Calandra Feat Probabilities

[Sevwall]

Thanks to Thunder_God for the feat numbers.



This is pretty incredible. Just look at those crit chances! Just look at what you hit/damage! Playing her a ton, I always new it jumped up the dice, but I had no idea how much.

Excuse me while go play some games, and crit slam a windrushed Sorcha over half the time...

The 100%s are indeed not 100%, they are 99.99 rounded up. The Crit percentages are assuming you need a crit, and are willing to reroll a successful hit to get it.

[Saerko]

Nice presentation! I feel like this is another good candidate for the sticky under "Miscellaneous".

[Sevwall]

Oh, well, if its gonna get stickied....

Second image is for Fortune on Doomshaper. The crit rates between Fate Bound and Fortune are due to the fact that Fate Bound can reroll sucessful hits while Fortune cannot. This translates to high crit rates with Fate Bound if you absolutely need the crit.

Thus, the reason you are more likely to crit on a 4 than a 3 with Fortune is that you crit with the same dice rolls, but miss if you roll a 2,1. So that roll would get rerolled if you need a 4 where it would not get rerolled if you need a 3. It was interesting to account for.

[Saerko]

Boom-shaka! This is the kinda stuff we like to see!

[StinkyJim]

Gah - My Brain hurts.

Seriously though , excellent charts - the probablitys are even higher than I thought. Although I presume the 100% listings are still like 99.9999repeter as its always possible to roll 1 after 1 after 1 despite all the rerolls.

Man I love this stuff - reminds of the time I spent an afternoon at work calculating the insane courage chances for Lizardmen with a BSB.(It was a VERY slow afternoon.) This chart makes a mockary of thatnthough - how much work did it take?

[Thunder_God]

Uh, your N Dice w/Fortune Crit in post #3 do not fit any of the columns in the chart at the top, certainly not the "Critical Hit Percentage w/ Fate Bound" column.

[Thunder_God]

BTW, for those wondering at the Critical Hit % with Fortune (and Feat), it assumes you re-roll if you didn't get a crit before, not if you only missed, but if you landed a non-critical hit.
"Hit percentage with fate bound" is what happens when you re-roll on a miss, and again, look only for a hit.

[Sevwall]

Yeah, Thunder_God has expressed some concerns with the numbers, so hold off on printing this til I get some confirmation.

The 100%s are indeed not 100%, they are 99.9999999 rounded up. The Crits are also assuming you need a crit, and are willing to reroll to get it.

[Sevwall]

Numbers are correct as far as I know. Thunder_God confirms.

[tallted]

If you roll a set of dice and get a 1 and a 2, then re roll those dice, your probability of getting any number combination does not change. Every time you roll a dice you have a 1 in 6 chance of any number being rolled, regardless of the previous outcome.
Fortune does not increase your odds, it gives you a second chance at the same odds.
This is why at a roulette table the payoff rate is consistent, even if a certain number just hit. The next spin has equal probability of that number coming up again as it did in the initial spin.

[SteakAndSpirits]

I wonder if Fortune does not increase you odds, but it gives you a second chance at the same odds, what the cumulative effect would be?

For instance, what would happen if two friends had a little wager about flipping coins. One friend would flip his coin and if he got Heads, he would give himself a point. If he got tails, he wouldn't. The other friend would flip his coin, and if he got Heads, he would give himself a point, but if he didn't, he'd reflip one more time to try again before denying himself a point for that round. First one to ten points wins?

Might one accurately say that the second friend had increased his chances of victory by allowing a reflip?

Of course. That's because when probability is evaluated in what we'll losely call a series of events, we can (in this case) bunch the outcome around a nice little bell curve.

You are correct that a single die has equal distribution between 1, 2, 3, 4, 5, and 6 when rolled infinitely.

Two dice, however, do not have equal distribution between 2 and 12, when rolled together infinitely. They congregate around 7, with only 1/18th of the results being either 2 or 12.

By the same token, when dice are rolled multiple times against a target number, adding the potential of additional rolls increases the overall liklihood that a successful result can be found in any given series of rolls.

This is why that same roulette table will give you 2:1 on Red on any given spin of the wheel, but would never give you 2:1 on the possibility of Red eventually being spun in a series of spins. (They might give you 2:1 divided by the total number of spins, however, and still have a 'house edge' with those green squares. )

-s&s

[Mod_Redphantasm]

If you roll a set of dice and get a 1 and a 2, then re roll those dice, your probability of getting any number combination does not change. Every time you roll a dice you have a 1 in 6 chance of any number being rolled, regardless of the previous outcome.
Fortune does not increase your odds, it gives you a second chance at the same odds.
This is why at a roulette table the payoff rate is consistent, even if a certain number just hit. The next spin has equal probability of that number coming up again as it did in the initial spin.

Fortune does give you a second chance with the same odds, this absolutely increases your probability of hitting a target. Why? Because you never re-roll successful rolls.

Say I need a 7 to hit a target. There is a 58% chance I will hit (roll of 7 or greater). I will miss 42% of the time. But, with Fortune I get to re-roll each of those misses. I'm not re-rolling all of my attacks, I'm only re-rolling those that miss. Of the 42% that miss, 58 % will hit.

So, if I need a 7 to hit a target, and make 100 attacks. It will normally look like the following:

Attacks: 100
Hits: 58
Misses 42

When my misses get to be rerolled:

Attacks 100
Initial Hits: 58
Initial Misses: 42
Misses that become hits: 0.58 * 42 = 24
Total Hits: 82
Total Misses: 18

Good odds no?

[redcap71]

I haven't done the math but the numbers look a bit suspect. At least in terms of the crit percentages. The higher the number you need "to hit" the percentage you need "to crit" should consistently go down. Check the math again.

I love the chart BTW. I just want to make sure it's accurate. (I'm looking specifically at the 2 dice with fortune column). Taking a look at the original chart it just looks like a transcription typo.

On a side note those "feat with fatebound" numbers are really helpful too. If you can squeeze 'em into the presentation I'd be muchly appreciative.

Thanks again Sevwall!

[Thunder_God]

I haven't done the math but the numbers look a bit suspect. At least in terms of the crit percentages. The higher the number you need "to hit" the percentage you need "to crit" should consistently go down. Check the math again.

I'm not sure what you mean by the percentage I "need" to crit. I assume you mean the higher the number I need to hit my chances of critting should go down? Obviously.

But, look at say, 2d6. A crit means I have at least (2,2). If I have 3d6, the lowest that gives me a crit is (1,1,2), the next one is (2,2,1), and then (2,2,2,) and (3,3,1), etc. With enough dice, and Calandra's feat slanting the distribution, your chances of a crit are still good.

They are however, lower than your chances of hitting, in all cases but the extreme. 12 on 2d6 can always be had by 6,6, so if you need 12 or higher to hit, you'll crit. Always.
The same is true for 16+ in 3d6. Other than that, your chances of critting are always lower the higher the Target Number, and lower than your chances for hitting.

To clarify, the reason the chances are so slow to deteriorate to begin with come from your chances of getting a "match", that is, your chances of having at least two of the numbers be the same. But as I showed above, you're only losing 1 crit combination in the lower numbers (2,2,1, in any combination, or three combinations), losing 3 combinations out of many (roughly 43% of the rolls) is not a big deal. Later, it adds up, especially with numbers you can have by multiple results (to hit 7, you can have 2,2,3; 1,1,5; 3,3,1. Already 9 combinations lost when you go up to 8), and so it goes.

Please run the numbers, and if you find something wrong, let me know. A friend of mine and I are working on a GUI Java based calculator, and it seems he managed to do Ashlynn's Feat, which has some pretty great results. But that's still some time off before we make it (or the results, sorry) public.

[Thunder_God]

The second post with numbers Sevwall posted seems to track something else, so it should be clarified. I didn't generate those numbers, so I'll check them later.
Anyway, it seems to check your chances to hit, you re-roll if you miss, not if you fail to get a crit. So all those times you hit and don't get a crit, you don't re-roll. This reduces your "crit" percentage, because you're just looking for a hit.

[sepher32]

Awesome, thanks for the number crunches.

[Saerko]

A friend of mine and I are working on a GUI Java based calculator, and it seems he managed to do Ashlynn's Feat, which has some pretty great results. But that's still some time off before we make it (or the results, sorry) public.

As soon as you do, let us know! I think there's quite a bit of interest for it in a faction with so many abilities that modify or depend on dice rolls.

[Thunder_God]

Well, you can use the Troll Calculator, with the code in my description. It just requires copy-pasting code and modifying for adding Fortune, Calandra's Feat, etc. But it's almost all there.

This calculator, when it's done, will make it much easier for people... enter the numbers, pick modifiers by the way of check-boxes (or perhaps you'd enter "1" or "0", I don't know Java), and voila!

But don't hold your breath, my friend does work on it mostly when he's bored and has some free time.

And don't worry, when it'll be done, people will know

[Sevwall]

Second image is for Fortune on Doomshaper. The crit rates between Fate Bound and Fortune are due to the fact that Fate Bound can reroll sucessful hits while Fortune cannot. This translates to high crit rates with Fate Bound if you absolutely need the crit.

Thus, the reason you are more likely to crit on a 4 than a 3 with Fortune is that you crit with the same dice rolls, but miss if you roll a 2,1. So that roll would get rerolled if you need a 4 where it would not get rerolled if you need a 3. It was interesting to account for.

[redcap71]

Ahh, that makes sense. And I mis-read there a bit as well. Awsome number crunching. And thanks for the explanation.

[Sevwall]

Its really not a problem, it looks completely wrong on paper, and is so very situational that it hardly comes up (who doesn't boost a fortuned Impaler?)

[Thunder_God]

Well, maybe you cast Fortune on a unit buffed by Pyre/Slag or something? Or the Long-riders/Runeshapers in a weird list

[Thunder_God]

BTW, for two-caster games where "Turn" also includes your friend's turn. Calandra's Feat and "Signs and Portents" or an equivalent (Pin Cushion, Manifest Destiny) working together. I'll give you just the average:
1d6, 4.96.
2d6, 9.56.
3d6, 14.
4d6, 18.38.
5d6, 22.7.

[Sevwall]

This may be incorrect if the feat doesn't interact with Fate Blessed like I thought it did. You may only be able to reroll 1's and 2's once, even if you reroll the whole thing.

[Sevwall]

Confirmed. You can only reroll 1's and 2's once. Chart will be amended to fix.

Ugh. Ruining my plans.

[Ger]

The fortune thing is very awesome to behold. It's more significant in certain roll ranges then I honestly expected it would be.