Path of Exile

PSA: Calculating Expected returns from gambles with prime regrading lens.

Content of the article: "PSA: Calculating Expected returns from gambles with prime regrading lens."



I made a simple google spread sheet for fast calculation on what type of gems might be worth to gamble on with prime regarding lens, with 3 different gamble scenarios.

Link @ Alt Q. Gem Gamble

To use the sheet, copy it (need to be logged in to gmail account) and than you can change the values. Than you need to enter (highlighted fields in the sheet):

  1. Weight of each quality as found on poedb.
  2. Cost of each gem.
  3. Cost of prime regarding lens.

After that you will see the expected avg. profit from 3 gambling ventures:

  1. Using the prime lens on superior (normal) gem and selling any result.
  2. Using the prime lens on the bad alt. quality gem and selling any result.
  3. Using the prime lens on superior gem. if you hit good alt. quality, you sell it. If you hit the bad alt. quality, you use prime lens on it again.

You should than pick the result that give best Avg. Gross profit % (basically how much chaos you get back per 1 chaos spent).
Fare warning: Though I double check the math, I of course recommend you go over it yourself before you make any big investment based on the spreadsheet. If you don't have the require knowledge to do so, just wait on the thread and see replies, I'm sure other math geek around here will go over it and post their impression.
Also, if someone find an error, please post a comment and if I check it to be true, I will update the spread sheet accordingly.

Before I go into the math, I should explain that prime regrading lens will re roll a gem quality to a new type, not already on the gem. That is, superior (normal) gem can only roll into alt. quality and non-normal gem can only roll into normal or the other type of alt. quality.

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From poedb you can get the weight of each quality type, for example for determination the weights are: 50/100/10 for Superior/Anomalous /Divergent respectively.



You can see than, that if you use the lens on a superior gem, you have 100/110 (~91%) to roll anomalous (flop) or 10/110 (~9%) to roll divergent (win).

if however you roll on an anomalous gem, you have 50/60 (~83%) to roll superior (flop) or 10/60 (17%) to roll divergent (win).

Therefore, in a world where all the non divergent determination cost the same, you can almost double you winning chance by rolling on anomalous gem, instead of superior one.
However, since this is already relatively common knowledge, the price of anomalous determination reflect it, and while you can get regular determination basically free from the vendor, the anomalous variant sell for 25-30 chaos on the trade site, even though, to the best of my knowledge, no meta build use it.

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The sheet I made take this into account to find the best gambling strategy based on the price of each gem and the chance to roll the good alt. quality variant from either the normal/bad alt. quality gem.

For those that are interested in the math it pretty simple statistics. I will use the determination gem weights + giving anomalous gem cost of 30c and divergent gem cost of 915c (about 10.5ex) so all the formulas will have numbers + will try to put the calculation in words for those that might find it easier to understand:



For gamble strat 1:
cost: normal gem cost + lens cost. (fix cost per try).
avg return: <(100/110)*30> +< (10/110)*915>
(91% to win 30c + 9% to win 915c)

For gamble strat. 2:
cost: anomalous gem + lens cost. (fix cost per try)
avg. return: <(50/60)*0>+<(10/60)*915>
(83% to win 0c + 17% to win 915c)

For gamble strat. 3:
cost: <(100/110)*lens cost> + <(10/110)*2 lens cost>. variable cost: (91%2 lens cost) + (9%*1 lens cost)*
avg. return: <(10/110)*915> + (100/110)*{<0*(50/60>+<915*<10/60>}
(9% to win 915c) + 91% to (83% to win 0c + 17% to win 915c).

You should also take into account that this is the AVERAGE return, that is, that will be your profit if you gamble very large amount of gems. In real life, where the amount of tries is limited, you can go into a bad streak and burn all your currency before you manage to hit a good streak to offset the loss (and of course, opposite can happen as well).

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Good luck in your gambles exiles.

Source: reddit.com

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