Close this discussion please

Close this thread please, I'm not having fun having this discussion

 

What the... I don't even...

 

exactly

 

can someone translate this to english

 

It doesn't worth taking not completely scrolled item that has reached high stat and trade it for just 1 stat more, the fact that so many people still do that add to something in psychology that makes it interesting in my opinion.... I'm sorry bom3 if you read everything and got nothing it wasn't my intention.

Sorry guys, I didn't mean to waste your time, I thought I found some interesting data I wanted to share, but I guess this isn't the audience to such a post, mods can close this thread.

 

Can't believe I understand this, 5/5 for your way of explain

 

Tldr; people rather cash out than continuing to gamble even if the returns *might* actually be favorable

 

From my understanding the reason for the need for a risk aversion/utility function is because of diminishing marginal returns and it is a function of wealth.

• Consider a gamble where you have a 50% chance to win $10 or lose $5. Most people would take this in a heartbeat because it profits on average and is small compared to their overall wealth.
• Now, consider a gamble where you have a 50% chance to win $10 million or lose $5 million. Most people would refuse because though gaining $10 million would be cool, losing $5 million would crush them forever. However, to like a billionaire this is nothing so they'd probably take it in a heartbeat as well.

What's the point?: Risk tolerance is just a matter of how much wealth you have. The more wealth you have, the more risk tolerance you can have. Loss aversion is another topic but is more like a placebo affect/behavioral phenomenon not grounded in rational or quantitative thought.

You can translate this to scrolling gear as well. Though you might profit on average from scrolling a 18/1 or similar bfc, most players don't have enough wealth to take on this risk in terms of expected utility from the outcome so they are better off selling it.

 

this is some dank shit

 

• 
  

I completely agreed with you, I even mentioned it in the part where you gamble to either getting 1 billion or losing any ability to get any money.
The thing is when it comes to maplestory, the person (the person who took the risk in the first place) that has reached the 14/1 item is the same one that started scrolling it, and decide to sell it when it comes to the big money. It is most likely to be the same guy who would probably spend CS on negative expected value items (just because they are cheaper and he doesn't care that he is losing), and would probably decide to scroll 9/1 but not 14/1, and that's the essence of that anomality I was speaking of in this matter.

 

believe it or not, i did a calculator on brute-forcing all the possibilities of a chaosed gear and to my surprise, x attack/1 slot price approximates nearly to x+1 attack/0 slot. Especially for attack gears near what i consider midrange. The market naturally tends to the right approximation sometimes

 

That's exactly why I chose as an example 15 and 14/1 because between 8~12 those numbers make what I called an insurance fee pretty reasonable.
But also, I've seen people trading 11/3, 14/3, 15/1 without any proportions to their real value.

Below 8 you don't really see people trading for +1 att -1 slot just because they are not afraid to lose (worst case is 3b it doesn't hurt so much). people start being weary at around 4~5b from what I've witnessed (seen some 9/1 10/1 that were willing to trade for 10/0 or 11/0 which kind of made sense to me). But people who scrolled a bfc into 12+/2+ and then just wanted to trade it to something that is complete, that must be that fear of losing that we all have.

I think that you have missed the point. It's not about the cashing out, it's that they lack the ability to compare in term of value +1 att -1 slot relationships making them lose billions unknowingly because they are more motivated by fear than greed.

 

Be careful with the wording especially when defining variable. I assume you meant the monetary outcome of the scrolling process. The word "gain" confused me at first glance.

I also assume you meant E(Y) is "composed of both the outcome of the item and the money spent on CS/WS to scroll it" instead of Y?

I am lost here and I made a quick table to reflect the actual numbers. Also, keep in mind that shay's price guide is a reference and doesn't necessarily reflect the actual price of high att items. Data reference is very important. A quick example: 19att fs was previously sold at ~60b instead of 75b (1,2)
Also, you assumed the cs results of "0" leads to a monetary outcome of "0", which is false. Assuming the price of 11/1 == 12/0, one should have "-1" as the meso outcome


*a minor issue: consistency helps the reader a LOT. So if you put "Price" before your "P(X=x)" in your original model, then please write the actual number in that order too. And I noticed a sign change from "+ E(CS)" to "-(10/6)*1 ". I might know what you mean by that, but make sure you re-format it so we may read it more easily. In addition, just use "-(10/6)*1" in the original model, why bother with the "E(CS)" at the first place if you don't define it

I always wanted to create a math model for the chaos scroll. I think you are heading in the right direction, but of course, more work needs to be done

 

I'm sorry, my English isn't so good when it comes to the field of mathematics as I studied it in Hebrew and I'm not sure about the terminology I assumed and hoped people from the field would understand what I meant. Thank you for clearing those points out I'll edit the post.

About the outdated shay's scroll price guide - it is influenced from supply and demand more than chances and probabilities, and it was right at some point of time where the prices of FS/sock/CS/WS remained the same. The thing I was trying to do in this post is the connection between the supply and the probabilities and how much it is reasonable to value them.

About the E(CS) it means the average amount of money you will spend on CS/WS for the next scroll to succeed. I think it is important to take it into account especially when we are talking about scrolling 7 slots sock from 1 ATT. In that particular case I only demonstrated the scrolling of the last slot so it was used once, but if someone were to use that kind of mathematics in approximating values they should put a coeffecient of how many slots they are going to use before that term.

Also something that might have confused you is that I had a typo writing "Examine the scroll of 11/1" where in my number I ran 14/1

 

Fair enough, my bad that I was under the assumption that you are modelling the last slot only. Adding more slots is very ambitious and I very much like what you did. I really hope that you may complete the model one day! I am going to list something that I thought about before but didn't dig into, which might be helpful for your future model (just some brainstorming points):

• The exponential increase in the price, as the attack goes higher. Can the model apply to both low and high att gear?
• Can the model apply to other gear? eg. spec goggle, bfc?
• When should one use cs, or cs+ws? and how to implement this into the model
• What is the equivalent meso value of the slots?

Edit: I noticed that you missed a very important point in your last edit.
One should have 6 negative, 1 zero, and only 4 positive meso outcome assuming the last slot == 1 attack

 

The example about the expected value of scrolling last slot on 14/1 FS was given just for a point of reference to those who decide to sell it so they understand what, and why they are losing. The addition of 3 slots IS making the value of the item at least 3 times more expensive because of the exponential increase in price as stats go higher. The anomality is someone who is thinking "hey, I have extra CSs and I just farmed a 3 ATT BFC let's scroll it" and BAM it gets 8 ATT, and 12 ATT right after and it has 3 slots. Trading it for 15 ATT and start scrolling a new BFC is the mad thing to do, because although the expected stat gain from CS is 0, the disproportion between value gained for success at that point to value lost for failure is so big. yet people are "chickening out" to risk 4b that they just gained out of thin air rather than going for the actual real chance that RNGesus gave them.

The rest of the points are super interesting, and if it wasn't a mushroom killing game and my business needed that information I'd probably fill 2-3 blackboards making calculations to get an exact model for all those questions.
Something I can easily do is a python script containing all the chances and values for vanilla items, CS and WS, and run simulations to see how rare everything is and get some better estimations to what they should worth in a world that is trading probability more than demand and supply. (from the histogram, and total money spent you can get raw value rather than formula for everything)

That's the thing I don't assume that. last slot == 1 attack is the thing i'm trying to challenge. People treat it as a unifrom rule that applies to any item with any stat. as if swapping 1 slot for +1 stat gain is something that should always be valid. In my analysis I threw away the 1 slot (because we are using it in the process of scrolling) and I only look at the result which is the difference in value of the item + the cost of scrolling it.

 

Hello,

your idea is very good and you see the problem in a mathematically correct way.

Let me just add this; Chaos Scrolling is mathematically bound to make you lose ON AVERAGE, and that's just the way prices are set in this game. The reason people keep chaosing is for the thrill of doing so, and for the POTENTIAL gain.

In your example, the difference is that we find ourselves in a situation where the gain is positive. In other words, starting from a clean FS and reaching 14/1 (or 15/0) means we're already making a profit (unless we had like 15 failures on CS + WS, but let's face it, the odds of that are small).

Again as you mentioned, it gets tricky when we combine several slots of a given item, as this is where the real chaos happens.

Take a clean FS (2 atk, 5 slots) as an example. One may ask, what is the probability of the FS having atk X once it reaches 0 slot (using CS + WS).
Well, here is the probability for every stats on the FS after 5 slots.


if you attach a price tag to each and every single one of these probabilities, and you calculated the expected value (as stated above, Sum ( Price * Probability)), and from this subtract the expected cost, you are bound to make a negative profit. This is because 0 atk is an absorbing state, meaning once you reach it, you cannot go out of it.

Reading the table above, one can see that starting with a clean FS, the probability of reaching 0 atk is nearly 65% (obviously if you reach 0 before the 5th slot, you stop scrolling).
One can also ask questions such as: "Starting with a clean FS, what is the probability of reaching AT LEAST 15 atk?"

In that case, simply sum the probabilities shown above. Answer is roughly 3.67% chances of getting 15+ atk on a clean FS. This is very small.

Nevertheless, you are correct that if someone is already lucky enough to get to the point where he/she has a very decent FS with some slots left on it, on average they will make a profit by continuing their scrolling.

From a clean item however, it is the opposite. On average, we lose.

Proof. (I tried to put the following in a spoiler but it doesn't seem to work, anybody knows why? LOL)

*Heavy math alert.
To compute these probability, we need to acknowledge the fact that the CS process is effectively a Markov Chain.
First, we compute the probabilities of the Atk after the 1st CS+ WS passes.

Shown here.


From there, we can compute the Probability of X2, Given X1 = k.
It looks like this.

Read the table as follows:
Given X1 = k (let's use X1 = 5 as an example), the Probability that X2 = 10 (given that X1 = 5) is 1/11.
The Prob. that X2 = 11 given that X1 = 5 is 0, because the range of the CS goes up to + 5.

With those, we compute the unconditional Probability of X2, that this the Prob. that X2 = k.
To do so, we acknowledge that Pr(X2 = k) = Sum (Pr(X2 = k Given X1 = z) * Pr(X1 = z)). It is therefore a sum of the product of Pr (X1) (first table above) and Pr(X2 given X1).

We obtain this:


Rince and repeat all the way up to the 5th slot. We obtain the very first table shown above.

 

First of all, I enjoyed reading your comment so much! the first 2 comments made me feel like I wasted both my time and the forum members time.

I was speaking about it. Your table shows yet another example to the anomality is that we don't see the market overflowing with 1~5 att FS with 1 slot left (it means people keep scrolling them or npc them) they making about 10% of all scroll attempts of FS that had ATT stat remained. My angle, and the point I was trying to give, is that once someone has reached a point where the expected value of the scrolling is ACTUALLY high (it means it already got to the top10 percentile of your table), at that point keep going up have the same chances of going down but it is so much more rewarding, that someone would, at too many cases, just let someone else scroll it for him by "buying insurance" of 1 stat to work. I'm 100% sure that the people that are trading those items have NO IDEA how lucky they were to get to that point (as you have shown in the table you added), and thus they don't appreciate enough the chance they were given.

Thank you for your input I learned a lot from your table! The way you constructed that table actually might answer @xMightyx

 

You are also very correct

To be honest, I think the reason for people acting as such is simply due to a lack of funding.

Take the average player, for example. A player who doesn't have multiple B coins in spare. Based on your calculation, if that player is lucky enough to get to 14/1 FS, he could look at your table and say:
"Even though I have the chance to make a 40b profit, I also have the chance to lose 7b. If it takes me several months, or even a year, to make up 7b in the event I lose it, am I really willing to take that risk?".

For some risk averse individuals, the answer is no. Hence this is why they'd rather buy the insurance!
Anyways, this is also how insurance is able to function in real life!

Cheers