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# So which Mystic Clover method is worth it? 1 or 10 method?

### #1

Posted 05 January 2013 - 05:34 AM

### #2

Posted 05 January 2013 - 05:52 AM

### #3

Posted 05 January 2013 - 05:52 AM

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.

### #4

Posted 05 January 2013 - 06:10 AM

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

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.

### #5

Posted 05 January 2013 - 06:44 AM

- 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.**

### #6

Posted 05 January 2013 - 09:31 PM

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).

### #7

Posted 06 January 2013 - 06:42 AM

### #8

Posted 06 January 2013 - 11:39 AM

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.**

### #9

Posted 06 January 2013 - 11:43 AM

### #10

Posted 06 January 2013 - 12:08 PM

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

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.

### #11

Posted 06 January 2013 - 10:05 PM

### #12

Posted 06 January 2013 - 11:41 PM

### #13

Posted 07 January 2013 - 12:45 AM

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

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

### #14

Posted 07 January 2013 - 10:51 AM

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

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

10 clovers at 10 recipe = 10 crystals = 6 skill points

### #15

Posted 24 April 2013 - 06:11 PM

### #16

Posted 25 April 2013 - 11:01 PM

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.

### #17

Posted 25 April 2013 - 11:06 PM

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.

### #18

Posted 26 April 2013 - 08:24 AM

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.

### #19

Posted 26 April 2013 - 08:32 AM

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

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.

### #20

Posted 27 April 2013 - 01:59 AM

### #21

Posted 29 April 2013 - 09:25 AM

Bad luck I guess

### #22

Posted 30 April 2013 - 01:31 PM

### #23

Posted 13 May 2013 - 12:40 PM

### #24

Posted 30 May 2013 - 03:19 PM

### #25

Posted 03 June 2013 - 12:53 AM

### #26

Posted 03 June 2013 - 02:46 PM

OT: I used the 10-clover recipe to get the first 70, and the 1-clover recipe for the rest. Took me an average amount of materials to complete.

**Edited by dzanikken, 03 June 2013 - 02:47 PM.**

### #27

Posted 24 December 2013 - 10:58 PM

### #28

Posted 25 December 2013 - 04:04 PM

### #29

Posted 08 January 2014 - 12:00 AM

My suggestion - always risk But hey .. I'm a gambler.

**Edited by bodydoc, 08 January 2014 - 12:00 AM.**

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