[Phlow]

So I've been reading a LOT about COR, and personally I love the job. Why? Because it's what I do for a living - evaluate risk taking opportunities, and if the numbers add up, take the risk. So I started to compile information on COR in order to know exactly when to roll 'em and when to fold 'em. So far I have information gathered on Chaos Roll and Healer's Roll. Of course, there are rolls where we'll never be able to get the definative numbers, such as Hunter's Roll and Ninja's Roll, but hopefully we can extrapilate this data and decide for ourselves when it would be best to play our Double-Up and when it would be best to keep our current roll.

What I need, though, is your help. I've got somewhat limited time on the game because of my job - As such, I can't gather the raw data from higher rolls, such as Evoker's and such. Any measurable roll you can gain data on, PLEASE, send to me in a PM. I will stock everything I get, and use various sources to confirm something before I begin the payoff matrix on it. I need all sorts of measurable data too, what was it like with a WHM in your PT? Without? Etc.

How it's figured:

Basically, every roll must be weighed and it boils down to a simple question: Is there a good chance that I can get something better than what I already have if I reroll? Let's break this question down. What you have vs. What you could get. Well, let's consider your first roll was a 1 on a Healer's Roll. If you were to Double Up, you could get a 2, 3, 4, 5, 6, or 7. Let's assume the game is TOTALLY random, and won't be affected by moon, date, time, position of a Rarab's tail in San D, etc. All six of those options have an equal chance of landing. Therefore, you'd weigh the payoff of each by dividing it by the probability it would land on that number, i.e. Payoff x Probability. Well, in this particular instance, if you were to land on a 5, you'd get 6 total. According to my data, a roll of 6 is equal to +3 hMP. Well, since there is a 1/6 chance that you'd land on 5, you'd take the payoff, 3, and multipy it by the probability 1/6.

To get down to it, this is how it was figured in a mathmatical equation:
Current Payoff vs. Expected Payoff
1 vs. ((1 x (1/6)) + (1 x (1/6)) + (7 x (1/6)) + (2 x (1/6)) + (2 x (1/6)) + (3 x (1/6)))

1 vs. 2.66666

If the left is ever greater than the right, you stay. If it's the other way around, you Double Up.
So, you should reroll on a 1 during a healers roll (der).

Healer's Roll Self & Party Roll



Basically what was explained earlier: Compare what you have, and then compare the chance of what you might get. If the chance payoff is higher, take it. If not, stick with what you got.

Chaos Roll Self & Party Roll

Since Chaos Roll is more of a range than a definate number, I went ahead and posted the ranges according to extreme highs and extreme lows. As we would expect, it looks a lot like Healers, where one should double up on 6 and on the unlucky, but staying on the lucky.

One thing to notice here, though, is that double'ing on a 6 roll for the COR as an individual is against the payoff tables. Meaning, if the COR was playing by himself, they shouldn't double up. Now, I could take this a step further, and actually crunch the numbers to say "Well, there are 6 people in the party, let's weigh the benifit of 2-3 melee's vs. the risk of 1 COR losing the effect", but I think that's going overboard.



Evoker's Roll Party, Self, With & Without SMN



Yayayay. New table is up. This one is interesting, especially since I've got /some/ data on it with a SMN. I'm not sure how accurate it is, it was a vague post so I'm just posting what I have here for the time being. Intrestingly enough, with a roll 7 in a PT without a SMN, you should Double Up o_O); Sounds wierd, eh? Not really, though, if you think about it. Roll 7 is just 1mp/tick. That's... Nothing. You could get a lot more if you take that chance. Anyway, go over it and dispute if you feel like it. I'm open to convorsations.

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Data Sources:
http://ffxi.allakhazam.com/db/jobs.html?fj...2;num=11;page=1 -- TwoDeuce (WHM Roll)
http://ffxi.allakhazam.com/db/jobs.html?fj...;num=139;page=1 -- Trinitee (DRK Roll)
http://ffxi.allakhazam.com/db/jobs.html?fj...853396149189767 - Rastlin & Davricle (SMN Roll)

I plan on continueing on all of these, as long as there are still measurable rolls out there.

Edit: Done editing the file, only roll changed was Chaos Roll on an extreme low range (Double-Up on 7's is the dominant stratagy for extreme low, but not extreme high). I'll post the pics tomarrow.

[Uchiha121486]

Dear Ambelina, the prise wishes you to watch over me~

[Screamer]

Only half of the time I reroll when I get an addup of 6 >.>
Most CORs I know (and myself too) notice that the 6>6 >Bust frequency is too high. Roll a 6 and we most likely do nearly a 40% chance of bust. Id rather be constant then be a COR that busts every 10 rolls ><

[Sugami]

Hehe I find this quite fascinating, great post

I've read people saying if there's a probability of 50% a better roll they'll take it (if not busts), I don't really like those odds, half the time it'll go against me I want bit more than 50% to take the risk (unless sitting on an unlucky number).

About the double VI frequency; you only precieve it as high because you notice going Bust more than not going Bust. I recorded my results from Doubling up on 6, 7 and 8. I didn't really do 8 much so the results can't really be used. I'd mark a tally if the result was better or if the result was Bust, if the result was onto Unlucky number I wouldn't record it (bit bad of me I know ^^ but then it'd be a tally on 7 or 8 anyways.

Anyways the probability of getting better on a 6 is usually 4/6 (considering was mainly using rolls that had 7 or 8 as unlucky) which is 66%, my results matched this estimate. In fact I had 70% better rolls (6 busts to 14 better rolls).
For doubling up on a 7 I got 5 busts to 10 better rolls, which is 66% better rolls. If we say 8 is unlucky that'd make 50% chance of getting better rolls, if there isn't an unlucky number between 8-11 then it'd be 66% chance of better rolls. So either way my results match the estimate

[Phlow]

Uchiha121486 :
Dear Ambelina, the prise wishes you to watch over me~

^^

Only half of the time I reroll when I get an addup of 6 >.>
Most CORs I know (and myself too) notice that the 6>6 >Bust frequency is too high. Roll a 6 and we most likely do nearly a 40% chance of bust. Id rather be constant then be a COR that busts every 10 rolls ><

I can only say this: I'm basing these numbers off an equal probability that all numbers are equally likely. If you have evidence that will prove otherwise, I'll be glad to look it over and even include it in my post as best as I can to calculate risk vs. payoff. But until then, as Sug stated, it could be just perception.

I've read people saying if there's a probability of 50% a better roll they'll take it (if not busts)

See, that's only half of it. You should only take the risk if there's a suitable reward for taking that chance. If you're better off with what you have, then keep it =P

[Sonos]

Interesting...

For me I stop at 6 on Healers (I have frequent 6s on a 6) no matter what because any hmp is better than nothing. Melee I Double up to 7 because while its great to have the melee rolls on its not as absolutely necessary as mp in my opinion. In regular setups.

But sometimes I just think certain party members are lucky. I was busting/double busting everything I rolled the other night. A guy had to leave and we got a replacement...I had to TRY to bust something. Rolling on 8s didnt matter. Superstition and heresay...I love this job.

[Delekii]

The buff offered by most rolls at 6 is very very miniscule, really. No reason not to double on a 6. The only roll I dont double on 6 is Healer's roll, and even then only if there are 2 rolls I need to have on myself, and dont want a bust. Sometimes a bust is actually useful for getting good rolls on people (faster to cycle them).

I think the 6>6 higher chance is placebo rather than based in fact, its just that its much more apparent when you bust (you think about it more, remember it more, etc).

[Phlow]

Another thing to consider is the rolls WITH the person of that job in your party. I know the buffs increase, but do they debuffs from bust increase as well? If not, seven and even eight might be worthwhile to roll on.

As far as "some better than none" on healer's roll, perhaps it is situational and if you are on chain 6 with the mages running extremely low that assured 2hMP is better than the 1/6 chance you'll get 9hMP and 1/6 chance you'll get a bust, I dunno. I'm just laying out payoffs tables from my days in Game Theory classes.

[Sugami]

Delekii :I think the 6>6 higher chance is placebo rather than based in fact, its just that its much more apparent when you bust (you think about it more, remember it more, etc).

That's what I said

As for better results I go on the basis a higher number is better than a not higher number (lucky and unlucky aside) since I don't carry about a table of which numbers have what effects on which rolls

[rocketh]

here's my suggestion on Double-Up: you have 45 seconds, use the wisely. :love

Evoker's Roll example:
- You don't have to PR (VI) > Double (IX) > Double (Bust!) in, like, 10 sec, because that would mean 0Mp/tick for about 50 sec, right until you can PR again.
- Instead, do PR (VI) > Double (IX) > WAIT 40 sec > Double (Bust!). You'll still fail because of the bad luck, but you will still give a 1mp/tick for 40 sec, and 0mp/tick until PH, and that means 20 sec.


This little tactic, imho, is worth when you're ready for a risky Double-up. If luck is against you, there's nothing that will save you from busting but, at least, you party will still gain something until the next PR.

[Sugami]

Hehe well if you don't mind standing around trying to time it then sure, me personally I want to get the roll done and out the way in the quickest amount of time, busts and all
Incidentally the Bust will still last for 5mins

[Lithiani]

It's not raw numbers that just count either. In some situations, doubling up will get you a higher grade of buff, but if the current grade off buff is enough, then any chance of bust is not worth the risk. The COR in my PT yesterday kept busting Healer's Roll going for higher numbers, and I eventually had to say to him "look, any +hMP is fine, don't risk a Bust if I have enough hMP to maintain the chain". Even Doubling up on a 4, 5 or 6 isn't worth it if +2hMP is enough to keep me in MP (I was WHM at the time).

[Phlow]

I won't argue with that; no job is simply do A, then B, then C, repeat, level up. Some will argue with me, but those people don't realize that sometimes shit happens. You have to be dynamic in a party in order to adapt to all situations thrown at you. Otherwise, you'll find that your parties die. A lot. As far as situational, yea, what good is +9hMP when everyone's MP tank is full, but a bust on Chain 6 and the mages are tapped out? This is why you're leveling your Corsair, and I'm leveling mine.

However -- I can guarentee you that if you and I were to stand around all day, you rolling with your stratagy and I with mine, overall, I would gain more hMP (assuming SE made the rolls totally random). Like it was stated before, a roll 6 isn't actually that much. On healer's roll, it's a +2hMP. I'd probably risk that for a chance at 4hMP, 5hMP, or 9hMP.

Also, you were a WHM at the time. I don't have the data on Healer's Roll with a WHM in the PT, so it could really be skewed. I mean, what if a roll 6 was something like 6hMP, and a perfect was 11hMP? I'd have to crunch the numbers to see if it was worth it or not.

[Lithiani]

Yeah, I totally agree with your points (and I hadn't considered being WHM with regards to Healer's Roll). It's Risk vs. Reward. if +2 hMP is enough, then any number over +2 might as well be +2. Conversly, if +2 isn't enough, then you're going to break chain regardless, so why not chance it... Such is the life of a gambler.

[Phlow]

Posted Evoker's Roll results. Bumping it so people don't forget about it ; ;

But yea, I need more suggestions and data. Even if it's links to other pages. I know I'm beggin, but I'm stuck in the hell levels (Quifim) with my COR >_>

[Kip_]

Phlow... That is so awesome.

[Kaoru_Atsumori]

This thread should probubly be stickied, it has some very useful information.
and speaking of stickies someone should compile the usefull information into a guide and get it stickied. . .i would start working on it myself right now but its 3:40AM and i need sleep D: Maybe i'll start tomorrow if i find time inbetween classes.

[Sugami]

I'm possitive I only got 1mp/tick from a roll of 8 the other day o_o;;
Wonder if there's some other element that may change things a bit?
I'm sure people were disputing over which numbers gave what amounts a bit back too... o_o;;

[Loqiel]

I have a private spreadsheet I use that looks pretty much like this one, broken down the same etc. For sake of discussion, I assume that all rolls like Ninja roll and Hunter's roll mimic Chaos roll in roll number strength: ie, Ninja roll will increase the evasion on a given number the same percent that Chaos roll will increase attack, since there's no real good way to test this.

Good work.

[kylen]

First, I want to say that your goal of trying to maximize the expected values of each different type of roll is the absolute right way to go about finding an optimal rolling strategy, rather than all the people who oversimplify their strategy by saying stuff like "I never double up on an 8 because that's a 50% chance of busting." However, I've taken a few classes in game theory, probability, and expected outcomes as well and I see one flaw in the way you're calculating your rerolling strategy.

You're starting at a roll of 1, looking at the possible outcomes of a single roll from it, deciding whether to reroll based on just the possible outcomes of that roll, then moving on and doing the same thing for 2, 3, etc. until you reach 11. What you're not taking into account are the expected values of possible future rolls after the first one. Your calculations work, but only if you're assuming that you can only double-up once and you have to stop at whatever number comes up next.

Consider this hypothetical scenario for Healer's Roll (I know these numbers aren't realistic at all, but they illustrate the example I'm trying to make - bear with me). Suppose that instead of the current +hmp values, you got the following rewards from Healer's Roll:

1: +2 hmp
2: +1 hmp
3: +1 hmp
4: +1 hmp
5: +1 hmp
6: +1 hmp
7: +1 hmp
8: +10 hmp
9: +10 hmp
10: +10 hmp
11: +10 hmp

Using your methodology, you'd start at a roll of 1, and determine that you shouldn't reroll a 1 based on the following calculation: 2 vs. ((1 x (1/6)) + (1 x (1/6)) + (1 x (1/6)) + (1 x (1/6)) + (1 x (1/6)) + (1 x (1/6))) = 1. You know that from a roll of 1 (+2 hmp) that if you re-roll once your +hmp after that roll will be lower (expected value of +1 hmp). However, what your method fails to take into account is that you have the option of rolling yet again and having an extremely good chance at hitting 8,9,10, or 11 which will give you a much larger bonus than if you had stayed on 1. If you take future rolls like that into account, your expected value of re-rolling on 1 is a lot higher than the value you get from your first roll alone.

The correct way to take the expected values of future rolls into account is to basically do the same thing you did, but start at 11 and work your way back to 1. I'll do this for Healer's Roll in a Party (expected value of 0 for busting) as an example.

First, start at a roll of 11. Like your method, we simply compare the expected outcome of staying (+9 hmp) vs. that or rerolling (+0 hmp). Obviously we want to stay.

Next, look at 10. Same thing that you did: Expected outcome of rerolling is 1.5 ((1/6 * 9) + (5/6 * 0)), so you'd want to stay on that as well and get +5 hmp.

Rolls of 9, 8, and 7 produce the same results that you got, since in each of those cases the optimal strategy for every roll above them is to stay. However, as your data shows, the optimal strategy on 7 is to re-roll for Healer's Roll (+2.33 hmp vs. +1 hmp).

Looking at whether to reroll on 6, your data shows that rerolling would get you an expected value of +3.833 hmp = ((1/6 * 1) + (1/6 * 4) + (1/6 * 4) + (1/6 * 5) + (1/6 * 9) + (1/6 * 0)). However, by using a value of +1 hmp for a roll of 7 in this calculation, you're assuming that you'd stay on a 7 if you rolled it. Since you already determined that it's best to re-roll on a 7 rather than stay, you want to use the expected value that you'd get from re-rolling on a 7 in this calculation instead, which is 3.66. So your new expected outcome would be ((1/6 * 3.666) + (1/6 * 4) + (1/6 * 4) + (1/6 * 5) + (1/6 * 9) + (1/6 * 0)) = 4.277. This is your actual expected +hmp value from re-rolling on a 6, taking future rolls into account.

Doing the same thing and working your way back to 1, you get the following expected values for each roll:

Roll Healer's Roll Expected value for double-up Re-roll?
0 0 5.021 yes
1 1 4.828 yes
2 1 4.710 yes
3 7 4.211 no
4 2 4.322 yes
5 2 4.991 yes
6 3 4.277 yes
7 1 3.667 yes
8 4 3 no
9 4 2.333 no
10 5 1.5 no
11 9 0 no
12+ 0

(sorry for the formatting if that table's hard to read ><)

Turns out that the optimal strategy is the same in this case (re-roll 1,2,4,5,6,7 and stay on 3,8,9,10,11), however the expected values for the lower numbers are a bit higher. Interestingly enough, on your very first roll (starting at 0), your total expected value from using Healer's Roll without a WHM in the party, taking all future double-ups into account, is almost exactly +5 hmp. Basically the same thing that you'd get if all the mages in your party were eating Ginger Cookies, which unfortunately they often don't bother to do in the parties I've been in ><.

Anyway, not trying to discourage you from working more on this since the data you've put up so far is still more accurate than any other rolling strategies that I've seen posted yet, and in many cases such as for Healer's Roll the optimal strategy you came up with is the same that you'd get from taking future rolls into account anyway. I also agree with you that it's hard to put a numeric value on the effects of busting, since the effects may have different consequences depending on the setup of the party that you're in, and whether you've already busted once already.