The Optimal Retention Rate for Unlucky Points

This note should provide some guidance to those interested in gaining unlucky points. Those who aren't won't care much for this.

It is easily seen that if one would like to gain unlucky points while breaking a minimal amount of lockpicks, then opening chests with a high retention rate is the way to go about it (each broken lockpick translates into an amount of unlucky points equal to 2.5 times the retention rate).

But what if one doesn't care about the amount of lockpicks broken and instead only cares about gaining unlucky points as fast as possible, that is, opening a minimal amount of chests.

As the retention rate increases, the (average) amount of unlucky points per chest increases (which is good), but the chance of breaking the lockpick decreases (which is bad). It turns out that opening chests with a 50% retention rate will maximize the (average) amount of unlucky points per chest.

The calculation can be performed as follows: denote the retention rate (in %) by n. The average amount of unlucky points per chest is the chance to break the lockpick (1-n/100) times the unlucky points gained (2.5n). This is 2.5n - n^2/40 which is maximized at n=50, yielding 62.5 unlucky points per chest.

Note that there is not that big a difference when n (the retention rate) is close to 50. For example, 40 < n < 60 yields an average of over 60 points per chest. Nevertheless, when n differs substantially from 50, say n=14 for example, the average number of points per chest is reduced to about 30. This means that it will take a player twice as long to gain unlucky points when opening chests with this retention rate.

A player can't control the retention rate exactly but the above information may be considered when deciding where to farm unlucky points, and in which mode to do it (normal or hard).

Thank you for the guide. I learned a lot from this.

A nice note to add is that at max character retention (max lucky and teasure hunter titles), the optimate chests to run may be 1250g chests (deep,urgoz,DoA,FoW) giving the maximum point gain of ~62 points, HM chest give ~61 pints, and availablity at least to me seems better.

Edit: Ignore post, mis-read premise.

Hmmm. Taking you're initial statement as true (values for lockpick breaking etc),
ottomh, I make expression ( n-n^2 ) / 40
Looks like you dropped a 2.5 when doing your /100.

This throws out your max value calculations also.

differentiate f w.r.t. n; stationary point is when df/dn = 0
gives (1 - 2n)/40 = 0
1 = 2n
n = ½

then w/e that is in unlucky points.

(Proof reading wanted plz)

Wrong, his expression is right:
2.5n * (1 - n/100) = 2.5n - 2.5n^2/100 = 2.5n - n^2/40

In fact you don't need to expand or differentiate to find the optimum, you just have to know the 2 roots (i.e., it gives the value 0 to the expression, here you can easily see it's 0 and 100) of the expression, and the shape of "parabola" that the corresponding function takes. The optimum (here maximum) is just in the middle of the 2 roots (due to the parabola shape), i.e. 50. Of course differentiating works too .

1-n/100 should not to be confused with "(1-n)/100", the error you made.

Are you kidding me? You really needed to go about doing all of this unnecessary math just to determine the best way to get unlucky points if you're not concerned about breaking them?

Highest value (locked) chests in hard mode. Period. These give you your lowest retention rate, thus your highest chance of breaking, keeping your lucky title down so your retention rate increases at the slowest rate possible. This also minimizes the amount of chests opened thus keeping treasure hunter increase rate down, also maintaining a low rentention rate.

Honestly...this did not require more than 5 seconds of my daily thought process.

Cliff notes: open locked chests in hard mode. Period.

Actually, if you care to actually read, HM locked chest are NEVER optimal. They become near optimal at highest retaintion rates (5+ lucky and r6+ teasure hunter). Below these title lvls HM lock chest don't net you enough points when compared to other NM chest out there. The sweet spot is between 40-60% retaintion, then by the nature of the math, diviation from that range come at a greater and greater cost at point gain per chest.

I also wonder if you sit on the center ring at 9 rings?

He is just trolling like usual. Ignore him.

Meh, ambiguous notation.
My answer is correct ofc for (1-n). I guess I should have thought more about the guildwars logic than the maths

Meh...I wasn't aware that the amount of points you get per break is dependent on your retention rate. I thought it was a constant number. Carry on.

It really doesn't matter anymore, someone who starts the treasure hunter title now at zero chests opened and does all 600g key chests will max unlucky title before they max treasure hunter. In fact they will have 576,365 unlucky points when they get the treasure hunter title and r7 is only 500,000. No need to calculate anything because they will get the title automatically. However veteran grandmaster treasure hunters who have already maxed the treasure title come up over 300,000 unlucky points short of the title. More than that if they maxed the title using keys before lock picks were introduced. The veteran GTH only choice is to go out and break another 5000 lock picks. Why this stuff was not made retroactive is a mystery and another stab in the back to old school GW players. I have max r7 TH and have 2,968,576 lucky and 191,405 unlucky points so according OP's formula I need to break another 4,983 lock picks to max a title Anet is giving away now? Never, Anet is full of crap these days.

When I first saw this update, I was pleased because at ~5000 chests opened I was no where even close to maxing unlucky. But as I reached 6000 chests I noticed just how fast the unlucky points were rolling in - too fast imo. I have to agree with Shadowspawn, that this title is no longer the prestigious and elusive title to have after GWAMM.

Math is complicated makes brain bleed.
/ragequit

Well, the nice thing about math, is that when it can be used (such as in this case) then it is absolute and useful, there is no room for dozens of opinions of the form "I think differently", which is refreshing every now and then in forums such as these.

As I started on my Treasure Hunter, Lucky and Unlucky titles after the update, I soon discovered that maxing Unlucky would be the least of my problems. It will be maxed long before the other two even comes close.
Rank 6 Treasure hunter (5.1K), Rank 5 Lucky (1.4 million), Rank 4 Unlucky (80K) when I started
Rank 6 Treasure hunter (5.8K), Rank 5 Lucky (1.6 million), Rank 5 Unlucky (145K) at present
As you can see the amount of unlucky points gained far outweigh the points I have gained in the other two title tracks. All chest have been run in normal mode.

Answer....HARD MODE BOXING.

Here is the formula

The angle of the dangle is directly proportional to the heat of the meat or inversely proportional to the fall of the balls.


Just run HARD MODE BOXING. It gives worst retention rate in the game and you can get 1 chest every minute or so.

Geesh...

Not really yang, its nto far out numbering ur lucky because unlucky has another rank, so for ur 7% gain in teasure hunter title, you gained 8% on ur lucky and 12% gain on ur unlucky title. Plus when running normal chests with ur current retention rate,63% very near the sweet spot for unlucky points.
And this is how the title should have been all along.