All right, I've been thinking about this for some time.
Now I have a Gran Faust, and a Divine Avenger.
I would love for GF to have an ASI at least med and DA CTR med.
Should I spam 20k CR punch for these or should I wham it on 225k and hope for 1 out of 3 good UVs and 2 all right UVs to boot?
With 225K you have 3 chances of getting ONE UV that you want. At 20K a pop, for that same amount you can try for your desired UV (or better mind you) 11 times. 3 chances versus 11. Seems pretty obvious to me, unless you're hoping for extraneous good UV's. Because you'll most likely get 3 damage UV's, all low.
One can analyze the expected payoff using basic rules of probability. The short version is: A 2- or 3-UV ticket gives you 2 or 3 chances to get the UV that you want. But a 2- or 3-UV ticket costs more than 2 or 3 times what a 1-UV ticket costs. So, if you really just want one specific UV, you should buy many 1-UV tickets, rather than just a couple 2- or 3-UV tickets.
Or even better, unless you are very lucky : buy a Sealed Sword with the UV and upgrade it again. It saves you the random part, especially as you want a specific UV, and they are often underpriced. That's what I did and it's totally worth it.
I'm too lazy to calculate how much tickets the upgrade cost are worth, but it's not that much tickets. And the odds for ASI : med or better are low.
Else, as already said, 1 UV tickets are the way to go.
The majority of your rolls are going to be lows. The vast majority of the Medium+ aren't going to be UVs you are looking for. Like Fradow said, it is far more economical to buy the UVs you want, particular if they are still Sealed Swords since the unbind won't be as expensive.
If you do roll, do so on a fresh Sealed Sword, that way it can go either way. How sad would it be to get CTR Medium on your Gran Faust, when you really wanted that on your Divine Avenger?
This thread contains a lot of data on the matter:
http://forums.spiralknights.com/en/node/43427
3 vs 11...
Doesn't add up that way, but you're still right.
1/8 11 times vs 1/8+1/7+1/6 once.
Binomial distributions calculator tells us that if you were to roll all 11 times...
Number of a specific UV being rolled / Percent chance
1: .362
2: .258
3: .111
4: .032
5: .006
6: .001
That means that you should expect to end up with 2 or 3 UVs that are "correct" out of your 11 rolls. OR a .75ish chance of getting it.
Now then, lets look at a triple roll.
You have a:
.125 chance of getting it on the first of the UVs
.143 chance of getting it on the second of the UVs
.166 chance of getting it on the third of the UVs
You would have in essence, a .434 chance of getting that specific UV in one of the three.
But wait, there's more!
The chance of getting a med of higher is approximately 35 percent. That means that you have a .434 chance of getting to try that out. Lets multiply that...
You have a .159 chance of getting a med or higher in that specific area, with the other 2 as a bonus if you triple roll.
If you single roll, you'll have a .35 chance for every one you get. If you get two or three of them, like you should probably expect/hope for...
A .35 chance of getting it with one roll of 11 hitting
A .577 chance of getting it IF you get two rolls to hit
A .724 chase of getting it IF you get three rolls to hit
Factoring these in and ignoring the chance of getting 4 rolls, which is insignificant and I'm lazy, we get that there is about a...
40% chance that you will end up with a medium or higher using 1 UV tickets.
Versus a
16% chance that you will get a specific medium or higher using a single 3 UV ticket.
I hope that answers your question.
I would choose 225k if I could. Because im pretty sure with 3 UVs, your weapons will sure be more valuable and maybe more cahnce of wanted UVs
Nothing better than a Beast Low, Gremlin Low, Slime Low DA, right?
And three chances is way better than 11 chances for the same price, right?
Think a bit before you post.
*
Anyway, I agree with Fradow. Buy, don't punch.
Yeah, If I would have been smarter back in the days I would have just bought a sealed sword with the UVs I wanted.
But I was a noob back then, so I wasn't even sure what I wanted.
Should I just start fresh with a new sealed sword or run punch for UVs then?
I know my chances are low, but even ASI/CTR med sealed swords go for 300k in AH.
Let's do some maths. You said 300K for a med so I'll trust you on that (back in the days before my break, I found some for less than 200K, but I guess sellers finally learned it was way underpriced).
The upgrade 3* to 5* is 400 + 800 CE, which is 1200 CE. The CE <-> Cr is approximatively 66Cr for 1 CE, so that makes 79200 Cr to upgrade. Let's say 100K, to accomodate for the Cr prices, mats and all ...
So the cost for your 5* GF/DA with the good UV is 400K. That equals to 20 UV punch (assuming you go for 1UV tickets).
Now, according probabilities (don't forget, it's random), for the Punch path. I'll try to calculate that, but please correct me because I'm bad with probabilities. According to Fehzor "The chance of getting a med of higher is approximately 35 percent". Now, there are 8 possible UVs, and you only want 2 in those 8 (assuming they all have the same chance. I can't back up that claim tho).
That makes 35% * 25% = 8.75% chances to get the UV you want.
So the odds would be 11.42 rolls to get one of the 2 UVs or 22.84 to get one exactly.
Oh well, that seems good for the Punch option, but it seems very unlikely to me, so I must have made a mistake, or the claims (35% med or higher and equal chances for all UV) are wrong.
Edit : the 300K for those UV seemed high to me. Well, it IS high, there is currently a CTR Med Sealed Sword for 120K, and a ASI Med one for 180K. That makes (120+100) / 20 = 11 punch for the CTR one and (180+100)/20 = 14 punch for the ASI one.
Seems like the biggest decision factor is the price of the Sealed Sword, regarding the upgrade cost is equal to 5 punch at most.
Fradow, where did you get your numbers from? Isn't there a lower % chance to get high UVs versus low ones?
Eh, ask around on the forums. You can get a CTR Med for 2k CE or under easily. I saw one on the AH for about that much but didn't buy it because the profit from reselling would have been minuscule if any.
@Coatl : as I said, the 35% comes from Fehzor post. You can also find a similar nubmer following the link Culture posted : http://forums.spiralknights.com/en/node/43427
As for the equal chances for all UV, I made it up for easy calculation, but the same link have data which tend to prove it's true.
Edit : I added something at the previous post, because the sealed sword price of 300K is way off compared to what I just saw on the AH.
Go to the AH and buy your desired SS right now, Coatl. Heh.
Or you could get a CTR High on the forum for 5k CE or less.
Sorry for bumping an old thread(I was trying to look at all threads and try to reply to the latest ones I suppose from the search results), but I'm wondering if you keep rolling UVs on the same weapon without selling it(I know it's hard to not want to sell a pretty good uv item) does that count as conditional probability as Fradow implied? Is there a topic that specifies this that you can show me, Fradow or anyone else?
Cause I've chosen Pulsar to roll on and did x51 tries and the best I've ever gotten was ASI meds and I sold them relunctantly, so in that case does the probability start over or "reset" and become independent or random or does it update its probability like a conditional probability would? Hope it's not too confusing, but if it is conditional, conceptually I would assume that my number of rolls would actually be lower than x51 since it only counts or increases the probability if rolled on the same weapon right? But then how does that explain crafting, would they be independent and separately random?
I think that you're asking whether successive roles are independent of each other. That is, do the odds change as you do more and more rolls, or are the odds identical on every roll?
As far as we know, the rolls are independent. The odds are identical on every roll. As far as we know, this is true for both crafting and Punch.
Probability doesn't care if you roll once each on 100 swords or 100 times on one sword. The odds are the same. Of course, if you roll 100 times on the same sword, you lose a lot more money, as you aren't selling the extra decent UVs. . . .
The independence of each roll (unless interdependence has been coded in, which as far as we know it is not) is not a feature of SK. It is a mathematical reality.
Well in Fradow's first post he suggested to buy a weapon already with a UV to increase your chances, so I'm assuming he implied there is some probability conditioned to the same weapon that already had a UV. It seems that he also implies that it needs to be the same weapon, not identical ones. So I'm guessing you can't roll on another brand new weapon if that were the case? Hm, if the rolls are independent then we would be given the same calculated set of odds on each roll. That seems like with each successive roll we are not getting closer to getting the desired UV? Hm, ouch, that doesn't sound good if it were something like that. But most threads seem like the more we roll the closer we are to getting the UV. I know this is confusing, so I hope you guys won't be frustrated.
Hm, I see Derpules. Thanks for the help guys. I guess I don't have to worry about re-rolling on a good UV then and can have extra gear on stock or I guess roll on the same weapon/armor/shield name and then roll on a different type of item that's not identical, and if I'm not getting results there, I can go back to the previous gear I've rolled and...still have those previous rolls added to the total amount of rolls(my increased chances still stays with the previous gear?)?
I don't speak for Fradow, but he was probably getting at this feature of the SK economy: UVs are often underpriced by AH sellers.
For example, a Brandish with CTR+3 sells for 400,000-600,000 crowns these days (I don't have a current price in front of me). That sounds like a lot, until you realize that that UV would cost you maybe 1,280,000 crowns at Punch. (Getting CTR happens 1/8 of the time, and getting +3 or +4 happens maybe 1/8 of the time, so you expect to roll 64 times to get CTR+3 or +4. Of course, you might get +4, which is really awesome, but the chances of that are low.)
So, if you want a specific UV, you can often buy it cheaper than you can roll it (and cheaper and faster than you can craft it). If you want two specific UVs, then you're unlikely to find that particular combination on the AH. So you buy an item with one of them, and keep it on while rolling for the other.
Suppose you keep a CTR UV on your sword, while rolling for an ASI UV on the same sword. Your chances of getting ASI are 1/7, because you can't get CTR for your second UV. As far as we know, they are 1/7 every time you try. Does this help?
It does, basically the probability will always be the same every time you roll, and mostly for the total number of UV types you can get, as well as the UV levels, even though the levels are set on way different probabilities and changes the likelihood of getting the desired UV, that usually being very low most of the time with most people(it is like with set probabilities for promo items like Dragon/Valkyrie wings color types). It is a uniform distribution definitely, since we already know all the possible items and aren't guessing with statistics(well we need sample statistics for the UV experiments, that is real useful organized info that we need without pure guessing), with the distribution not skewed by random changes in data values, etc. But then how does that explain how some people came to the conclusion, including myself at one point(sorry guys), that your chances increases for the desired UV as you roll more of the identical/craft gear(not counting branch lines of the base 2-3* gear etc). It seems like they may also imply that the UV types and levels you've already rolled are mostly already accounted for and will not reappear as often as you roll more and get closer to that desired UV or whatever.
On the other hand, going off from what you guys have explained, I guess you get a different UV most of the time(even though some of us get the same). I guess the basic concept is, is that the probability is set still for each gear, and they are all pretty similar, but that we also get different ones normally(I know some of us get the same UV types and levels yes, but for a few of them) from each different roll. Hope the terms we're using isn't confusing, I know it comes down to that sometimes.
I don't know about that. Can you show me the data? I mean, exactly what were the results, when which items were rolled on? If the rolls are not independent, then I'd love to know.
You may be perceiving a pattern that is not really there. I don't mean that as an insult; it happens quite naturally when humans try to understand random phenomena.
My data list covers like almost 10 pages or so, so I don't know if I want take all day to post it, unless you can detect a pattern with a min sample size I guess that gets up to the UVS that got a VH or two and stop from there. I will have to refer you to a post that I've seen that says there's a 63% chance to get an ASI VH on a weapon out of 1/264 rolls. Let me see if I can find it. I thought it was this topic, but I can see that it is confusing and since I'm the only one claiming it.
Here it is:
http://forums.spiralknights.com/en/node/43427
It is Culture's 2nd post. I have seen other posts that have come to similar conclusions as well. It seems to suggest that our odds get higher in our favor, probably implying that the coding "counts" the total amount of rolls you have made on the identical gear and based on that data increases your probability. I'm assuming that this implying isn't similar to independent random probability?
Well on second thought nevermind. Culture's numbers in of itself is set so he is also suggesting the rolling are independent random events. I guess I have gotten increasing your chances on a desired UV with more rolls confused with it being conditional probability. A good example of conditional probability are I guess billard balls or a deck of cards(not counting card counting methods, probably a whole new ballpark there, and maybe not billard balls). I forget what good example I remember reading it from(probably from Against the Gods: A Remarkable Story of Risk; optional book for my risk and uncertainty resource economics class way back then in college) that illustrated conditional probability well, so it probably was a different example from billard balls, since there seems to be a random element(not including the player's geometrical skills or whatever else, but where the balls are going to be after say a break). I guess the point is the probability is now updated for each numbered ball after accounting for the billard balls that are already hit in the pockets.
But yeah, you guys already knew the somewhat opposite concept of independent random events(that being assumed for normal distributions, and I'm sure the coding wouldn't get too detailed...maybe). But I'll just stop there before I confuse myself and anyone else already. I'm sure some people getting good UVs early or get to the times I've rolled for the Pulsar was precisely because each UV Type has an equal chance of getting their UV Levels equally and of whatever probability it has been set to just because they've haven't tried rolling as much, tried rolling with moderate amounts, or a lot. Maybe it all evens out with various amounts of rolls on one type of gear each. Since some of the same UV type and level reappears for some players. Plus, I would think it would be too easy to get the desired UVs if it were somehow based on conditional probability maybe.
So on that note, I will quit rolling Pulsar and try with whatever cr I have for now to roll some more on Antigua since they both still have the same probability of getting that desired UV despite the number of rolls already made for them, and then just buy the Pulsar line.
Listen to the advice of crafting if you are doing 2-3* items that you can get recipes for(not boss items). I've gotten at least x3 good items from crafting with er 2 other characters. One of them crafting 2 of the 3. That being Autogun CTR VH(can't equip this on my main unfortunately since I already have High, don't know why I didn't hold onto it since now it's binded as a Blitz on another, but it brings in the wading runs) and the other Auto with ASI VH. The 2nd character made an Elemental Hood with Shock Max which was pretty decent. And this was before approaching 30-50 UVs each. The ASI VH was probably around the 40th UV, more or less. But those were 2 out of 5 players, not including my main and a few other possibilities had I known to make the right decisions with info.
You want one specific UV, after all.