Phantom roll probability:

[Darus Grey]

I'm fully aware that this isn't hard to figure out, but I'm also assuming someone has already done all this and I just can't find it. Thank you in advance for any responses.

Basically what I'd like to know is the exact probability of each result assuming you doubled-up every time until you busted, as well as assuming you never doubled-up on a number like 6 or 7. Is there any resource out there that has a lot of the probability's already figured out?

Closest I found was http://www.bluegartr.com/forum/showt...ll+probability
Which only measures a single use, and wasn't really what I want anyways(it's measuring "real" probability in the same sense you measure a roulette table for weighted results).

[Kylen]

Basically what I'd like to know is the exact probability of each result assuming you doubled-up every time until you busted,

This one's easy. Probability of Bust: 100%. Probability of any other outcome: 0%.

as well as assuming you never doubled-up on a number like 6 or 7

This thread might have your answer:
http://www.ffxionline.com/forums/cor...long-math.html

It's an old thread and it doesn't address optimal double-up strategies, but the math behind it is sound.

Why would you want to know those probabilities, though? Neither is an optimal strategy to be following if you're trying to maximize your rolls' average effectiveness over time.

I made a spreadsheet when COR first came out that would calculate the optimal double-up strategy for each roll by starting at XI, taking the expected value of doubling up and making the decision to double-up or stay based on that, and working backwards to 1. Spider-Dan was kind enough to host it and has kept it updated as new rolls were released and the values of old ones were changed:

http://venomweb.150m.com/ffxi/roll_calculator.xls


The one snag I ran into was coming up with an accurate approximation of the expected value of a Bust, so right now it's set to 0 (you can change this value on the spreadsheet though and the other numbers in the table will automatically update). There are so many variables that affect a Bust's "value", such as how many rolls in your cycle, number of players affected, whether the negative penalty of the Bust affects your own performance, and whether your Fold/Random Deal timers are up, that coming up with even a vague approximation is pretty much impossible. In reality, Bust would normally be a small-ish positive number, though, since most of the time you're only going to lose 1 minute without the buff waiting for PR recast (again, assuming no Random Deal and that this is your first Bust), so if anything I would recommend taking a more adventurous approach to your double-up strategy than what's listed on the spreadsheet.

[Darus Grey]

This one's easy. Probability of Bust: 100%. Probability of any other outcome: 0%.

You'd be taking the last result before the bust actually occured and using those as the sample. By result I mean 1/2/3/4/5/6/7/etc. The wording obviously implies you'd bust every time. More accurately what I wanna know is, if you say, had a computer program that did that 100,000+ times, what would the distribution of the last #s before the bust actually be.

Your link answers my second scenario perfectly, for which I'm very grateful. First scenario is the one that's actually important to me though ;0

[nekura]

Double up on 6 god damnit!

Edit: Except for Evoker's.

[Alistaire]

What level of merits are you going to consider in this equation? Snake Eye, Fold, Winning Streak, even Random Deal recast + Loaded Deck will alter these numbers. And exact behavior for each roll: In meripo I don't double up on 6 for Evoker's in most cases cause there's not a lot of benefit or need. I will double up on chaos roll on a 6 assuming I either have no busts and/or Fold available. Assuming I don't have Snake Eye up but do have fold up, I'll do a double-up on an 8 for chaos roll right before double-up wears off. For Corsair's roll it depends on my mood, but I generally want that roll as good as possible too, and that roll depends on the luck I have with chaos and vice versa.

Edit: oh and

This one's easy. Probability of Bust: 100%. Probability of any other outcome: 0%.

made me almost lose a good swig of energy drink.