Luck titles guide

Please note: the following analyses describe the expected values for tickets won and games lost at the various games of chance. By nature of statistical statements, even after hours of playing there is no guarantee that the actual, individual results will be exactly as or even close to what has been calculated here. If you are convinced you have found a flaw in the calculations, please present the flaw as precisely as possible and discuss it in the article's talk page before changing the article.

Overview

The Unlucky and Lucky titles are account-based titles which are obtained through various in-game activities:

• Playing the Shing Jea Boardwalk games Nine Rings and Rings of Fortune. These games last for certain special events and will return in the future.
• Opening chests with a lockpick. Retaining the lockpick adds points to the Lucky title; breaking it adds points to the Unlucky title. This is a permanent feature of the game.
• Using a Four-Leaf Clover and having 15% DP removed from the character awards 4 Lucky points. The clovers were part of the Lucky weekend event.
• Participating and winning in the ring game during the finales of the Wintersday 2006 and Wintersday 2007 event awarded Lucky points.

Boardwalk games analysis

• Nine Rings
  • The amount of tickets gained is statistically equal in every location, but more games are lost on corners (awarding more Unlucky points and the same amount of Lucky points), so the following analysis will be based on playing on a corner ring.
• Rings of Fortune
  • All locations are equally advantageous.

	Nine Rings	Rings of Fortune
Cost	10 Tickets	2 Tickets
Winner	55 Tickets (Corners) 40 Tickets (Edges) 25 Tickets (Center)	12 Tickets
Runner-up	15 Tickets	3 Tickets
Length of Games	8 Seconds	8 Seconds
Length of Speech	35 Seconds	35 Seconds
Number of Games per cycle	19 Games	20 Games
Length of cycle	187 Seconds	195 Seconds
Games per hour	365.8	369.2
Loss of Tickets per Game	-5/9 Ticket	-1/8 Ticket
Loss of Tickets per Hour	-203.2 Tickets/Hour	-46.2 Tickets/Hour
Ticket Wins per Game	9.444 Tickets/Game	1.875 Tickets/Game
Ticket Wins per Hour	3,454 Tickets/Hr	692.3 Tickets/Hr
Games lost per Hour	243.9 (Corner)	230.75
Cost of Playing	3048 gold/Hour	692.3 gold/Hr
Tickets Per Gold	1.13 Tickets/Gold	1.00 Ticket/Gold

Achieving one title only

• If one wants to achieve the Unlucky title with the least amount of Gold spent, Rings of Fortune is optimal.
• Otherwise, Nine Rings is better. Notably, it is faster for either title.

Lucky	Nine Rings		Rings of Fortune
Charmed 50,000 tickets	5,294 games 14.5 hours	44.1	26,667 games 72.2 hours	50.0
Lucky 100,000	10,589 games 28.9 hours	88.2	53,333 games 144.4 hours	100.0
Favored 250,000	26,472 games 72.4 hours	220.6	133,333 games 361.1 hours	250.0
Prosperous 500,000	52,944 games 144.7 hours	441.2	266,667 games 722.2 hours	500.0
Golden 1,000,000	105,887 games 289.5 hours	882.4	533,333 games 1,444.4 hours	1,000.0
Blessed by Fate 2,500,000	264,720 games 724 hours	2,206	1,333,333 games 3,611 hours	2,500
Unlucky	Nine Rings		Rings of Fortune
Hapless 5,000 games	7,500 games 20.5 hours	62.5	8,888 games 24.1 hours	16.7
Unlucky 10,000	15,000 games 41.0 hours	125.0	17,777 games 48.1 hours	33.3
Unfavored 25,000	37,500 games 102.5 hours	312.5	44,444 games 120.4 hours	83.3
Tragic 50,000	75,000 games 205.0 hours	625.0	88,889 games 240.8 hours	166.7
Wretched 100,000	150,000 games 410.1 hours	1,250.0	177,778 games 481.5 hours	333.3
Jinxed 250,000	375,000 games 1,025 hours	3,125	444,444 games 1,204 hours	833
Cursed by Fate 500,000	750,000 games 2,050 hours	6,250	888,889 games 2,408 hours	1,667

Achieving both titles at the same time

• It is beneficial to play both games in order to reach both titles of the same tier at the same time.

Tiers	Nine Rings			Rings of Fortune			Total
Hapless and Charmed	4,615 games 12.6 hours	38.5	43,588 Tickets won 3,077 games lost	3,419 games 9.3 hours	6.4	6,410 Tickets won 1,923 games lost	21.9 hours	44.9
Unlucky and Lucky	9,231 games 25.2 hours	76.9	87,176 Tickets won 6,154 games lost	6,838 games 18.6 hours	12.8	12,820 Tickets won 3,846 games lost	43.8 hours	89.7
Unfavored and Favored	23,077 games 63.1 hours	192.3	217,939 Tickets won 15,385 games lost	17,094 games 46.3 hours	32.1	32,051 Tickets won 9,615 games lost	109.4 hours	224.4
Tragic and Prosperous	46,154 games 126.1 hours	384.6	435,878 Tickets won 30,769 games lost	34,187 games 92.6 hours	64.1	64,102 Tickets won 19,230 games lost	218.8 hours	448.7
Wretched and Golden	92,308 games 252.4 hours	769.2	871,757 Tickets won 61,539 games lost	68,375 games 185.2 hours	128.2	128,203 Tickets won 38,461 games lost	437.6 hours	897.4
Cursed by Fate and Blessed by Fate	115,385 games 315.45 hours	961.5	1,089,575 Tickets won 76,939 games lost	752,137 games 2,037.01 hours	1,410.2	1,410,241 Tickets won 423,092 games lost	2,352.46 hours	2,371.7

Lockpick analysis

A Lockpick has a certain chance of breaking after opening a chest. If a lockpick breaks, it will add [250 * retention rate points] to the Unlucky title; on the other hand, if the lockpick is retained, it will add 250 points to the Lucky title. The numbers are the same in Normal and Hard Mode. (The points are doubled during a lockpick bonus weekend, if you enter the zone after the bonus period has begun.)

The rate at which (Un)Lucky points are gained depends on the number of chests opened per unit time and the chance of retaining lockpicks. The chests-per-unit-time depends on the difficulty of the area, the amount of chests there and the skill of the player/team. It cannot be quantified and will be omitted in this analysis.

The calculations below are based on purchasing lockpicks at merchants for 1,500; you can save money at Discount Merchants (price: 1,200) or from other players (typical price: 1,250 ).

The following formulas are relevant to the lockpick analysis:

Let R be the chance to retain a lockpick after use. (See Lockpick for details on how to calculate R). (1-R) is then the lockpick's chance of breaking.

Unlucky points per key = 250R

Unlucky points per chest = 250R(1-R)

Price per key = 1500

Price per Unlucky point = (Price per key) / (Unlucky points per key) = 1500/ (250R) = 6 / R

Lucky points per chest = 250R

Price per chest = 1500(1-R)

Price per Lucky point = (Price per chest)/(Lucky points per chest) = (1500(1-R))/(250R) = 6 (1-R)/R = 6/R-6

For the purpose of calculating in the Treasure Hunter title with the Lucky titles and when they will change R when they "level", here are some additional formulas:

Chests opened per key = 1/(1-R) = Treasure Hunter points per key if chest is "high end"

Unlucky points per key = 250R

Lucky points per key = (Lucky points per chest) * (chests opened per key) = 250R / (1-R)

Keys needed for next title = points needed for next title / points per key

These results mean the following:

• The highest rate of Unlucky points per chest is achieved when your rate is 50%.
• Reaching the maximum Unlucky title via lockpicks alone would require spending 12,000, if you only opened chests at a 50% retention rate.
• The price of Lucky and Unlucky points decrease as R increases.

start and end values:

At the minimum R = 0.1, 1 Lucky point costs 54, 1 Unlucky point costs 60.

At R=0.98, 1 Lucky point costs 0.122, 1 Unlucky point costs 6.122.

• For illustration, these are the most extreme prices to reach the maximum Lucky title (2,500,000 points), starting from zero Lucky points. These calculations take into account improving retention rates from increasing Lucky and Treasure hunter title rank:
  • At Treasure hunter rank 7 and only picking Ascalonian chests on Normal mode, on average 10,600 chests have to be opened and 887 have to be spent.
  • At Treasure hunter rank 0 and only picking Hard mode chests, on average 26,300 chests have to be opened and 24,450 have to be spent.

Comparison to Nine Rings

Question: a level 20 character with rank 0 Treasure Hunter wants to farm Lucky points. Which method is more favorable, playing Nine Rings or farming Ascalonian chests on Normal mode?

• Nine Rings can be played while AFK and requires no user action whatsoever beyond buying tickets beforehand.
• Nine Rings awards 3454 Lucky points per hour. At 65% base retention rate, this equals opening one chest every $60 minutes * 250 * 0.65 / 3454 = '''2.8'''$ minutes. This figure already includes breaking lockpicks.
• At 3048 per hour and 3454 points per hour, each Lucky point costs 0.882 at Nine Rings, whereas at R=0.65, each point costs 6*(1-R)/R = 3.2 for chest farming. Chest farming for Lucky points becomes cheaper at R > 0.87, not considering chest drops and discounted lockpicks. Assuming discounted lockpicks and 100 value per drop, break-even occurs at R > 0.83.
• Unlucky points cost 12.5 each for Nine Rings and 60 each for chest farming.
• Chests can be run all the time, while Nine Rings is only available during special events.
• Chest farming has added value in the sense that it also increases the treasure hunter (assuming high end chests) and wisdom titles (from identifying gold chest drops). It also potentially gives useful item drops and equipment modifications that can be sold and the proceeds re-invested into lockpicks.

The best method depends mostly on the chance to retain the lockpick and therefore mostly on the Treasure Hunter and Lucky title track. Chest running is more cost-efficient at >85% retention rates and is available all year long but requires farming with all the tediousness involved, while Nine Rings awards a lot more points per day and can be played without interaction but is only rarely available.

Notes

If you intend on leaving your character in a boardwalk game overnight, be sure to first reset your connection to the server by closing the game and signing in again. Otherwise you may be disconnected after 24hrs of continuous play. If you are disconnected then you will have lost some opportunity to farm these titles.