# Misfortune Maths

I haven't seen it posted anywhere else, so FYI, the effect on a D20 is:

- 3.325

i.e. expected results on a D20 are:

Ordinary: 10.5
roll 2x and take lower: 7.175
roll 2x and take higher: 13.825

Richard

Ok.

The effects on criticals (critical threats) are even more pronounced.

Chances of a critical threat:

crit 20: normal 5%, take lower 0.25%, take higher 9.75%
crit 19-20: normal 10%, take lower 1%, take higher 19%
crit 18-20: normal 15%, take lower 2.25%, take higher 27.75%

Basically, a misfortuned person pretty much waves goodbye to any chance of criticalling.

Richard

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Note that this bonus varies with the number required to succeed. If the number required is 11, then the chance of success changes from 50% to 25%, the equivalent of +5. If the number required is 2 (or 20) then you have about the equivalent of a +1 bonus. +3.325 is an average assuming that all numbers required for success are equally likely. Which is probably a bad assumption.

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Ok, so I've just done a bit more maths (actually, I did it the long way, so I'm not sure how the actual maths works), but I get that:

If your change of hitting is x %, then your effectiveness changes by 100 - x %, better if you roll twice and take the highest, worse if you roll twice and take the lowest.

So, if you need an 11, so you are 50% likely to hit, your effectiveness changes by 50% (of the 50%), so you are now 25% on the poor effect, 75% on the high effect.

If you need a 15, with a 30% chance to hit, your effectiveness changes by 70%, i.e. now 9% on lower and 51% on higher.

It you need a 1, then it makes no difference.

Here's the full table:

need a 20: normal 005.00%, take lower 000.25% (-95%) take higher 009.75% (+95%)
need a 19: normal 010.00%, take lower 001.00% (-90%) take higher 019.00% (+90%)
need a 18: normal 015.00%, take lower 002.25% (-85%) take higher 027.75% (+85%)
need a 17: normal 020.00%, take lower 004.00% (-80%) take higher 036.00% (+80%)
need a 16: normal 025.00%, take lower 006.25% (-75%) take higher 043.75% (+75%)
need a 15: normal 030.00%, take lower 009.00% (-70%) take higher 051.00% (+70%)
need a 14: normal 035.00%, take lower 012.25% (-65%) take higher 057.75% (+65%)
need a 13: normal 040.00%, take lower 016.00% (-60%) take higher 064.00% (+60%)
need a 12: normal 045.00%, take lower 020.25% (-55%) take higher 069.75% (+55%)
need a 11: normal 050.00%, take lower 025.00% (-50%) take higher 075.00% (+50%)
need a 10: normal 055.00%, take lower 030.25% (-45%) take higher 079.75% (+45%)
need a 09: normal 060.00%, take lower 036.00% (-40%) take higher 084.00% (+40%)
need a 08: normal 065.00%, take lower 042.25% (-35%) take higher 087.75% (+35%)
need a 07: normal 070.00%, take lower 049.00% (-30%) take higher 091.00% (+30%)
need a 06: normal 075.00%, take lower 056.25% (-25%) take higher 093.75% (+25%)
need a 05: normal 080.00%, take lower 064.00% (-20%) take higher 096.00% (+20%)
need a 04: normal 085.00%, take lower 072.25% (-15%) take higher 097.75% (+15%)
need a 03: normal 090.00%, take lower 081.00% (-10%) take higher 099.00% (+10%)
need a 02: normal 095.00%, take lower 090.25% (-05%) take higher 099.75% (+05%)
need a 01: normal 100.00%, take lower 100.00% (-00%) take higher 100.00% (+00%)

And perhaps more interestingly:

need a 20, effective d20 addjustment +/- 0.95
need a 19, effective d20 addjustment +/- 1.80
need a 18, effective d20 addjustment +/- 2.55
need a 17, effective d20 addjustment +/- 3.20
need a 16, effective d20 addjustment +/- 3.75
need a 15, effective d20 addjustment +/- 4.20
need a 14, effective d20 addjustment +/- 4.55
need a 13, effective d20 addjustment +/- 4.80
need a 12, effective d20 addjustment +/- 4.95
need a 11, effective d20 addjustment +/- 5.00
need a 10, effective d20 addjustment +/- 4.95
need a 09, effective d20 addjustment +/- 4.80
need a 08, effective d20 addjustment +/- 4.55
need a 07, effective d20 addjustment +/- 4.20
need a 06, effective d20 addjustment +/- 3.75
need a 05, effective d20 addjustment +/- 3.20
need a 04, effective d20 addjustment +/- 2.55
need a 03, effective d20 addjustment +/- 1.80
need a 02, effective d20 addjustment +/- 0.95
need a 01, effective d20 addjustment +/- 0.00

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For those playing DnD 5e, this is the mechanism of Advantage and Disadvantage.

This math also applies to ill omen- a no save spell with this roll twice mechanic.

It is a bit hard to say which is better. Ill omen affects a single d20 roll at level 1, and scales up to affect 5 rolls a level 20. Depending on the target, it might last longer than misfortune (which lasts 1-3 rounds). A melee character could eat that up in one full attack, but a caster might only trigger if when you use your own SoS spells.

Ill omen has no save, but there is a mechanic where characters can perform a prayer in order to cancel out the effects on a single roll. But that takes up a move action, and the character needs to know that the prayer would work (spell craft is cited, but I could see a superstitious character might do it anyway).

This spell is on the medium's spell list, and it seems like a key support spell for a melee medium (since it doesn't have a save DC).

This will all be very helpful for when I roll the die, and then roll it again, and use the lower result.

TheGreatWot wrote:
This will all be very helpful for when I roll the die, and then roll it again, and use the lower result.

It will certainly help me when I roll a die and roll another and need and have to pick the higher. I'll finally have the math to help me do that

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Nothing wrong with doing some math for the sake of math. It is good to know how effective various options are.

I hate math, so I'm gonna have to disagree there.

I know firsthand how effective Misfortune is because the witch in my group shuts down every monster I throw at them with it. :(

TheGreatWot wrote:

I hate math, so I'm gonna have to disagree there.

I know firsthand how effective Misfortune is because the witch in my group shuts down every monster I throw at them with it. :(

Yes, but this thread can be a record that allows people to avoid doing math.

If I wanted to know some factoid like this, my first instinct would be to do a search of past threads.

I love this math but I don’t know how to it myself, ergo, love this thread.

I actually didn't do the maths, BTW - I wrote a computer program to enumerate all the possibilities.

Obviously, there is some sort of neat mathematics behind this, because it's so symmetrical, but I haven't figured it out!

Richard

TheGreatWot wrote:
I know firsthand how effective Misfortune is because the witch in my group shuts down every monster I throw at them with it. :(

I have the same problem - it's a killer. I just wanted to point out just how much of a killer it is.

Most of the encounters my PCs face will be hitting them on about a 15. Misfortune effectively reduces their hit rate by 7 in 10, and criticals disappear completely.

Richard

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You’ve already shown the numbers but to calculate misfortune you take your odds of hitting and square them. If you hit on 11 or better then 10 out of 20 rolls will normally hit. With misfortune you square those numbers so 100 out of 400 roll sets will hit, which is 25%.

For advantage you do something similar but square the odds for missing instead of for hitting to find the new miss chance. To convert the miss chance to a hit chance, then just subtract the result from 1, or subtract from 100% if you already jumped to making it a percent.

You’ve already shown the numbers but to calculate misfortune you take your odds of hitting and square them. If you hit on 11 or better then 10 out of 20 rolls will normally hit. With misfortune you square those numbers so 100 out of 400 roll sets will hit, which is 25%.

For advantage you do something similar but square the odds for missing instead of for hitting to find the new miss chance. To convert the miss chance to a hit chance, then just subtract the result from 1, or subtract from 100% if you already jumped to making it a percent.

OMG, that's so obvious now you've said it!

Richard

Here's the math:

It starts with the number you need to succeed. [I started at 2 since any number lower acts the same as 2.]
Next is what the normal success rate is.
Next is what the success is if you take the worst of two d20 rolls
The next 6 are the crit success if you need a 20..15 to crit and are under the worst of two d20 rolls.
Next is what the success is if you take the best of two d20 rolls
The next 6 are the crit success if you need a 20..15 to crit and are under the best of two d20 rolls.

Columns are delimited by the vertical bar.

Need|Normal|worst of 2|20|19|18|17|16|15|best of 2|20|19|18|17|16|15
2|95.00%|90.25%|0.23%|0.90%|2.03%|3.61%|5.64%|8.12%|99.75%|9.73%|18.95%|27. 68%|35.91%|43.64%|50.87%
3|90.00%|81.00%|0.20%|0.81%|1.82%|3.24%|5.06%|7.29%|99.00%|9.65%|18.81%|27. 47%|35.64%|43.31%|50.49%
4|85.00%|72.25%|0.18%|0.72%|1.63%|2.89%|4.52%|6.50%|97.75%|9.53%|18.57%|27. 13%|35.19%|42.77%|49.85%
5|80.00%|64.00%|0.16%|0.64%|1.44%|2.56%|4.00%|5.76%|96.00%|9.36%|18.24%|26. 64%|34.56%|42.00%|48.96%
6|75.00%|56.25%|0.14%|0.56%|1.27%|2.25%|3.52%|5.06%|93.75%|9.14%|17.81%|26. 02%|33.75%|41.02%|47.81%
7|70.00%|49.00%|0.12%|0.49%|1.10%|1.96%|3.06%|4.41%|91.00%|8.87%|17.29%|25. 25%|32.76%|39.81%|46.41%
8|65.00%|42.25%|0.11%|0.42%|0.95%|1.69%|2.64%|3.80%|87.75%|8.56%|16.67%|24. 35%|31.59%|38.39%|44.75%
9|60.00%|36.00%|0.09%|0.36%|0.81%|1.44%|2.25%|3.24%|84.00%|8.19%|15.96%|23. 31%|30.24%|36.75%|42.84%
10|55.00%|30.25%|0.08%|0.30%|0.68%|1.21%|1.89%|2.72%|79.75%|7.78%|15.15%|22 .13%|28.71%|34.89%|40.67%
11|50.00%|25.00%|0.06%|0.25%|0.56%|1.00%|1.56%|2.25%|75.00%|7.31%|14.25%|20 .81%|27.00%|32.81%|38.25%
12|45.00%|20.25%|0.05%|0.20%|0.46%|0.81%|1.27%|1.82%|69.75%|6.80%|13.25%|19 .36%|25.11%|30.52%|35.57%
13|40.00%|16.00%|0.04%|0.16%|0.36%|0.64%|1.00%|1.44%|64.00%|6.24%|12.16%|17 .76%|23.04%|28.00%|32.64%
14|35.00%|12.25%|0.03%|0.12%|0.28%|0.49%|0.77%|1.10%|57.75%|5.63%|10.97%|16 .03%|20.79%|25.27%|29.45%
15|30.00%|9.00%|0.02%|0.09%|0.20%|0.36%|0.56%|0.81%|51.00%|4.97%|9.69%|14.1 5%|18.36%|22.31%|26.01%
16|25.00%|6.25%|0.02%|0.06%|0.14%|0.25%|0.39%|0.56%|43.75%|4.27%|8.31%|12.1 4%|15.75%|19.14%|22.31%
17|20.00%|4.00%|0.01%|0.04%|0.09%|0.16%|0.25%|0.36%|36.00%|3.51%|6.84%|9.99 %|12.96%|15.75%|18.36%
18|15.00%|2.25%|0.01%|0.02%|0.05%|0.09%|0.14%|0.20%|27.75%|2.71%|5.27%|7.70 %|9.99%|12.14%|14.15%
19|10.00%|1.00%|0.00%|0.01%|0.02%|0.04%|0.06%|0.09%|19.00%|1.85%|3.61%|5.27 %|6.84%|8.31%|9.69%
20|5.00%|0.25%|0.00%|0.00%|0.01%|0.01%|0.02%|0.02%|9.75%|0.95%|1.85%|2.71%| 3.51%|4.27%|4.97%

/cevah