in such a way where you scan the best ruby quests you identified and assign your highest earner to all the 4 hour ruby quests (depending on merc level, run time left, and bonus). Starting from the bottom row, go through the quest priority listĤh ruby > 2h ruby > 1h ruby > 30m ruby > 15m ruby > 8h ruby > 5m ruby > 5m-4h non-ruby > 24h ruby > 8h-24h non-ruby > 48h ruby > 48h non-ruby Assuming shorter quests is better unless you have very high level mercenaries. Starting from the bottom row, identify the best ruby quest in each row. Prioritize quests you can instantly complete based on which ever time lapse length is better for you. If you are very close to ascending, and you can use time lapse at the start of the next run. Use the estimate of how long your current run will be and the level of your mercs to determine if you should assign long quests. Pr(kth priority quest gets chosen) = (1 - (k-1)/45) 4 - (1-k/45) 4ĭenote the vector of probabilities as P, vector of all 45 quest duration as D, vector of all reward multipliers (death chance included) as M.
First of all, among the 45 choices, for 1 <= k <= 45, Here, we need to expand the space of possible solutions to become all possible no-tie rankings among the 45 types of quests. But as you saw, if the average non-ruby wait is less than an hour, why go on these long 2 day ruby quests? The main drawback of previous solution was the assumption that all ruby quests take priority over all non-ruby quests.
The average ruby gain rate of this strategy is 0.76 per day. In a similar way, you can compute the realistic reward rate of each of the 9 ruby quests, and rank them in order - this becomes the priority. So, even though a 5 minute quest has really good multiplier, it on average takes (5 + 26.77 = 31.77) minutes to get to the next ruby quest - a six-fold reduction in reward rate. Combine with the earlier statement, the average wait between two ruby quests is 0.69 * 38.58 = 26.77 minutes. With this, you can work out the average duration of a non-ruby quest is 38.58 minutes. Pr(kth lowest duration quest picked | no ruby quests) = (1-(k-1)/9) 4 - (1-k/9) 4 If we say the lowest duration is 5min, second lowest duration is 15min, etc, then since we always want to pick lowest duration non-ruby quest available, So after every ruby quest, we on average need to do 0.41 / (1 - 0.41) = 0.69 non-ruby quests If we suppose the optimal strategy always prioritizes ruby quests over non-ruby quests, shorter non-ruby quests over longer ones, then the optimal strategy can be computed in the following steps: Questing - Intuitive but Suboptimal Solution The other is optimal but more mathematically abstract. I will present two approaches: one makes a certain assumption about the priority, hence is suboptimal, but is easier to understand. There are 5 types of rewards (ruby, skills, gold, relics, and hero souls, not counting recruitment quests here) and 9 different durations: 45 total possibilities. By not considering the merc level, we're in the imaginary world where the merc never levels up and stays at level 1, and we're trying to find the questing strategy to maximize its rubies per day. The key is to balance duration with the multiplier, while considering the time-sink of non-ruby quests. Then, any strategy would boil down to a priority list - among the 4 options given to you, you pick the quest with highest priority. Since we're dealing with one single merc only, I assume that the optimal strategy is the same regardless of the merc's level and ruby bonus. Here I try to determine the optimal way to send mercenaries on quests, absent any timelapse.
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