Strain

[othercourt]

When using Special Abilities, instead of spending Focus points, the character is *gaining* points of Strain. One can safely have (Focus x 1/2) points of Strain. Once Strain gets over this threshold, the GM can decide, at any time, to spend a character's Strain, in any amount he chooses.

Each point of spent Strain is a 1d10 to be rolled. Any 1's which come up are set aside as a Strain Successes. The rest of the dice are rolled one more time. By this, characters have aprox a 1 in 5 chance of a point of Strain becoming a Strain Effect Level. See below as to how bad this is for you.

Also, keep in mind that (Focus x 1/2) number. It's your Threshold. Your Threshold is the amount of extra Strain you are allowed to take on in a single Special Ability use, via Overspending rules (each extra point is a +2 to the roll).

Strain Effects are below. Note that up to Level 3, the Effect can be eliminated by another Psychic touching you and taking on Strain themselves. This is an automatic ability of Psychics... they can take on each other's Strain. Just think of it as lending someone temporary Focus points, only instead of giving them currency, you are taking on their debt.

Yes, Strain can kill you. That's the point. It's a risk taking your Strain over your Threshold.

Strain Effects

(1): Weak Effects
Headaches, bouts of dizziness, minor nausea. -3 PEN, Duration 1 Scene
Relief cost 6 Strain points.

(2): Moderate Effects
Powerful headaches, constant dizziness, nausea. -6 PEN, Duration 1 Scene
Relief cost 12 Strain points.

(3): Debilitating Effects
Massive headaches, terrible dizziness, violent nausea. -9 PEN, Duration 1 Scene
(2): Duration 1 Hour
(1): Duration 1 Day
Relief cost 20 Strain points.

(4): Damaging Effects
1 Light Strain Wound
Blackout, Duration 1 Scene
(3): Duration 1 Hour
(2) and (1): Duration 1 Day

(5): Lasting Effects
Lose 1 Focus
1 Light Strain Wound
Coma for 1d6+1 Days

(6): Major Effects
Lose 1d6/2 Focus
2 Light Strain Wounds
Coma for 1d6+1 Days

(7): Dangerous Effects
Lose 1d6 Focus
1 Severe Strain Wound
Coma for 1d6+1 Weeks

(8): Deadly Effects
Lose 1d10 Focus
1 Critical Strain Wound
Coma for 1d6+1 Weeks

(9): Terrible Effects
Lose 3d10 Focus
1 Mortal Strain Wound
Coma for 1d6+1 Months

(10): Horrible Effects
Lose 5d10 Focus
1 Mortal Strain Wound
Coma for 1d6+1 Months)

[othercourt]

Another note: When it comes to losing Focus, these dice are rolled like any other.... roll, take highest single die total, 10's can explode. Maximum loss is 20 Focus. Since any character with 0 Focus is brain dead, even a single d10 loss of Focus can potentially kill a Focus 20 character.

[lord carnifex]

So I ran the numbers on this. Taking the scenario of the Ref rolling 10 Strain effect dice: rerolling any that don't come up 1's, with the threshold for permanent damage at five successes. Under this scenario, permanent damage (the loss of one Focus) will occur roughly 22.1 times in one million rolls.

The math is available via e-mail upon request.

[othercourt]

Which seems a bit low to me, landing about 1 in 45,000 for 10 dice. Granted, I am no statistics expert. The following attempt to break this down is to be taken as "English Major" math.

With 5 dice, figuring the chance of them all coming up 1, is a 1 in 100,000 occurrence. The only number between 1 and 100,000 with five 1's is 11111. So we have to roll that, or we don't get 5 successes. Trying to figure anything else after this is hard for me to wrap my head around. But, essentially, any of those digit placeholders that fails to hit the first time, I get to reroll. So in my first swing, I get "1 1 2 3 6", I get to reroll the last three digits of the number string.

5 dice All coming up 1 in the first roll, 1 in 100,000.

If only 4 of 5 dice come up 1, I can have these 45 results:
11110, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119
11101, 11121, 11131, 11141, 11151, 11161, 11171, 11181, 11191
11011, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911
10111, 12111, 13111, 14111, 15111, 16111, 17111, 18111, 19111
01111, 21111, 31111, 41111, 51111, 61111, 71111, 81111, 91111
...with a 1 in 10 chance after that of getting all 5 successes. So, again, roughly, I get it another 4.5 times on average, for a total of 5.5 in 100,000.

If only 3 (or less dice) come up 1 on the first swing, I would think that I wouldn't improve much more often than 5.5 in 100,000, so for the sake of space I'll discount these.

So for 5 dice, I have about 5.5 in 100,000 chance, or 1 in 18,181.

For 6 dice, I have a 1 in 10,000 chance of 5 of the 6 all coming up 1's (is this right?).
If I only get 4 of the 6 (is this 10 in a 10,000?), either of my two reroll dice could come up 1s, so about 20% of the time, this works, for another 2 in 10,000.

So for 6 dice, I have about 3 in 10,000 chance (or 30 in 100,000 chance), or 1 in 3,333.

For 7 dice, I have a 1 in 1,000 chance of 5 of the 7 dice all coming up 1's (correct?).
If I only get 4 of the 7 (10 in 1,000?), this will score about 30% of the time, for another 3 in 1,000.

So, for 7 dice, I have a 4 in 1,000, or 1 in 250.

For 8 dice, I have a 1 in 100 chance of 5 of the 8 dice all coming up 1's.
If I only get 4 of the 8 (10 in 100?), this will score about 40% of the time, for another 4 in 100.

So, for 8 dice, I have a 5 in 100 chance, or 1 in 20.

At this point, I know my math is getting pretty off. I'm making some assumptions that are biting me on the ass. What is the right way to work through this?

[othercourt]

Attacked the problem again.

Methodology: Use of this probability calculator to figure the chance of success for the number of dice vs. difficulty 10.

Took these totals, then the checked for probability of remaining dice in pool to try to make the total number of successes 5 or more.

Added all totals for each pool to come up with chance of reaching 5+ successes. Results as follows, with working data below:

5 dice: .0251705 percent: 1 in 3973
6 dice: .12762 percent: 1 in 784
7 dice: .3702466 percent: 1 in 270
8 dice: .8538772 percent: 1 in 117
9 dice: 1.6384798 percent: 1 in 61
10 dice: 2.7697323 percent: 1 in 36

I find it really, really interesting that our "gut" feeling of about 2% actually sang in at 10 dice.

Data:

5 dice: .0251705 percent: 1 in 3973

5 successes: .001 percent: 1 in 100,000 (1st roll)

4 successes: .045 percent, conversion (1 dice) .0045 percent
3 successes: .081 percent, conversion (2 dice) .0081 percent
2 successes: .729 percent, conversion (3 dice) .00729 percent
1 success: : 32.805 percent, conversion (4 dice) .0032805 percent
0 successes: + .001 percent

6 dice: .12762 percent: 1 in 784

6 successes: .0001 percent (1st roll)
5 successes: .0054 percent (1st roll)

4 successes: .1215 percent, conversion (nds 1+ from 2 dice, success 19% of this): .023085 percent
3 successes: 1.458 percent, conversion (nds 2+ from 3 dice, success 2.8% of this): .040824 percent
2 successes: 9.8415 percent, conversion (nds 3+ from 4 dice, success .37% of this): .0364135 percent
1 success: 35.4294 percent, conversion (nds 4+ from 5 dice, success .046% of this): .0162975 percent

0 successes: .0055 percent

7 dice: .3702466 percent: 1 in 270

7 successes: .00001 percent
6 successes: .00063 percent
5 successes: .01701 percent

4 successes: .25515 percent, conversion (nds 1+ from 3 dice, success 27.1% of this): .0691456 percent
3 successes: 2.29635 percent, conversion (nds 2+ from 4 dice, success 5.23% of this): .1200991 percent
2 successes: 12.40029 percent, conversion (nds 3+ from 5 dice, success .856% of this): .1061464 percent
1 success : 37.20087 percent, conversion (nds 4+ from 6 dice, success .127% of this): .0472451 percent

0 successes: .01765 percent

8 dice: .8538772 percent: 1 in 117

8 successes: .000001 percent
7 successes: .000072 percent
6 successes: .002268 percent
5 successes: .040824 percent

4 successes: .45927 percent, conversion (nds 1+ from 4 dice, success 34.39% of this): .1579429 percent
3 successes: 3.306744 percent, conversion (nds 2+ from 5 dice, success 8.146% of this): .2693673 percent
2 successes: 14.880348 percent, conversion (nds 3+ from 6 dice, success 1.585% of this): .2358535 percent
1 success : 38.263752 percent, conversion (nds 4+ from 7 dice, success .2728% of this): .1043835 percent

0 successes: .043165 percent:


9 dice: 1.6384798 percent: 1 in 61

9 successes: .0000001 percent
8 successes: .0000081 percent
7 successes: .0002916 percent
6 successes: .0061236 percent
5 successes: .0826686 percent

4 successes: .7440174 percent, conversion (nds 1+ from 5 dice, success 40.951% of this): .3046825 percent
3 successes: 4.4641004 percent, conversion (nds 2+ from 6 dice, success 11.4265% of this): .5100904 percent
2 successes: 17.2186884 percent, conversion (nds 3+ from 7 dice, success 2.56918% of this): .4423790 percent
1 success : 38.7420489 percent, conversion (nds 4+ from 8 dice, success .502435% of this): .2031439 percent

0 successes: .089092 percent


10 dice: 2.7697323 percent: 1 in 36

10 successes: .00000001 percent
9 successes: .0000009 percent
8 successes: .00003645 percent
7 successes: .0008748 percent
6 successes: .0137781 percent
5 successes: .14880348 percent

4 successes: 1.1160261 percent, conversion (nds 1+ from 6 dice, success 46.8559% of this): .5229240 percent
3 successes: 5.7395628 percent, conversion (nds 2+ from 7 dice, success 14.96944% of this): .8591804 percent
2 successes: 19.37102445 percent, conversion (nds 3+ from 8 dice, success 3.809179% of this): .7378769 percent
1 success : 38.7420489 percent, conversion (nds 4+ from 9 dice, success .8331094% of this): .3227636 percent

0 successes: .1634937 percent