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I have been hearing a lot of talk about how a high WC army will shut other lists completely out of the psychic phase. I was curious if this were true as my experiences thus far do not really follow it though I have not have a 6 (average dice for a Lv2 libby) vs 46 (d factory) psychic phase yet. Keep in mind that I will go up to 5 WC. This is because you can throw more dice at a power to get more WC on it and thus proof it against Deny the Witch! attempts. I will limit them to a certain range (30-80% range) as you can find sheets/apps to do this around now but I wanted tables to have an easy reference.

BTW Deny the Witch! must always be capitalized or the witch's will not be properly denied. Please don't break the rules and let the witch's win.

The chances to Deny the Witch! on a blessing (ie needing to roll a natural 6).

WC 1 (50% to manifest with 1 dice)
2 Dice: 30.56%
3 Dice: 42.13%
4 Dice: 51.77%
5 Dice: 59.81%
6 Dice: 66.51%
7 Dice: 72.09%
8 Dice: 76.74%
9 Dice: 80.62%

WC 2 (50% to manifest with 3 dice)
7 Dice: 33.02%
8 Dice: 39.53%
9 Dice: 45.73%
10 Dice: 51.55%
11 Dice: 56.93%
12 Dice: 61.87%
13 Dice: 66.35%
14 Dice: 70.40%
15 Dice: 74.04%
16 Dice: 77.28%
17 Dice: 80.17%

WC 3 (50% to manifest with 5 dice)
12 Dice: 32.26%
13 Dice: 37.19%
14 Dice: 42.05%
15 Dice: 46.78%
16 Dice: 51.32%
17 Dice: 55.65%
18 Dice: 59.73%
19 Dice: 63.57%
20 Dice: 67.13%
21 Dice: 70.44%
22 Dice: 73.48%
23 Dice: 76.27%
24 Dice: 78.82%
25 Dice: 81.13%

WC 4 (50% to manifest with 7 dice)
17 Dice: 31.13%
18 Dice: 35.21%
19 Dice: 39.30%
20 Dice: 43.35%
21 Dice: 47.31%
22 Dice: 51.16%
23 Dice: 54.88%
24 Dice: 58.45%
25 Dice: 61.84%
26 Dice: 65.06%
27 Dice: 68.09%
28 Dice: 70.93%
29 Dice: 73.58%
30 Dice: 76.04%
31 Dice: 78.32%
32 Dice: 80.42%

WC 5 (50% to manifest with 9 dice)
23 Dice: 33.50%
24 Dice: 37.06%
25 Dice: 40.63%
26 Dice: 44.16%
27 Dice: 47.65%
28 Dice: 51.05%
29 Dice: 54.36%
30 Dice: 57.57%
31 Dice: 60.64%
32 Dice: 63.59%
33 Dice: 66.40%
34 Dice: 69.06%
35 Dice: 71.57%
36 Dice: 73.93%
37 Dice: 76.15%
38 Dice: 78.22%
39 Dice: 80.15%

As you can see you need 3 times the opponent's dice to have a 50% chance to stop the power. Even then your opponent will get a bit less than 25% of their powers through. If you want to "shut them out" which I would consider stopping 80% of their powers from going off you would need about 4.5 times your opponent's dice. Keep in mind though Deny the Witch! has an advantage in efficiency by being able to see if the opponent's power goes off before applying their dice. When you are facing an overwhelming number of Deny the Witch! dice you should probably use all the dice you can to ensure you get your powers off. If you 50% chance your powers you will find the other player could very well shut you out of the psychic phase after your first failed power.

In the above 6 vs 46 dice the Lv2 libby will almost assuredly be shut out. Their best bet is to try WC1 powers on 1 dice to avoid perils and hope the other player gets incredibly unlucky. It should be noted however that any list with 15+ WC has a fair chance to get powers off against a ~45 WC list.

Anything less than 3 Deny the Witch! dice per manifesting player dice will allow for the manifesting player to have a mostly successful phase.

Let me know what you all think and any specifics that might be interesting.

I think the other half of the balancing act keeps getting forgotten when it comes to Psykers manifesting their abilities. Perils of the Warp is a LOT nastier now, with rolls of 1 now sucking up part of the squad with the psyker.

So the added risk to rolling more dice to manifest means more chances to Peril, thus helping the player trying to DtW not have to worry about an obscene number of dice being thrown at them.

I do have a question since you seem to know this equation which I am not sure of as I am not familiar with percentages or what the equation is.

What's the percentage chance with 1 Reroll of the dice?

For example

What would be a percentage chance on a WC 3 power cast with 4 dice but rerolled?

What's the percentage chance on WC 1 w/ 1 Dice?

So in the case of rerolling all the dice you rolled (which as per my understanding of the rules it would be).

You would just square your rate of failure. This would give you the new rate of failure which when subtracted from 100% would give you the rate of success.
http://www.dakkadakka.com/dakkaforum/posts/list/596200.page

So as an example for a WC1 power with 1 dice used you have a 50/50 chance or 0.5/0.5 of failure or success. If you square 0.5 you get 0.25 and subtracted from 1 or a 100% you would get 0.75 which is 75%. So with a reroll you would have a 75% chance on a single dice for a WC1 power.

All of the 50% chance to manifest such as WC3 using 5 dice would be the same 75% chance when you have a reroll.

So for a WC3 power using 4 dice we would have a 31.25% chance of success or a 68.75% failure rate. With a reroll it would go to 47% failure rate and 53% success rate.

Chaos Sorcerer , Spell familiar : Chance of Success w/ Reroll
Warp Charge 1
1 = 75%
2= 86%
3 = 93%

Warp Charge 2
2 = 50%
3 = 70%
4 = 82%
5 = 90
Warp Charge 3
3= 35%
4= 51%
5= 70%
6= 80%
7=87%

So two casting Warp Charge 1s would be a like 86% chance.


Automatically Appended Next Post:
Let me know if this is correct please.

well, it depends how you look at it.

the probability of success of the second die is not dependant on the first. as you have to reroll all the dice, the probability of succeeding the second time is the same as the first.

the only thing that changes is that you get to try twice.

the averages work when you pick & choose the dice you reroll.

so the probability of rolling a 4+ on one dice is 50:50, whether you reroll it or not.

but it's the same as rolling 2 dice and seeing if either rolls a 4+...

I've confused myself.

It always confuses me odds always do. I don't know why and I professionally do math at my job like all day long.

WC1:
1 dice 50.00% 75.00%
2 dice 75.00% 93.75%

WC2:
2 dice 25.00% 43.75%
3 dice 50.00% 75.00%
4 dice 68.75% 90.23%

WC3:
3 dice 12.50% 23.44%
4 dice 31.25% 52.73%
5 dice 50.00% 75.00%
6 dice 65.63% 88.19%
7 dice 77.34% 94.87%


BTW while it is true that any single roll the odds don't change. The odds given are the expected odds for multiple rolls. ie if you roll a d6 10,000 times your should expect half of them to be a 4+

We will ignore that non casino dice actually have a bias for certain numbers in this discussion. It is however good to understand statictics enough to recognize that statistics does NOT guarantee that you cannot fail two 99% chance tests in a row or that two 1% tests won't succeed. It does however tell you what the most probable outcome is therefore informing your decision making.

Odds notwithstanding in my two games so far under the new rules I haven't seen a single Witch denied. Also the psyker-heavy forces stomped all over the less heavily psyked-out armies.

I am not encouraged.

 ansacs wrote:
WC1:
1 dice 50.00% 75.00%
2 dice 75.00% 93.75%

WC2:
2 dice 25.00% 43.75%
3 dice 50.00% 75.00%
4 dice 68.75% 90.23%

WC3:
3 dice 12.50% 23.44%
4 dice 31.25% 52.73%
5 dice 50.00% 75.00%
6 dice 65.63% 88.19%
7 dice 77.34% 94.87%


BTW while it is true that any single roll the odds don't change. The odds given are the expected odds for multiple rolls. ie if you roll a d6 10,000 times your should expect half of them to be a 4+

We will ignore that non casino dice actually have a bias for certain numbers in this discussion. It is however good to understand statictics enough to recognize that statistics does NOT guarantee that you cannot fail two 99% chance tests in a row or that two 1% tests won't succeed. It does however tell you what the most probable outcome is therefore informing your decision making.

that's with a reroll correct? I may copy that in my FAQ. I wonder how I got my numbers. Nevermind I realized what I did. I was squaring the inital number and not the miss percentage.

Ugh the worst now is that I need to figure the square of the chances to Peril when rolling.

Use excel or google docs. Paste '=1-(1-'cell')^2' into the cell you want to calculate where 'cell' is the cell with the %chance to miscast (make sure it is a fraction ie 0.5 rather than 50).

Feel free to link, copy, borrow, disseminate as you will. I posted this in an effort to inform so you will be furthering my diabolic aims.

Wait with that calculation be offset by the chance of them not rolling it?

Because perils is on 6's there is a higher chance to fail and not perils than to succeed and perils. So the way I proposed is not correct but will give you a slightly high prediction. Doing it correctly would require the chance to perils 1st attempt with the chance to fail to manifest and then perils the second attempt. While doable I don't plan on taking that much effort to do it. There are a few people on here however that are good enough they can do it fast.

Anyone in particular I recall there being another thread based on percentages.

Honestly there should just be a "Mathhammer" thread and people could easily post in it or you could post easy ways to figure out percentages.

It'd actually be a really good thread to have, maybe even a sticky thread as I know I see that alot.

I know people would appreciate it.

There actually was a thread on dakkadakka like that. It wasn't stickied though.

I don't remember the exact people I just remember there are about 2-3 people on dakkadakka that are significantly better practiced than me. The guy that corrected my peril on doubles in the other thread might be able to rig it up quickly.

I'll check the thread and PM him thanks.