Cauldron

Cauldron can be unlocked by upgrading the Alchemist's Hut to lvl. 2. By throwing items into the Cauldron, the player will receive experience points and random resources. To receive any reward 7 items must be thrown. Items can be any mix - the same 7 items, or 7 different items. There are currently 105 items that can be thrown into the Cauldron. 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.). Experience gained from each throw can be increased by acquiring the Porcelain Vase, which gives +10% extra experience points. With Tetrachloroaurate (craftifact) the player gets +5 Coins per Gold ingot.

*By throwing items into the cauldron, you will receive experience points and random resources.*

Sound of throwing 7 items into the Cauldron.

Throwing 7 x Petards into the Cauldron.Rewards after 7 x Petards were thrown. Porcelain vase added +4 experience points.By pressing the "x7" button you can throw items multiples of 7 (7, 14, 21, etc.) up to 49 items.Only 4 items were thrown into the Cauldron. The blue bar around the cauldron represents 4/7 or ~57% of the whole circle. 3 more items need to be thrown to receive any reward.By throwing 3 more items into the Cauldron a rewards will be received. *The "x7" button is not tappable.*Cauldron rewards with Tetrachloroaurate craftifact.Receiving Mental power from Cauldron from certain items.

## Rewards 'algorithm'

The item rewards that the player will get are randomly calculated following a complex formula, but it can be roughly approximated as follows:

* Chances of getting items are based on the sum of the "weights" of the 7 items thrown into the Cauldron.
	+ When throwing a multiple of 7 items, it is considered as multiple throws of just 7 items (e.g. a throw 49 of the same item is the same as 7 throws of 7 of the same item).
* The weight of each item can be calculated dividing by 7 the amount of XP received (without the Porcelain Vase bonus) when throwing 7 of said item.
	+ For instance, the weight of 7x Shuriken is 17, or the weight of 1x Shuriken is 2.429.
* The items that can be obtained are Wood, Stone, Steel, Charcoal, Gunpowder, Iron sand, Chemicals and Gold Ingot.
* The chances of obtaining a Gold Ingot are the total weight of the items thrown multiplied by 0.003.
	+ Or, in other words, the average amount of Gold ingots per throw is the total weight multiplied by 0.003.
* The chances of obtaining one of the other items are equal to the total weight of the items thrown multiplied by 0.01, for each of the other 7 types of items.
	+ Or, in other words, the average amount of each other item per throw is the total weight multiplied by 0.01, and the total number of non-ingot items, in average, will be the total weight multiplied by 0.07 (i.e. 0.01 times 7).
* There will be at least one item rewarded, although the exact formulas for this "compensation" are not known.

It can be deduced from this that to compare the expected benefits of different items to be thrown into the Cauldron, it's enough to compare their XP return when 7 are thrown into the Cauldron. For instance, the player is likely to get the same rewards (on average) when throwing Wood as when throwing Stone. When throwing 5x7 Wood (weight=50/7 each) and 10x7 Iron Sand (weight=50/7 each), the total weight would be 750, but if the player crafts each Wood into 4 Charcoal (total 20x7) and along with the 10x7 Iron sand into Steel (total 20x7) and those in turn into 4 Shuriken each (total 80x7), then throw all those Shuriken (80x7, weight=17/7 each) into the Cauldron, the total weight is 80 x 17 = 1360 (much better than the initial 750 before processing the Wood and Iron Sand into Shuriken, which compensates the processing time if the player can spare it).

Examples:

* The items thrown into the Cauldron are 7 Katanas.
	+ The total weight is 67.
	+ The chance of getting a Gold Ingot is 67 x 0.003 = 0.201 = approx. 20%.
	+ The average amount of each other item is 67 x 0.01 = 0.67, and the average total of non-ingot items is 0.67 x 7 = 4.69
		- As an example then, when throwing 3x7=21 Katanas, the average amount of non-ingot items would be 3x0.67x7 = aprox. 14, so the player might get 14 Wood or, more probably, 2 of each Wood, Stone, Steel, Charcoal, Gunpowder, Iron sand and Chemicals, or some other combination thereof. Keep in mind, these are just average amounts, so this can always vary.
* The items thrown into the Cauldron are 49 Mortars.
	+ The total weight is 250 x 7 = 1750.
	+ The average amount of Gold Ingot the player will get is 1750 x 0.003 = 5.25.
	+ The average amount of each other item is 1750 x 0.01 = 17.5, and the average total of non-ingot items is 17.5 x 7 = 122.5
		- As an example then, when throwing 2x49 Mortars (or rather 49 Mortars twice), the average amount of non-ingot items would be 2x17.5x7 = 245, so the player might get (always on average) 245 items, which might be 245 Wood or, more probably 35 of each Wood, Stone, Steel, Charcoal, Gunpowder, Iron sand and Chemicals, or some other combination thereof. Keep in mind, these are just average amounts, so this can always vary.
* The items thrown into the Cauldron are 1 Charcoal, 2 Shuriken, 3 Fans and 1 Boomerang.
	+ The total weight is 15 x 1/7 + 17 x 2/7 + 22 x 3/7 + 30 x 1/7 = 20.714.
	+ The chance of getting a Gold Ingot is 20.714 x 0.003 = 0.062 = approx. 6%.
	+ The average amount of each other item is 20.714 x 0.01 = 0.2071, and the average total of non-ingot items is 0.2071 x 7 = 1.4497, so the player might get one or maybe two other items (which might be different, or the same). Keep in mind, these are just average amounts, so this can always vary.

## Expected rewards table

The following table shows the expected average rewards when throwing items in the Cauldron:

The values in the table are valid for throwing the same 7 items into the Cauldron. When different items are thrown into the Cauldron, the items received will be a combination of the results shown in the table, based on the combined weights of the items thrown.

## Porcelain vase bonus

The experience points gained from the Porcelain vase are always rounded down the the nearest whole number. The rounding happens after the multiplication by 110%. For instance: when throwing 7 x Katana the player receives 73 experience points (73.7 rounded down); however, when throwing 14 x Katana (in a single throw, using the x7 button and then the slider), the player receives 147 experience points (147.4 rounded down) versus the 146 the player would receive (73 x2) if doing 2 throws of 7 x Katana each; throwing 21 x Katana will give the player 221 experience points (221.1 rounded down) instead of 219 for 3 throws of 7. The most effective (for experience points gain) throwing amounts are:

* 14 for Bomb, Charcoal, Ramen, Cup of coffee;
* 21 for Katana, Shuriken;
* 35 for Elixir of insight, Fan, Spikes, Petard, Steel, Gunpowder, Salmon, Tuna.
* For other items throwing multiples of 7 is just as effective as throwing 7.

## To next level

After there are only 2 000 experience points needed to reach the next level a text will appear after each throw, showing how much experience points are still needed to reach the next level. After reaching a new level with throwing items into the Cauldron the text "New level!" will appear instead.

Experience points to next level.New level!
## See also

Players can input data from their throws into the Cauldron in this spreadsheet - instructions should be displayed on the *"Summary\_7"* sheet (on the cells with a grey background). Questions can be addressed to the administrators. If a player doesn't feel comfortable editing the spreadsheet, they can always post their data in a comment below and someone else will happily update the spreadsheet. One of the uses of this spreadsheet is seeing how the statistical results match, or differ from, the theoretical values from the expected rewards "algorithm".