased duration. So with 2 botch dice and 100,000 trials, I would expect to see about 13 or 14 longer duration twilights episodes. While randomness can account for this once, the repeated nature of it and the increasing likelihood as the number of botch dice increase make it seem like there is something incorrect in the algorithm.
Chris
Yes, having had the original answer (my quote was the closest to an erratum at the time since there was nothing in the errata about it until later) I didn't look to see it reversed later. I like the extra die, too. Otherwise you never see the big effects, as you mentioned.
Chris
Thanks. I fixed up the table. (Stupid conflated variable names.)
Based on the original post, it sounded like the magus in question willingly accepted Twilight, so I assumed (s)he would not try to avoid it.
One more problem. It looks like you have twilight episodes occurring on single botches. However, a double botch is required. With only one botch die there should never be a chance of a twilight episode.
Chris
Unless the magus is Twilight Prone, then a single botch will suffice. I suppose I could extend the table to include more botches, but I've never seen anyone get more than 4.
I once rolled twenty-eight botch dice.
I was using a lot of vis 
I totalled exactly 4 botches. Let myself enter twilight to get it over with, failed comprehension, it was messy and I barely survived.
Sounds like fun.
I failed an attempt to invisibly cast a death spell on a frost giant, while invisible and flying. The old fasioned way, using Auram magic and maintaining concentration. Giant had second sight, saw right through me, tried to freeze me, I resisted, cast Perdo Corpus with a ton of vis, I botched, went into twilight, fell out of the sky and broke both my legs, was rescued by grogs, and another magus killed the giant for me and lied and told me I did it so I could save face.