CBoE stats


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Tartarus Sorceror

Posts: 1774

Joined: Tuesday, 23rd December 2014, 23:39

Post Friday, 17th July 2015, 17:59

CBoE stats

There's some misleading information about CBoE floating around. If it fails, it does not actually trigger divinations miscasts. It selects from three possible outcomes, including losing all your MP (the most common result), confusion (a bit less common), and int drain (rare).

It's handled by the _ball_of_energy() function in
https://github.com/crawl/crawl/blob/be3 ... e/evoke.cc

I wrote a short program to see the probabilities of the different outcomes. These are randomized over 10k trials rather than exact, because there are a lot of dice rolls involved and calculating all the possible dice outcomes would be tricky/time consuming.

The first row of output tells you the best case scenario (average mp gain if you succeed).
Each subsequent row tells you the likely outcomes for a given percentage of MP. For instance, here's a row from the evocations = 10 table:
  Code:
MP: 10% int drain: 0.0348 mp loss: 0.8669 confusion: 0.0854 success: 0.0129 avg net mp: -4.21195

That means that if you're at 10% mp and evoke CBOE, you have a 3.5%% chance of int drain, an 87% chance of losing all your MP, an 8.5% chance of confusion, a 1.3% chance of success, and on average, a single use of CBOE will result in you losing 4.2 MP, assuming your max MP is 50. Note that your max MP only affects that last column - all the other columns are unchanged if your max MP is not 50. All other things equal, the average MP gain goes up as your max MP goes down, because you have the potential to lose less MP on a failure.

Here's the table for 10 evocations.
  Code:
Average mp gain if success: 9.5
MP: 10% int drain: 0.0348 mp loss: 0.8669 confusion: 0.0854 success: 0.0129 avg net mp: -4.21195
MP: 20% int drain: 0.0318 mp loss: 0.7365 confusion: 0.0822 success: 0.1495 avg net mp: -5.94475
MP: 30% int drain: 0.033 mp loss: 0.3896 confusion: 0.0847 success: 0.4927 avg net mp: -1.16335
MP: 40% int drain: 0.0326 mp loss: 0.1326 confusion: 0.087 success: 0.7478 avg net mp: 4.4521
MP: 50% int drain: 0.0325 mp loss: 0.0856 confusion: 0.0798 success: 0.8021 avg net mp: 5.47995
MP: 60% int drain: 0.0334 mp loss: 0.0807 confusion: 0.0814 success: 0.8045 avg net mp: 5.22175
MP: 70% int drain: 0.0315 mp loss: 0.0819 confusion: 0.085 success: 0.8016 avg net mp: 4.7487
MP: 80% int drain: 0.0323 mp loss: 0.0862 confusion: 0.0811 success: 0.8004 avg net mp: 4.1558
MP: 90% int drain: 0.0335 mp loss: 0.0818 confusion: 0.0845 success: 0.8002 avg net mp: 3.9209


Here's the table for 15 evocations.
  Code:
Average mp gain if success: 12.0
MP: 10% int drain: 0.0271 mp loss: 0.8832 confusion: 0.059 success: 0.0307 avg net mp: -4.0476
MP: 20% int drain: 0.0188 mp loss: 0.6095 confusion: 0.0558 success: 0.3159 avg net mp: -2.3042
MP: 30% int drain: 0.0206 mp loss: 0.1903 confusion: 0.054 success: 0.7351 avg net mp: 5.9667
MP: 40% int drain: 0.0214 mp loss: 0.0711 confusion: 0.0553 success: 0.8522 avg net mp: 8.8044
MP: 50% int drain: 0.0237 mp loss: 0.0714 confusion: 0.0553 success: 0.8496 avg net mp: 8.4102
MP: 60% int drain: 0.0232 mp loss: 0.0653 confusion: 0.0574 success: 0.8541 avg net mp: 8.2902
MP: 70% int drain: 0.0226 mp loss: 0.0677 confusion: 0.0549 success: 0.8548 avg net mp: 7.8881
MP: 80% int drain: 0.0226 mp loss: 0.0721 confusion: 0.0585 success: 0.8468 avg net mp: 7.2776
MP: 90% int drain: 0.0233 mp loss: 0.0704 confusion: 0.0537 success: 0.8526 avg net mp: 7.0632


Here's the table for 20 evocations.
  Code:
Average mp gain if success: 14.5
MP: 10% int drain: 0.0167 mp loss: 0.8614 confusion: 0.0396 success: 0.0823 avg net mp: -3.11365
MP: 20% int drain: 0.016 mp loss: 0.3518 confusion: 0.0443 success: 0.5879 avg net mp: 5.00655
MP: 30% int drain: 0.0162 mp loss: 0.0686 confusion: 0.0402 success: 0.875 avg net mp: 11.6585
MP: 40% int drain: 0.0159 mp loss: 0.0606 confusion: 0.0452 success: 0.8783 avg net mp: 11.52335
MP: 50% int drain: 0.0172 mp loss: 0.0605 confusion: 0.0443 success: 0.878 avg net mp: 11.2185
MP: 60% int drain: 0.0154 mp loss: 0.0594 confusion: 0.0398 success: 0.8854 avg net mp: 11.0563
MP: 70% int drain: 0.0164 mp loss: 0.0635 confusion: 0.0434 success: 0.8767 avg net mp: 10.48965
MP: 80% int drain: 0.0169 mp loss: 0.0667 confusion: 0.0444 success: 0.872 avg net mp: 9.976
MP: 90% int drain: 0.0179 mp loss: 0.0621 confusion: 0.0414 success: 0.8786 avg net mp: 9.9452


Here's the table for 27 evocations.
  Code:
Average mp gain if success: 18.0
MP: 10% int drain: 0.0101 mp loss: 0.5506 confusion: 0.0323 success: 0.407 avg net mp: 4.573
MP: 20% int drain: 0.0119 mp loss: 0.0589 confusion: 0.0305 success: 0.8987 avg net mp: 15.5876
MP: 30% int drain: 0.0132 mp loss: 0.0526 confusion: 0.0292 success: 0.905 avg net mp: 15.501
MP: 40% int drain: 0.0111 mp loss: 0.0567 confusion: 0.0319 success: 0.9003 avg net mp: 15.0714
MP: 50% int drain: 0.0107 mp loss: 0.0536 confusion: 0.0309 success: 0.9048 avg net mp: 14.9464
MP: 60% int drain: 0.0131 mp loss: 0.0575 confusion: 0.0273 success: 0.9021 avg net mp: 14.5128
MP: 70% int drain: 0.0139 mp loss: 0.0569 confusion: 0.0308 success: 0.8984 avg net mp: 14.1797
MP: 80% int drain: 0.0106 mp loss: 0.0582 confusion: 0.0318 success: 0.8994 avg net mp: 13.8612
MP: 90% int drain: 0.0116 mp loss: 0.0539 confusion: 0.0316 success: 0.9029 avg net mp: 13.8267


(Actually, the "avg net mp" column is slightly inaccurate - an overestimate - b/c it doesn't account for not having enough max MP to gain the full amount. Shouldn't make too much difference except for MP near full, when you wouldn't want to use it anyway).
streaks: 5 fifteen rune octopodes. 15 diverse chars. 13 random chars. 24 NaWn^gozag.
251 total wins Berder hyperborean + misc
83/108 recent wins (76%)
guides: safe tactics value of ac/ev/sh forum toxicity

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Tartarus Sorceror

Posts: 1739

Joined: Tuesday, 13th March 2012, 02:48

Post Friday, 17th July 2015, 20:53

Re: CBoE stats

So it's basically one of the worst possible items an unspoiled character could use.

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duvessa

Tartarus Sorceror

Posts: 1774

Joined: Tuesday, 23rd December 2014, 23:39

Post Friday, 17th July 2015, 23:38

Re: CBoE stats

Yeah, I have little use for CBoE because of the disastrous effect of losing all mp. I only use CBoE if I have a zig character who has a staff of energy/wucad mu and 27 evo, in case of mp loss.
streaks: 5 fifteen rune octopodes. 15 diverse chars. 13 random chars. 24 NaWn^gozag.
251 total wins Berder hyperborean + misc
83/108 recent wins (76%)
guides: safe tactics value of ac/ev/sh forum toxicity

Ziggurat Zagger

Posts: 5382

Joined: Friday, 25th November 2011, 07:36

Post Monday, 20th July 2015, 18:57

Re: CBoE stats

So what would you consider the ideal Zig mana restoring method? I'd say CBoE + clarity, but is a staff of energy + XX evocations considered better? I would be swapping in the staff as I have other weapons I'm normally much more fond of wielding, so it just doesn't seem terribly fast. I suppose it's going to depend on just how much is around you. I could go sublimation of blood, but at high spell power that can do quite a lot of damage to you, when you're missing a lot of mana...And since you're doing a zigg, you probably have necromutation, which means a tons of necromancy spell power.

Tartarus Sorceror

Posts: 1774

Joined: Tuesday, 23rd December 2014, 23:39

Post Tuesday, 21st July 2015, 16:59

Re: CBoE stats

If you're able to be out of lichform with makhleb, the best MP recovery method is sublimation of blood. It reduces the int loss. (Although the int loss may no longer be important at all, now that it goes away with XP).

In lichform, CBOE @ 27 evo + staff of energy + clarity will be serviceable, but you really want CBOE @ 27 evo + staff of wucad mu + clarity. Use staff of energy/wucad mu to reach like 20% MP, then evoke CBOE.

(Actually - maybe now that int loss is less of a problem, simply evoking wucad mu and not switching to CBOE might be optimal) (edit: nope, switching to CBOE is better)
Last edited by Berder on Wednesday, 22nd July 2015, 01:38, edited 1 time in total.
streaks: 5 fifteen rune octopodes. 15 diverse chars. 13 random chars. 24 NaWn^gozag.
251 total wins Berder hyperborean + misc
83/108 recent wins (76%)
guides: safe tactics value of ac/ev/sh forum toxicity

Ziggurat Zagger

Posts: 8786

Joined: Sunday, 5th May 2013, 08:25

Post Wednesday, 22nd July 2015, 01:02

Re: CBoE stats

Just evoking wucad mu was always the best option after channeling was added to it.

Tartarus Sorceror

Posts: 1774

Joined: Tuesday, 23rd December 2014, 23:39

Post Wednesday, 22nd July 2015, 01:36

Re: CBoE stats

Wucad has a 25% fail rate. At 27 evo it gains on average 14 MP per success, but that's multiplied by 0.75 to get 10.5 average gain per evoke, not counting the fact that Wucad will sometimes drain your MP partially. From my 27 evo table for CBOE you can see that the expected MP gain if used at 20% or 30% MP is 15.5. So CBOE is better than Wucad at 27 evo, once you're above the minimum MP for CBOE.
streaks: 5 fifteen rune octopodes. 15 diverse chars. 13 random chars. 24 NaWn^gozag.
251 total wins Berder hyperborean + misc
83/108 recent wins (76%)
guides: safe tactics value of ac/ev/sh forum toxicity

Ziggurat Zagger

Posts: 5382

Joined: Friday, 25th November 2011, 07:36

Post Wednesday, 22nd July 2015, 20:34

Re: CBoE stats

In the average case CBoE restores more mana than Wucad, certainly. But I'd be more worried about hitting 0 mana than Wucad draining 10 mana, especially in the case I'm currently in: a character with multiple +mana items who has a mana pool of 90. If I use a CBoE at 50 mana, I could lose 50 mana, where Wucad would just drain some. I'm mostly just looking to pass some turns while waiting for tornado to kill things, anyways. As long as the net gain over several evokes is positive, Wucad seems stronger. It does have the significant downside of having to be wielded though, which matters when you're using a great stat stick for most of your resistances (the unrand +3 elemental staff). Come to think of it I may even go down to a staff of energy for slow but steady mana gain, again with the downside of having to wield it, but no chance of draining/confusion/etc.

It is true that int loss no longer matters at all in zigg running, as the next level 9 spell will net you huge amounts of exp.

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Arrhythmia

Tartarus Sorceror

Posts: 1739

Joined: Tuesday, 13th March 2012, 02:48

Post Wednesday, 22nd July 2015, 23:10

Re: CBoE stats

Berder wrote:Wucad has a 25% fail rate. At 27 evo it gains on average 14 MP per success, but that's multiplied by 0.75 to get 10.5 average gain per evoke, not counting the fact that Wucad will sometimes drain your MP partially. From my 27 evo table for CBOE you can see that the expected MP gain if used at 20% or 30% MP is 15.5. So CBOE is better than Wucad at 27 evo, once you're above the minimum MP for CBOE.


Wow.

Oh, but displaying monster AC and EV as numbers in-game would be too complicated for players.

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duvessa

Tartarus Sorceror

Posts: 1774

Joined: Tuesday, 23rd December 2014, 23:39

Post Thursday, 23rd July 2015, 02:56

Re: CBoE stats

tasonir wrote:In the average case CBoE restores more mana than Wucad, certainly. But I'd be more worried about hitting 0 mana than Wucad draining 10 mana, especially in the case I'm currently in: a character with multiple +mana items who has a mana pool of 90. If I use a CBoE at 50 mana, I could lose 50 mana, where Wucad would just drain some. I'm mostly just looking to pass some turns while waiting for tornado to kill things, anyways. As long as the net gain over several evokes is positive, Wucad seems stronger. It does have the significant downside of having to be wielded though, which matters when you're using a great stat stick for most of your resistances (the unrand +3 elemental staff). Come to think of it I may even go down to a staff of energy for slow but steady mana gain, again with the downside of having to wield it, but no chance of draining/confusion/etc.

It is true that int loss no longer matters at all in zigg running, as the next level 9 spell will net you huge amounts of exp.

Yeah - if you're much above the minimum MP percentage, then I wouldn't use CBOE. With 90 MP, if you use it at 20% MP that's still a good amount of MP you're risking losing. What I used to do was channel Wucad a couple times to get to 10 MP, then CBOE once (or twice, if the first time didn't gain any MP) and then cast spells until I'm out again.

Here's the 27 evocations table adjusted for 90 MP instead of 50. The only difference is the avg net mp column is reduced slightly due to the greater possible mp loss.
  Code:
Average mp gain if success: 18.0
MP: 10% int drain: 0.0129 mp loss: 0.5545 confusion: 0.0337 success: 0.3989 avg net mp: 2.1897
MP: 20% int drain: 0.0131 mp loss: 0.0595 confusion: 0.0312 success: 0.8962 avg net mp: 15.0606
MP: 30% int drain: 0.0121 mp loss: 0.0609 confusion: 0.0281 success: 0.8989 avg net mp: 14.5359
MP: 40% int drain: 0.0114 mp loss: 0.0585 confusion: 0.0325 success: 0.8976 avg net mp: 14.0508
MP: 50% int drain: 0.0126 mp loss: 0.0566 confusion: 0.0321 success: 0.8987 avg net mp: 13.6296
MP: 60% int drain: 0.012 mp loss: 0.0553 confusion: 0.0315 success: 0.9012 avg net mp: 13.2354
MP: 70% int drain: 0.0124 mp loss: 0.0561 confusion: 0.0318 success: 0.8997 avg net mp: 12.6603
MP: 80% int drain: 0.0127 mp loss: 0.0566 confusion: 0.0318 success: 0.8989 avg net mp: 12.105
MP: 90% int drain: 0.0112 mp loss: 0.0593 confusion: 0.0321 success: 0.8974 avg net mp: 11.3499
streaks: 5 fifteen rune octopodes. 15 diverse chars. 13 random chars. 24 NaWn^gozag.
251 total wins Berder hyperborean + misc
83/108 recent wins (76%)
guides: safe tactics value of ac/ev/sh forum toxicity

Ziggurat Zagger

Posts: 5382

Joined: Friday, 25th November 2011, 07:36

Post Thursday, 23rd July 2015, 18:26

Re: CBoE stats

Finished my third zig, started my fourth, and while I've used CBoE 23 times (I think I had one mana drain, might be misremembering) I think I'm actually leaning towards staff of energy, as crazy as that sounds. It might just be due to my odd advantages (90 mana, although I recently switched gear to 81 mana), but you usually have a 2-4 turns while waiting for tornado to kill things, I'd rather take it slow and channel energy safely 2-3 times, then tornado again. I don't really need to throw out glaciate while everything is spinning, the main limiting factor on how fast I kill everything is the amount of time it takes them to walk into tornado range. The biggest downside to this is that you have to give up the weapon slot, which is frustrating when I have the elemental staff. I'd love if the CBoE was changed to be safer and restore less mana because ideally all I really want is a staff of energy I don't have to wield; although that'd probably be bad from a design standpoint :)

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