In Mutant Year Zero, Alien RPG and Forbidden Lands, the designers include a lot of d66 tables, in which a d6 is rolled for the tens and one for the units, giving 36 possible results (11, 12, 13, 14, 15, 16, 21, 22, etc). How would I be able to simulate this in Any Dice?

# Tag: odds

## What are my odds of a critical hit with my level 20 Champion?

I’m trying to calculate what my odds are as a level 20 Champion to score at least one critical hit on my turn, and how many I can expect.

I make four attacks per attack action I take, and can Action Surge for another four, bringing my total to 8. I score a critical hit on a roll of 18-20, and if I get even one, my Great Weapon Master feat lets me make a fifth (or in this case ninth) attack.

I’d also be curious to know what my odds are if I’m rolling with advantage.

## Is it better to take the array and be Joe Average, or to roll for the odds of getting on average better scores?

I am new to D&D. I was looking at character creation for D&D 5th edition. There were a few ways one could generate ability scores. I assumed the optional method of taking the numbers 15,14,13,12,10,8 would be at least as good as the default chance method (roll 4d6, drop lowest die), and more likely, just a bit better than chance.

However, with the above method, the summed ability scores is 72, which is just a bit shy of the summed average one would obtain by rolling dice: the average ability score generated by dice should be 12.2446, which means the sum of the average ability scores is 73.4676.

What the 15,14,13,12,10,8 method accomplishes is to give some moderately high scores, but no exceptional ones, without giving any terrible scores (dice rolling typically gives at least one score of seven or less). To my mind that suggests that the rationale is that many players may find that “joe just-below-average” across the board is better than Achilles, who is amazing in some ways, but has that crazy heel weakness. He is also maybe better than “Joe Exactly-average” who has no high scores and no low ones?

Are those rationales good, i.e. is it actually better to have Joe Just-below-average-with-some-bright-spots than Joe Completely-average or Achilles?

**Correction**: The odds of rolling all ability scores at 8 or above are 70%, so I misspoke when I said usually one will roll one score below an 8. In fact, usually one does not, but not in a strong sense. It is no more unlikely to get a score below 8 than two coin flips coming up tails. It happens.

I provide a quick chart at the end, which makes the statistics easy to generate. As I generated the numbers quickly, I confess the possibility of error. For the 1296 possible rolls of four dice here are the number of ways you can obtain each value as the sum of the best three.

`Sum of best three | Number of possible rolls that give that sum of best 3 -------------------------------------------- 3 1 4 4 5 10 6 21 7 38 8 62 9 91 10 122 11 148 12 167 13 172 14 160 15 131 16 94 17 54 18 21 `

## What is the odds of rolling specific numbers on 4 d20s?

If I roll 1d20, then 1d20, then 1d20, then 1d20 (effectively 4d20), what are the odds that I’ll roll specific numbers? For example, all 20’s, or a combination of numbers such as (1, 16, 16, 1)?

## Odds of rolling the same results twice on advantage rolls

I know that this has probably been answered before, but I couldn’t find any specific threads on it.

This happened in a tabletop game recently, where all dice rolls are rolled with advantage anyways because of how the VTT system works.

So what are the odds that you get the same results twice in a row like this? Is it 1/400 or 1/160000, assuming order matters or not?

## My DM insists on rolling a single save for groups affected by AoE save spells. How does this affect my odds of successfully affecting the enemy?

As the title question, my DM rolls a single d20 save for groups affected by my area of effect spells that require a save, in order to save time. I can’t help but feel like I’m being ripped off by this as a wizard with primarily AoE save-or-suck spells. I don’t know if this is just a feeling or if the probabilities actually back this up. I know this can also work in my favor but it still feels off.

**How are the probabilities affected when a (homogenous) group gets a single save vs. each individual in the group having their own save?** I want to know specifically if this works more in my favor or more in the favor of my enemies, or if it is statistically speaking a 50/50 split. **I am looking for evidence that this is a bad idea (whether it benefits me or harms me) and that the DM should roll separately for each affected target in the area of effect.**

I realize this probably puts the odds in my favor when targeting weak saves in the group (i.e., WIS save on a group of ogres or orcs), but this will not always be the case and especially when there are mixed enemies in the AoE. So far we have only faced groups that contained single enemy types so I don’t know what happens when there are two different enemies with two different saves.

Ideally answers will address a sliding group size (2..N group members, 5 is probably a good stopping point) and a range of save DCs — DC 14-19 should address most levels of play.

## Using AnyDice to determine the odds of getting a specific number sequence on multiple dice

After a few hours trying to design the proper code in AnyDice, I had to admit I didn’t find a proper way to reach my goal, so I’m wondering if someone could give me a helping hand.

Here is the problem :

- I’m looking for odds of successfully rolling a
**specific**combination with a multiple dice roll; for instance, the exact combination [1,2,5] with 3d6, or [4,3,3] with 3d6, or [1,2,2,6] with 4d6, etc. (The latter examples emphasize the fact that the same number could be present a variable number of times, as a double, triple, etc. — increased complexity.) - I can easily isolate the odds for some “classic” combinations (like doubles with 2d6, triples with 3d6, etc.) but what I’m searching for is a
**generic**formula for any combination of*n*numbers for*n*d6 (or other number of faces).

Does anyone know how to code this? I’m guessing that AnyDice can do this, but I don’t know how to tell it to. I would be grateful if someone could at least point me in the right direction!

## Is my DM stacking the odds against us?

So, I’ll set the stage. We’re a party of 4, level 8 at the moment, with an allied NPC. In our most recent encounter we went up against:

- ~20 “minions”, (<35 HP, +4 to hit)
- 1 Winter wolf (75 HP, +5 to hit)
- 3 dire wolves (37 HP, +6 to hit)
- 1 modified Huskarl (<105 HP, +7 to hit)
- 1 Druid (~40 HP)

All of these enemies, Druid exempt, got at least 2 attacks. About half the minions had a harpoon attack that Grappled upon hit, so that kept us pinned pretty good.

Keep in mind, this was designed narratively to be a “challenging” encounter; it was set up as a raiding camp that we were vastly outnumbered for. But every encounter is set up narratively to be challenging in this way. So when the norm is something we’re not supposed to beat, that feels a little off base. If the smart answer is just to walk away from the story, that strikes me as setting us up to fail.

Am I overreacting, or was this fight a little harsh? We won this one, but I also lost track of the amounts of times that the DM crit-failed attacks, and he almost always rolled min damage. I only really have experience with this DM and it’s sort of always been this way. I just wanna know if this sort of setup (roughly 820 HP to slap grind through, 26 mooks w/ 35 HP, etc) is a good way to set up an encounter or if it’s just intentionally difficult for difficulty’s sake.

## What are the odds of rolling specific ability score totals in D&D?

I am about to start running a new game in 5e and I hate all of the ways of determining ability scores.

I have always felt that we play RPGs at least in part for the opportunity to pretend to be more than we are in real life and no one wants to play a character who’s just average. So I feel like characters should have the ability to become world-class in some area.

Using either standard array or point buy, you cannot start at level 1 with greater than a 15 in any ability. This means that you can’t have above a 17 with racial mods and that, in order, to achieve the highest possible level of 20, you must plan to use at least two feat opportunities to improve to 20, and you have essentially no chance of improving a secondary ability to anything significant if you want to take any non-ability feats at all.

And with rolling dice, you may have some chance of starting in a better position, but you have a significant chance of starting in a much worse position. If the consequences of such a catastrophe were a few sessions of difficulty, that would be one thing, but leaving to chance the possibility of playing, for months or a year, a character whose negative modifiers outweigh their positive ones seems unacceptable to me.

For this reason, I think, some DMs (including Matt Mercer from Critical Role) put lower caps on rolls, saying, for example, that if your total rolls for all six stats are below 70, you can roll again.

I like this idea, but I’m not sure it’s sufficient for what I want (giving my players a chance to be exceptional).

I know that there are 1296 possible results for rolling 4D6, and I know that the average result of rolling 4D6 and dropping the lowest number is 12.2446, which means (I think) that the average score for doing that six times is 73.46759.

I’m thinking about making 73 the “floor” for my players (so that they are at least hero-average so to speak) but I’m not sure I have a good enough grasp of the math to know that that is the right decision.

What I’d like to know is “what is the probability of getting a total of under 70 on these rolls?” So, if you roll 4D6 and drop the lowest one six times and total the six results, what is the probability that it is below 70?

I’d also like to know that for 71, 72, etc… up to 78. And I’d like to know what the probability of getting above about 80 is, and 81, 82, etc.. up to about 90.

I’m not a mathematician and I don’t know how to figure this out. I don’t even really know how to phrase the question. I hope this was clear enough to get an answer.

## Investment strategy based on winning/loosing odds of past trades

not being strong at math at all, I’m posting my question here hoping to find a good money allocation based on the odds an investment strategy returns.

With a certain strategy trading Forex and Bitcoin, I end up hitting my first take profit target between 31,5% and 52,1%. So, for every 3 trades I take, about 1 to 1,5 trades are reaching their target.

There’s also a 2nd and 3rd take profit target. Once the 1st is reached, the chance to have the 2nd profit target being reached is between 57,1% and 83,3%. Reaching the 3rd target is between 0% and 58,3%.

Since reaching target 2 is higher than reaching target 1, I think it would be wise to increase my investment once target 1 is hit. And reduce it again once target 2 is reached. Is there somehow a way to calculate the most optimal money allocation based on these odds?

I’ll give some more info on the investigation I did (maybe I need to do more to be statistically correct). Bitcoin trades: – Going long: 32 trades, 14 hit TP1, 8 hit TP2 and 5 hit TP3 – Going short: 27 trades, 9 hit TP1, 7 hit TP2 and 4 hit TP3 Forex trades: – Going long: 19 trades, 6 hit TP1, 4 hit TP2 and 0 hit TP3 – Going short: 23 trades, 12 hit TP1, 10 hit TP2 and 7 hit TP3

The take profit (TP) levels are increments of the same value. Let’s say the current price is 100 and if your TP1 value is 5 higher (105), then TP2 is 2*5 (110) and TP3 is 3*5 (130).

Thanks a lot!