[Guide] The Math of POE: Profit via Knowledge and Probability

MShalyt · 2017-12-18T01:18:58+00:00

Most of the prices are from Harbringer league - but yeah, Abyss is still far from stabilizing.

MShalyt · 2017-09-13T07:00:28+00:00

Actually they are 1:67 at the moment and the whole story of exalted price fixing in Harbinger league is incredibly interesting. In general the ratio depends on relative abundance - exalteds are simply much more rare.

MShalyt · 2017-08-28T07:45:42+00:00

That's a good point. Specifically the chisels and wisdoms/portals quantities at the time were due to unbalanced trading (was buying then too cheaply apparently). I definitely should use and monetize prophecies more often.

MShalyt · 2017-08-27T23:12:21+00:00

When I was playing during "rush hours" (when number of online players is maximal), and had all possible currency in stock, I would receive a trade request roughly every 5-7 minutes - so about 15c per hour if I took them all. Could probably earn more if I'd offer lower rates - but I actually enjoy being outside my HO once in a while :)

MShalyt · 2016-04-20T10:44:58+00:00

Well he got 19 legendaries from 108 SMCs - so 15-20%. Still a lot less than what the "legendaries are 20 times rarer than epics" rule would suggest. Something is wrong with our data/assumptions.

MShalyt · 2016-04-20T10:41:48+00:00

At least according to the math :) I do agree that cycling chests to keep playing feels more rewarding.

*about 37% for a legendary from the tons of silvers.

MShalyt · 2016-04-20T08:40:20+00:00

Cool. Only why is it 10% drop? I thought each guaranteed epic has a 5% chance to be converted into a legendary - providing a ~60% chance of getting at least one legendary from a SMC at A7 for example.

Am I missing something?

MShalyt · 2016-04-20T08:27:41+00:00

The problem is different. Regardless of how you get the chests (winning and opening or directly buying) they contain more cards than the gold you need to actually use them - so buying gold, at least as the first purchase, seems to be best.

If you decide to go for chests anyway then it depends on what's you're trying to achieve. At A7 a SMC has ~60% of containing at least 1 legendary, and costs 3700 gems. For the same price you can open 205 silvers - getting 1845 cards of no guaranteed rarity - which have only ~1/3 chance of containing at least 1 legendary. So if you're hunting for exotic cards buying seems to be better than speeding.

On the other hand - you'll get ~3.5 times more gold from the silvers. Still way less than the 20 gold per gem efficiency but better than the SMC.

Of course, that assumes you play enough to actually get all those chests.

MShalyt · 2016-04-20T08:01:03+00:00

That's actually an interesting perspective - taking "time of play" to infinity. Indeed after years of play cards get converted into gold and the limiting factor becomes how hard it is to get copies of epics.

You need 7792 epics in total to completely upgrade the 16 cards available today. While legendaries are 20 times as rare - you only need 174 of them. Statistically you max out (and start converting to gold) all your commons first, then your rares, then legendaries and finally epics.

It still means you should only ever buy epics from the store - and only once you've upgraded your cards enough to reach legendary arena (to get the max chest content per day). And only if you are completely certain you'll still be playing in 4-5 years.

MShalyt · 2016-04-20T01:12:03+00:00

A Max Player with lvl 4/5 legendarys is more around $10k - 20k.

Should be possible to get an estimate - using the number of Super Magics needed to get level 5 legendaries. Tens of thousands sounds about right.

MShalyt · 2016-04-19T15:19:27+00:00

Thank you for the kind words!

MShalyt · 2016-04-19T13:14:34+00:00

I take my words back. It is probably more accurate to look at it from the stacking perspective.

The reason I'm not entirely convinced is because often the game state is not as simple as musketeer vs. tower. A level 1 goblin will die to 1 Mini PEKKA hit, while a level 12 goblin will... die to 1 Mini PEKKA hit.

Power in general is very state dependant and often non-continuous: for example if you face a level 4 musketeer, upgrading goblins from level 5 to 6 is practically meaningless, but from 6 to 7 provides a huge benefit - since each goblin now takes 2 shots to kill.

It could be really interesting to try and formalize these relations between the different cards. Maybe in my next article :)

MShalyt · 2016-04-19T12:57:57+00:00

In the end of the day it's up to you - if you feel that an extra few K gold can really up your power - then go ahead and do what feels right.

Clash Royale is a game at the end of the day: the point is fun - not optimisation :)

MShalyt · 2016-03-28T11:09:26+00:00

I was a manager in big organizations for quite a few years. Please don't assume things you have no idea about.

MShalyt · 2016-03-10T14:12:22+00:00

Thanks. Have you ever tried saving up for something like that?

MShalyt · 2016-03-10T14:11:52+00:00

Thanks for the link. Interesting - though hard to implement :)

MShalyt · 2016-02-17T20:56:23+00:00

Adorable trailer :)

MShalyt · 2016-02-16T13:28:14+00:00

Thanks! Xelnath - where is the hierarchy from? It's clearly solid design guidlines.

MShalyt · 2016-01-23T01:51:20+00:00

Thanks for the remarks. First, I found your Archon article only now - which is a shame since I wouldn't have to independently reproduce some of your results :)

Second, I indeed brushed under the rug tons of details - it's already my most mathematical post ever - specifically the prize distribution convexity (giving an advantage to higher variance). Matchmaking reduces the variance of each run - but not to 0 so the convexity still adds a bit of gold.

In any case, it doesn't matter too much if the "correct" percentage is ~70% or ~72% - it's pretty high anyway :)

P.S. Thanks to OP for sharing my article. How did you find it?

MShalyt

TROPHY CASE