Luck titles guide

Overview

 * The Unlucky and Lucky title is obtained through playing Nine Rings and Rings of Fortune at the Shing Jea Boardwalk, which first appeared during Dragon Festival 2006. The Boardwalk returned October 20-22, 2006, and on February 23-25, 2007.
 * It was possible to get a few points toward the Lucky and Unlucky title during the ring game during the finale of Wintersday 2006.


 * Unlucky: Title granted to an account that has lost games of chance.
 * Lucky: Title granted to an account that has won tickets in games of chance.

Analysis

 * Nine Rings
 * Corners win 55 tickets, while center only win 25 tickets and the edges 40 tickets.
 * The amount of tickets gained is statistically equal in every location, however more games are lost on corners, so following analysis will be based on playing on a corner
 * Rings of Fortune
 * All locations are equally advantageous.

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.
 * The fastest way to reach the highest tier in either of these titles is to play Nine Rings for the Lucky title; the cheapest way is to play Rings of Fortune for Unlucky.

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.

Lockpick analysis
A Lockpick has a certain chance of breaking after opening a chest. If a lockpick breaks, it will add 25 points to the Unlucky title; otherwise it will add 250 points to the Lucky title. These numbers are the same in Normal and Hard Mode.

The rate at which (Un)Lucky points are gained depends on the chance of the lockpick to break and how many chests per hour can be opened. The latter depends on the difficulty setting, the difficulty of the area and the skill of the player/team, cannot be quantified and is thus omitted in this analysis.

The following formulas are relevant to the lockpick analysis:


 * Let R be the chance to retain a lockpick after use.


 * Lucky points per chest = 250 * R
 * Unlucky points per chest = 25 * (1 - R)


 * Price per chest = 1500*(1 - R)

As for the price of gold per (Un)Lucky point, we can calculate:


 * ''Price per Lucky point = 1500 (1 - R) / (250 * R) = 6 * (1 - R) / R
 * ''Price per Unlucky point = 1500 (1 - R) / (25 * (1 - R) = 60

These results mean the following:
 * The price of Unlucky points is constant for all values of R, because as R increases, the price of opening a chest and the unlucky points per chest drop at the same rate.
 * The price of Lucky points decreases quadratically as R increases, because the price per chest drops and at the same time the number of Lucky points per chest increase.
 * Example:
 * At the minimum R = 0.1, 1000 Lucky points cost 54,000 on average.
 * At R=0.5, 1000 points cost 6,000.
 * At the maximum R=0.98, 1000 Lucky points cost only 122.


 * Therefore, the higher the chance to retain a lockpick, the better.
 * For illustration, these are the most extreme prices to reach the maximum Lucky title, starting from zero Lucky points (the calculations include improving retention rates from increasing Lucky and Treasure hunter title rank):
 * At Treasure hunter rank 7 and only picking Ascalonian chests on Normal mode, 10.600 chests have to be opened and 887 have to be spent.
 * At Treasure hunter rank 0 and only picking Hard mode chests, 26.300 chests have to be opened and 24.450 have to be spent.