Talk:Lucky and Unlucky

I'm down with this page being a duplicate of/or redirect from Lucky. Either way... who cares.

Inaccuracies?
The lockpick tables are inaccurate in terms of the general cost to obtain the title, for the following reasons:

1) Both tracks have rounded the number of chests, but inaccurately calculated the gold costs because it tried to model the unrounded chest figures instead of the rounded ones, resulting in one of the lockpicks for a 90% RR costing 139 gold instead of 1250. Also note that any decimals should probably be rounded UP (ceiling) rather than using standard rounding.  11111 chests at 90% RR means that the 0.1 repeating is "left out" of the calculations, and it cannot be ignored accurately while maintaining an accurate "average".

2) Another fault in Lucky's calculations is an incorrect assumption it makes. In order to have enough lockpicks in a typical model to maximize the title, a player must have exactly one lockpick for every failed chest....plus one more, because you must have more lockpicks than you do failures since a failure destroys a pick, or else the title cannot be completed without maximizing the title prior to reaching the theoretical figure of 11111.  Or to put it in example form: suppose you try 90% RR chests starting out with no lockpicks (you buy all of them), and you reach your 1111th failure on attempt 11110 (meaning that the last chest maxes your Lucky title).  If you do not buy a 1112th pick, you cannot finish the title.  The only way, in said model, to need ONLY 1111 picks is to maximize the title by your 11110th attempt, which is breaking the "average model" rule and is thrown out as it does not match the statistical model being presented.

Ergo, the gold costs for Lucky should be calculated as (#-of-failures + 1) * 1250.

3) The Unlucky title track is totally wrong. The total cost for maximizing Unlucky, in theory, should be the number of lockpicks that must be destroyed in order to maximize it.  The chest count accurately shows that a user must have an equal number of failed chests at both 10% and 90% RR to get the title, due to the nature of the points....but it inaccurately states that it costs a user MORE to do this at 10% than 90%.  In actuality, it's equal, because the number of chests you must fail is exactly the same.  What I suspect happened here is that the user was trying to calculate the total number of chests to be opened (successes AND failures) but only calculated out the failures and then tried to base the costs on that while taking RR into account.  It no longer becomes applicable once the number of failures is known: we're not maxing Lucky in this case, so the lockpick count is exactly equal to the failed chest count, which means that the cost is simply #-of-failures * 1250.

Does anyone disagree with this reasoning? Don't want to adjust until people have verified that my logic makes sense. --BuildKitten 22:17, 22 November 2010 (UTC)


 * Yes the numbers do seem to be off. So, yes, I do think numbers reworking is in order. #1, I don't think rounding is too big of an issue, due to variance. #2, to determine how much it'll cost to get to a given tier, you have to factor in how many lost chests there will be for opened chests. If it's a 50/50 ratio, your cost is equal to chests needed * 1.25k. If it's 25% retention, the cost is 3x that. #3, I think that the numbers given are confusing themselves. lucky seems to be "successful opens" and unlucky seems to be "total opened. Oh, some theorycrafting relating both retention rate and lucky and treasure hunter was done over at guildwiki, if you want to look that over. Also, on the talk page there, I made a spreadsheet at some point that helps in determining how this all plays out. --JonTheMon 04:26, 23 November 2010 (UTC)


 * I'm not sure if this still confuses people but I will try to describe what I see here
 * The chests to max title columns for both unlucky and lucky are the number of chests required to be opened
 * For lucky the number is how many chests it takes to retain 10,000 times
 * with 25% rr you can expect to retain once every 4 chests you open so you need 4 * 10,000 or 40,000 chests
 * as a second example with 50% rr you can expect to retain every second chest so you need 2 * 10,000 or 20,000 chests
 * (the 4 and 2 to multiply the number of retains come from (1/(0.25)) and (1/(0.5)) respectively this can be generalized to (1/(rr)))
 * For unlucky the number is how many chests it takes to break 500,000 / (250 * rr) picks
 * with 25% rr you can expect to break 3 out of 4 times and gain 62.5 points for each break, meaning you have to break 8,000 times so you have to open 10,667 chests (or 8,000 + 8,000 * 1/3 if you want to know how to find that number)
 * as a second example with 50% rr you can expect to break every second time you open a chest, and gain 125 points every time you break, meaning you have to break 4000 times, meaning you have to open 8000 chests (or 4,000 + 4,000 * 1)
 * (the 1/3 and 1 for multiplying by number of breaks comes from (0.25 / 0.75) and (0.5 / 0.5) respectively this can be generalized to (rr / (1-rr)))
 * The cost columns display the cost of the number of picks broken to achieve max rank at that rr for each title respectively
 * For lucky subtract 10,000 from the number of chests required then multiply that by 1.25k to get the cost of picks broken
 * For unlucky the cost is 500,000 / (250 * rr) (this gives you the number of picks needed to max the title you can round to the ceiling number if you wish to be exact) take that result and multiply it by 1.25k for the total cost of buying that many picks.
 * The reason the chests to open for unlucky is symmetric is because you get more points as rr increases but break fewer picks
 * the example with 10% and 90% rr's, at 10% you break 9/10 picks and gain 25 points, at 90% you break 1/10 picks and gain 225 points, 1/9 as many breaks for 9 times the points thus the same number of chests required to complete the title. however the cost decreases between the 10% and 90% rr's because you have to break fewer picks to max the title as rr increases 1/9 as many picks with this example and thus 1/9 the cost.
 * keep in mind that we are not factoring in price of drops received so the cost is just a base start up average if you buy all your picks before opening chests or selling drops, we are also assuming you do not gain higher retention rates from increasing lucky and treasure hunter tracks, and that we live in a perfect world where after opening 100 chests with 10% retention you retained 10 picks for every set of 100 chests so your cost for lucky may be much higher or lower depending on your luck, pun possibly intended, also for the sake of formulas rr of 25% would be 0.25 you can extrapolate from there for others.
 * I hope my explanation cleared things up some
 * Also round-off error is a pain even more so when dealing with things that require a ceiling value but not using one --[[Image:User Tenri My image.jpg]] Tenri 13:49, 1 May 2011 (UTC)

Recent reverts and methodology questions
I recently reverted the page to (what turns out to be) my last edit of Lucky and Unlucky: no reason was given for reverting the edit, which several people have suggested was easier to read. However, that does not mean that that I am convinced that the current numbers paint the most accurate possible portrait of efficient pursuit of the title.

I think that the most usable version of this article should relegate the methodology (and its discussion) to a subpage and present the simplest possible advice, which is roughly:
 * It takes a long time.
 * 9 rings is a good way to throw money (and AFK time) at the title... and corner rings are generally better than the others.
 * Always open chests if you can.
 * The most efficient strategy varies, depending on your retention rate and whether you are pursuing other titles. (And, for that matter, how much you enjoy/hate grinding.)

Obviously, some meat is necessary to help people understand why the above is true, but most of the details will distract from the basic advice that people come to the wiki hoping to find. I am not, by any means, suggesting we ignore what most efficient really is, but we can move most of the gory calculations and comparisons outside the main article. (In particular, the optimum strategy will vary between 9 rings, keys, picks, and particular grinds over the course of pursuing the title. However, the title takes so long to achieve that it's probably unrealistic to assume that any single person is going to stick to optimal...so it makes sense to report those details elsewhere and instead use the article to provide more generally usable advice.)

It's quite possible that, in simplifying the article, I oversimplified or left invalid/incorrect impressions; those should be fixed. It's also possible that I left out a key point/principle; those should be restored. But I don't think we need to return to an article that was difficult for lots of people to read, especially since, even before my edits, the article contains a lot of info important to those interested in the title(s). — Tennessee Ernie Ford ( TEF ) 20:15, 3 May 2011 (UTC)


 * you make to much changing and hard to read. for 3 yrs time this page good information please leave a lone.OverKill


 * I'm going to side with Tennessee on his revert, simply because:
 * a) The Lucky and Unlucky article needs to put respective information first. Information regarding chests with 50g value should not be in the main section for Lockpicks.
 * b) Word chunks should be blended into simpler entities, or separated into subcategories if there's enough information. There are enough statistics not regarding Lockpicks retention specifically to warrant a subsection. Blue Clouded 22:23, 3 May 2011 (UTC)


 * Oh noes! Changing after 3 years! Anyhow, I like the fact that the TEF's version is less Wall-of-Text-ish and better organized. --JonTheMon 22:39, 3 May 2011 (UTC)


 * Any arguments against TEF's version? Any at all?  &mdash;  Raine Valen  [[Image:User_Raine_R.gif|19px]]  23:24, 3 May 2011 (UTC)

Possibility Theory versus Probability Theory
You do know that there is an enormous chance that the total price spent picks/tickets, points earned/time spent on boardwalk, and their respectable probabilities will not reflect the data in the tables?

Pseudo-Random variables completely destroy these probability tables.

Displaying information on how long it is going to take someone to max a title based on simple probability calculations will almost always be inaccurate.

The numbers represented in the table have never been achieved in-game, since they are merely the results of plugging variables into a probability equation.

Why?

...the coding (although not true random and instead pseudo-random) is intended to be random.

If you perform the following 500 times: [With a 90% retain rate you open 100 chests]  The number of times out of those 500 tries that you will get [90/100 retains] will most-likely not be 100% ..... instead its... OMG GET THIS..... Random! ....and I'd bet you that the percentage of the percentage is a lot further away from being accurate than you would like to believe.

The titles themselves are called unlucky and lucky. Think about that for 2 seconds before you go on calculating an ideal scenario that will never come to exist. (although I do not believe in fortune, I do believe in spontaneity)

Would it not be best to save all this hypothetical math and just leave the retention/title ratios up?

Also... for those of you who don't see where I am coming from, or still disagree... please research the "possibility theory" and supplement your knowledge of "probability theory" with it. (Since it should be taught hand-in-hand with probability in the first place)  71.239.152.236 16:37, 2 July 2011 (UTC)


 * I think you've misunderstood why it's important to include an estimate of hours and numbers of chests: people need to learn early on that a full week of AFK at the boardwalk or 40 hours of chest-running isn't going to do the trick. It's important the people realize that Nine Rings is much, much more efficient (for Lucky) than Rings of Fortune and Clovers are simply colorful (for title-grinding). Finally, it's also important to show that these titles require tons of cash.


 * In other words, these 0th order of approximations are very useful: someone opening chests using picks at a 90% retain rate is going to see something much closer to 450 retains than to 50; it's random, but it's not completely unpredictable. Better approximations are welcome (e.g. using results of Monte Carlo simulations or by plugging into the relevant statistical formulas). But in the meantime, these numbers paint a helpful picture. — Tennessee Ernie Ford ( TEF ) 17:30, 2 July 2011 (UTC)

I understand the entire "in the ballpark" thing, and I do agree that some might like an idea..... but a lot of the aspects should be removed, since it is relatively unpredictable. I still disagree with the ballpark figures since it is random. If a game assigns value to a pseudo-random variable (Value 1-10), and your title says that if the variable's value is 8 or lower... you retain a lockpick (ie a 80% retain rate) .... it is still pseudo-random... The conditions for a retain are altered, but the number of retains achieved still relies on a pseudo-random variable. Numbers can't be used to predict something intentionally randomized unless you know what the seed is for the random variable manipulation. 71.239.152.236 02:58, 3 July 2011 (UTC)


 * While any single use of a lockpick is a random event, you can easily predict trends. (Law of Large Numbers.) In particular, the ballpark estimates (in this article) are, erm, within the ballpark of reasonable expectations for length of time and cost (as you suggest, they aren't 100% accurate, in no small part b/c they offer specific numbers rather than ranges with a probability assignment) . In my strong opinion, it is far better to post those estimates than none at all. — Tennessee Ernie Ford ( TEF ) 04:03, 3 July 2011 (UTC)