AnyDice compare dice roll value to number on a multidice roll

Question

I've been trying to use AnyDice to calculate some stuff and got completely overwhelmed (never used it properly before).

I'm trying to do something along the lines of:

Roll n + p amount of d10 dice. If any of those result in 1, check for each 1 roll 1d10 + p.

In this sequence I'm trying to see what are the odds that at least one of the dice will result in 1 and what would the secondary roll result spread would be.

Is it possible to do something like this? Because I'm already failing at trying to compare the dice to a number and assigning variables does not seem to help. I think I jumped into something too complex for a first more serious use of the system.

EDIT: Basically the first roll is for casting a spell and 1s represent mishaps. For each 1 you roll onto table which has 10 entries (the higher the number, the more severe result). Adding extra dice p (pushing) makes those table results worse. I want to see how quickly and how bad that can go. If I add 1 extra die, what's the chance to get a mishap and how bad, if i add 2, etc (apologies if too much details, not sure how else to clarify this).

So far I managed to count number of 1s (i think)

function: hitme N:n plus P:n {
  X: N + P
  result: [count {1} in X d10]
}
output [hitme 4 plus 2]

EDIT2:

You guys are right. I think I was over-complicating the issue. The second half is indeed very straightforward (simple roll with static number value addition). The first one was the real issue.

Answer 1

Forget anydice; this is analytically trivial

What you are describing is a Binomial distribution with parameters (as per the Wiki page notation) of \$p=0.1\$, \$q=0.9\$ and \$n=\text{your }n+\text{your }p\$.

You can read through the details of how to determine the chance of any particular number of fails [the probability mass function] or at least any given number of fails [the cumulative distribution function]. Both Excel and Google sheets have built in functions for both.

Knowing the distribution of this random variable, you can combine it with the second (\$1d10+ \text{your }p\$) to get any numerical result you like. However, it appears that you are using a table for “mishaps - if these are something other than numbers then maths can’t help.

That said, you can build this Binomial distribution in anydice. Like this:

output (N+P)d{1:1, 0:9}

There is one scenario I would like to cover. Those dice that do result in one. Let's say we reroll them once. What's the chance that we still get a 1? That would cover all in my interest on the subject. Though that would probably just nesting the same function, i assume

More or less:

output (N+P)d{1:1, 0:9}d{1:1, 0:9}

Answer 2

It might just be a pure maths problem, so you don't need AnyDice.

If you want to know what the chances are of rolling a dice twice in a row, you multiply 1/N times 1/N, where N is the number of sides on the die: e.g. chances of rolling two 20s in a row with a d20 are 1/20 times 1/20, equals 1/400, or 0.25%.

You seem to be basing it on a d10 roll though, so here it goes:

• The chances of rolling a 1 once on a d10 is 1/10, or 10%;
• The chances of rolling a 1 twice in a row on a d10 is (1/10 times 1/10) 1/100, or 1%;
• The chances of rolling a 1 three times in a row on a d10 is (1/10 times 1/10 times 1/10) 1/1000, or 0.1%;
• and so on.

So if rolling three 1s in a row means that something catastrophic happens, then that is a 1 in a thousand chance.

If you don't like the odds, then just use a d20, where rolling three 1s in a row has only a 1/8000 chance of happening, or 0.0125%.

I hope this helps to make the tables you intend.

If you want spell "mishaps" to be rare I would use a d100 or percentile dice, this way you control this better. For example, 1-5 on a d100 equals a mishap. Then have a further table to determine the type of mishap; again a d100 gives you flexibility. For instance, if you roll 1-7, you turn into a Giant Frog for 1 minute MM p.325. You can have a lot of fun with this.

The DM in my current campaign has a similar system, where you role d20 to determine if something odd might happen. On a 1, something odd happens and then you roll a percentile die (d100) to determine what happens. I grew a second set of ears once, and had advantage on Wisdom (Perception) checks to do with my hearing, it lasted 1d100 hours.