You unlock Cauldron by upgrading the Alchemist's Hut to lvl. 2. By throwing items into the Cauldron, you will receive experience points and random resources. To receive any reward you have to throw 7 items. Items can be any mix - the same 7 items, or 7 different items. Items which can not be thrown into the Cauldron will appear faded (e.g. Coins, Rubies, Coffee beans, Treasure maps, Treasure map fragments, Gold ingot, Treasure, etc.).
Cauldron rewards statistics (work in progress) explanation:
In this table you add all your rewards you get from Cauldron and add how many times you have thrown. Once we have enough data, we can calculate the percentages. For example: You throw 14 x Fan (2 throws) into the Cauldron and you get 1 x Stone and 2 x Charcoal. Then you look at this table and you see that there's a 3 under Stone, 4 under Charcoal and 6 under "Number of times thrown into the Cauldron". You add those up and you write 4 under Stone, 6 under Charcoal and 8 under "Number of times thrown into the Cauldron". You always get the same experience, so that column stays the same. If there is still something unclear about updating this table, look into comments. If you still don't understand, then just leave it.
Don't forget to update the "Number of times thrown into the Cauldron".
The above table is valid if you throw the same item into the cauldron 7 times. If you throw different items into the cauldron, the resources received may be a combination of the results shown in the table.
This chart is the same data as the previous chart just normalized to a single throw (i.e. the total number of materials divided by the number of throws). While this table in essence tells you how much of each material you get PER throw (e.g. 0.30 wood per throw of 7 shuriken), you obviously aren't getting that much material per throw. You should instead use this table to tell you which item gives you the best chance of getting a certain type of material. E.g. the item which gives you the highest chance of getting a gold ingot is throwing 7 katanas. The highest number of each material type is in bold/underline.
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