22 replies to this topic

[TSLlol]

Since it's been 4 months since release, I'm hoping someone has figured which method is more "profitable", putting 1 obsidian shard or 10 in?

[Lunar Eclipse]

I've tried both and i found the 1 clover method better. Some ppl would say 10 is better, but trust me do the 1s, you wont regret it. =)

[Shana]

1 is safer.
10 is riskier.

It is your choice. I started with 10 and after 200 ectos I only had 40 clovers. Did 1 for the rest and really wished I had just done 1 from the start.

Neither is profitable in the long run.

[Lunar Eclipse]

Shana, on 05 January 2013 - 05:52 AM, said:

1 is safer.
10 is riskier.

It is your choice. I started with 10 and after 200 ectos I only had 40 clovers. Did 1 for the rest and really wished I had just done 1 from the start.

Neither is profitable in the long run.

Yup pretty much the same exprience i had. Did 100 ectos got 10 clovers and wished I had just done 1 from the start. I have since got my other 67 from about 200 more ectos.

[Obbdot]

What we know :

- The probability of succeeding a trial with the 1s is 1/3.
- A trial with the 10s costs 10 times what a trial with the 1s does.


What we don't know :

- What the probability of succeeding a trial with the 10s is. Not enough data with large enough sample sizes where ever documented in a reliable way by players, at least not publicly.


What can we reasonably assume :

- The probability of succeeding a single trial of the 10s is also 1/3.


What are we interested to know :

- What is the expected cost of achieving 77 successes with the 1s? 80 successes with the 10s? 70 successes with the 10s and 7 extra successes with the 1s? What should you do?


What is the expected cost? :

- It is the expected number of trials times the cost of single trial.


How to estimate the expected number of trials :

- This experiment fits exactly a negative binomial model. The expected value of such a distributed variable is the number of desired success divided by the probability of success. If you chain 2 negative binomial experiments upon success of the first one, their expected value is the sum of both.

-> Expected number of trials to achieve 77 cloves with the 1s = 77 / (1/3) = 231.
Expected cost : 231 units.

-> Expected number of trials to achieve 80 cloves with the 10s = 8 / (1/3) = 24
Expected cost : 24 x 10 = 240 units.

-> Expected number of trials to achieve 70 cloves with the 10s and 7 cloves with the 1s = 7/(1/3) + 7/(1/3) = 21 trials of 10s + 21 trials of 1s.
Expected cost : 21x10 + 21 = 231 units.


So far, the expected cost of doing either 70 cloves with either the 1s or the 10s is exactly the same. Doing 77 cloves with the 1s is expected to be cheaper than doing 80 with the 10s, but doing a mix of both as the same expected cost as doing only the 1s.


What about the risk?

Risk can be measured by variance, which is the expected squared deviation from the mean. I actually do not know how to calculate the variance of doing 70 cloves first with the 10s and then chaining upon success with doing 7 cloves with the 1s. It is much, much, much harder than calculating the average, which is simply proved as additive. I'll therefore calculate the variance for a comparable amount of cloves, which is 70. This number is also very meaningful, because the last 7 will be done regardless with the 1s.

If a random variable is multiplied by a coefficient, the variance will scale with the squared coefficient. In simpler words, if the cost of 1 trial 10 units, the variance of the cost will be 100 times the variance of the number of trials.

The variance of a variable with a negative binomial distribution is the number of desired successes times the probability of failure divided by the squared probability of success. I won't prove it, but I assure you that it is both the way to calculate it and that it is a meaningful measure of risk.

In this case,
- the variance of the cost of achieving 70 cloves with the 1s is 70 x (2/3) / (1/3)^2 = 140/27
- the variance of the cost of achieving 70 cloves with the 10s is 100 x 7 x (2/3) / (1/3)^2 = 1400/27

The risk, cost-wise, is much higher, as the standard deviation (square root of the variance), is about 3.2 times higher for the 10s than for the 1s. The 10s are indeed much riskier.

However, they do have the same expected cost, so if you are a complete gambler with no risk aversion, go ahead, but most humans like to have increased potential rewards with increased risk. For the 10s, if the probabilities are the same, there is no increased potential reward, but there is significantly more risk.

Multiple edits : I went full retard twice in my calculations and use of formulas/concepts as I did them on the fly, half drunk at 3:00AM.

Edited by Obbdot, 05 January 2013 - 08:34 AM.

[matsif]

One of my guildmates did 70 with the 10 recipe and had to use almost 400 shards (or so he said).  So I'm sticking with the 1 recipe, although I'm not getting 1/3 probability right now on a smallish sample size (11 clovers in 45 tries, so roughly 1/4).

I'm still building up karma overall, assuming I get average on all combinations you need roughly 1050000 karma for the 250 shards for the gift of mastery and for the clover recipe.  I need about 300k more to achieve that, although I have got some shards from fractals (only about 10).

[Lucas Ashrock]

Stick with the 1 one and play safe, except you know you're such a lucky guy, or with a pure gambler spirit, whatever is the result.

[artemist]

I tried method 1 so from 11 shards i made just 1 clover and bunch of crappy mats
Dunno but version10 works better for me - from 160 shards I made 90 clovers. I guess I'm just a lucky.

Edited by artemist, 06 January 2013 - 11:43 AM.

[Nabuko Darayon]

You can't actually say which is better they're all the same. But safer is 1 then 10. Why? Because I almost have 77 Clovers (short on Mystic Coins ) and the thing is, sometimes I get lucky and have 3-4 strikes of Clover and sometimes it'll eat 15 shards and I barely get 2-3. SO I would suggest you to go with the 1 method

[Gilles VI]

artemist, on 06 January 2013 - 11:39 AM, said:

I tried method 1 so from 11 shards i made just 1 clover and bunch of crappy mats
Dunno but version10 works better for me - from 160 shards I made 90 clovers. I guess I'm just a lucky.

If you're lucky 10 method is better, but statistically the 1 method is best.

[dss_live]

I used the 10 method, i think i had all the clovers i needed after putting in about 100ecto's , from the things i read above, it seems like i got lucky

[frags]

One thing to take into account is the difference in skill points needed for each recipe. 1 Mystic Clover requires 6 Philosopher's Stones @1 Skill Point per 10, while 10 Mystic Clover requires 10 Crystals @3 Skill Points per 5.

[Cobalt60]

frags, on 06 January 2013 - 11:41 PM, said:

One thing to take into account is the difference in skill points needed for each recipe. 1 Mystic Clover requires 6 Philosopher's Stones @1 Skill Point per 10, while 10 Mystic Clover requires 10 Crystals @3 Skill Points per 5.

(which is exactly the same number of skill points if you repeat the 1x clover recipe 10 times.)

[Gilles VI]

frags, on 06 January 2013 - 11:41 PM, said:

One thing to take into account is the difference in skill points needed for each recipe. 1 Mystic Clover requires 6 Philosopher's Stones @1 Skill Point per 10, while 10 Mystic Clover requires 10 Crystals @3 Skill Points per 5.

10 clovers at 1 recipe = 60 stones = 6 skill points
10 clovers at 10 recipe = 10 crystals = 6 skill points

[seppl]

10 trys.  1 by 1.    1 clover.      Ahhhhhh

[ChuyDog08]

I used the 1 recipe for my first 77 clovers, and the 10 recipe for the second set.  Both times I mixed a few of the other to test the waters.  I was more sucessful  (needed less suplies) on the 10 recipe.  I feel I was just lucky the second time around as I also got 10 Charged Lodestoves, 10 Dystroyer Lodestones, 10 Powerful Bloods, and 10 Crystaline dusts during my tries.  It took me 19 tries doing 10 to get my first 70.  It took another 21 tries at 1 to get the remaining 7.  All in all it was 201 sets of supplies for 77 clovers. That is well below the average.

Here is a helpful hint to follow before the end of April.  Use the SAB to get your Crystals, Philosopher Stones, and Obsidian Shards.  Speed run Zone 1 and 2 with shovel for 5 BB a day a character.  With all 8 of my alts I was getting 40 BB a day.  That funded my whole Mystic Clover run this time.  I got many SAB skins which I sold to buy the missing coins and ecto.

[LFk]

As far as I know, the two recipes produce the exact same expected value.

It's easiest to think about the effects of small vs. large sample size this way:

Consider flipping a coin 10 times, each flip worth 1 point (heads) or 0 points (tails).
Consider flipping a coin 1 time, each flip worth 10 points (heads) or 0 points (tails).

The average value from both scenarios is equal to 5 points. Think about how the results are likely to be distributed, and you'll know which recipe you want to use based on what kind of player you are.


From the second circumstance, you can see that you can only get the polar results. 0 (nothing) or 10 (maximum).
From the first circumstance, you can see that it's highly unlikely to get 0 or 10. The chance of either happening is 1/(2^10), or 1 in 1024. You are far more likely to get results closer to the mean.

What this means is that if you fancy the safe play, use the 1x recipe. The actual result will have a very high chance of landing close to the mean result. However, it's very unlikely for you to come out ahead, either.

If you really want to gamble, use the 10x recipe. The results are far more inconsistent than the above recipe, but the 'winning' potential is far higher, as is the 'losing' potential.

[ExkaeI]

It is all up to you.

Statiscally, you have the same chances to have clovers : 1 / 3

I used the 1 recipe for my 77 and had 10 clover in a row series twice then nothing for like 15-20 trys. Now imagine I had the same RNG with the 10 recipe...

Using the 10 recipe is riskier but can be more rewarding than the 1.

[Gilles VI]

TSLlol, on 05 January 2013 - 05:34 AM, said:

Since it's been 4 months since release, I'm hoping someone has figured which method is more "profitable", putting 1 obsidian shard or 10 in?

Both have a ~33% chance for a clover, but because of the lower amount of experiments you do with the 10 recipe the results will vary alot more, thus the 1 recipe is 10 times safer to use.

For example, people I heard that used the 1-recipe, normally it should be around 241 shards, some people get it with 200 shards, some with 300.
Where people who used the 10-recipe got it from 100 shards to 400 or even more.

Easy said, I see no reason to use the 10-recipe unless you just want to gamble or are extremely lucky in games.

[Mournblade]

In retrospect I don't know if it even matters. I got my 77 clovers but i'm considering going back for the chance to get t6 materials. (Not excited about farming them...)

[Duran Argith]

Personally it took me 263 tries (counting the lost obsidian shards) to get my 77 clovers using the 1 clover recipe.
Bad luck I guess

[The_Kaizz]

I've been hearing 1 is safer, 10 is riskier, BUT, 10 pays out more if you're lucky because of the T6 mats you most likely get afterwards. I, myself, am going to start by doing 1 at a time today, and see what happens.

[Skady]

crafted 693 clovers total so far, used X1 recipe - its safer. Got an average 30.56% rate total (464/1515), stopped running spreadsheet after 6th legendary - result is always the same, around 30%