'A Gateway into the Past' new-format starts in Beta on July 7th

[Sir Derf]

Normal event

1. RNG 3-of 9 chests
2. RNG selection-of-reward

A Gateway into the Past

1. RNG 1-of-6 Game-Piece-from-a-Cup
2. RNG 3x 1-of-12 Offers
3. RNG 1-of-??? Offer Recipes
4. RNG selection-of-reward
5. RNG Lucky Draw selection-of-reward

And that's assuming there isn't more than one Lucky Draw reward table...

Oh, the RNG haters are going to have a field day.

 

[Sir Derf]

Earlier, I solicited other people's opinions about "...the non-rotating-chest-i-ness decline-an-offer-and-wait change". My two cents worth, at least at the moment...

There will be players who have goals, and who will make strategies. That might be preferred and avoided Offers, purely based on the rewards tables. Or that factor in how expensive or inexpensive some offers are based on the recipes that combined with the offers. Bottom line, There will be players who will be willing to fulfill some offers, and who will want to decline other offers. Every declined offer is a 30 minute delay for one of the three offer slots. Okay, fine, there's still two other slots. But, keep playing with those two slots, and you'll eventually get another loser, and a decline, and now you're waiting on two slots and only playing with one. Until that slot gives an undesirable offer, and you deny your third. And now, you have to wait, probably for 20-odd minutes, for the first one to unlock. Bottom line, players who have discerning strategies are not going to be able to play in an uninterrupted blitz; they will frequently hit full-on delays, and either get back soon as 1, then maybe 2, offer slots unlock (only to lock again), or will go away for over half an hour.

Extend this out for a while, and these are a couple of consequences I see.

1) Strategic players might be enticed into accepting offers of lower quality than they want, so as to avoid having to trash offers and hit delays.

2) Strategic players who save their currency for a single blitz session, possibly because the like a particular Daily and will either focus on the natural Daily day, or keep Rerolling to get the Daily they want and then dump it all in, well, they won't be able to play all in a single uninterrupted blitz. This will either stretch out their play over many shorter sessions, or possibly even prevent being able to dump it all in a day. Which makes me think this is an INNO modification to work against players getting 10, 15, 20 of the same Daily. Or get multi-Daily hunters to spend diamonds on rushing blocked new offers.

3) Lastly, players will be pressured to not hold a lot of currency for the final day, as they might end up with currency to burn and be locked out of offers as the event ends. There will be more unused currency that will evaporate at the end of the game because of this. I'm not sure how that helps INNO.

 

[Sir Derf]

Updated RNG counts... forgot about the Reroll feature, present in both events, which offers a RNG of 1-of-however-many-Dailies-there-are, or probably 1-in-1-less-than-however-many-Dailies-there-are. Has anyone ever Rerolled and gotten the same Daily they already had? Is this weighted by number of occurrences, for those Dailies that are repeated in an Event? Whatever, the RNG count is now 3 in previous-style Events and 6 in 'A Gateway into the Past'.

 

[Sir Derf]

Here's an interesting thought....

In past events, you had to pick one out of the three chests/rings/whatever that were presented to you at a time, so while you might have a preferred non-Daily, non-Grand prize you preferred, be that KP, or troops, or whatever, and you would take that whenever offered, but you wouldn't always have that as an option.

But here, you can trash offers you don't want. So, if you aren't that desirous of Grand Prizes, or of particular Dailies, but instead have an interest in one of the 'regular' random prizes, you can attempt to exclusively accept offers that include that sub-prize. And possibly attempt to be pickier still and only accept desired offers with low-cost recipes...

Now, because of the delays when you trash an offer, if you're going to focus on this strategy, you probably need to start early. This version of the game lasts 20 days, so if you don't sleep, that's 20 days * 24 hours * 2 30 minutes * 3 offer slots = 2,880 offers that you can delay. If offers occur equally randomly, then I would be declining 11 offers out of every 12. If I can only afford to accept 100-200 Offers, that suggests I would need to decline 1,100-2,200 unacceptable offers. This suggests, for an Elvenar lurker, who can check in every half hour for most of the day for the whole event, this might be a workable strategy. If you are willing to accept 2 or 3 of the offers, this suggests this is really doable, and that you might even be able to exercise some discretion as to the costs of these offers.

Given my miserable luck in this current event at attempting to Reroll my way into winning a not-today's-Daily Daily, I'm pondering focusing my efforts on Extraordinary Request #1 and it's 10% chance at Pet Food. Not knowing the costs, or the odds at different costs, I can't make a guess at expected number of offers one could accept. If there is any similarity to past events, ,maybe I could hope to afford to accept that offer about 100 times if it's expensive, maybe closer to 200 if I can get it cheaper. At a 10% chance at Pet Food, that could give an expected 10-20 Pet Foods, maybe more, maybe less. Maybe Uncommon Request #2 for the 10% 2 Combining Catalysts, or Rare Request #3, with 22% Mana and 22% Seeds (and 14% 3 Lucky Draws, although I don't know how much to judge this as being really desirable.) Those look interesting to me, but fighters might be interested in troop instants or Vitality Surges, while others might want those AWKPs.


If Beta players could try and collect some good statistical numbers, it would be interesting. Whether they do or not, I would recommend anyone attempting this to pay close attention to the behavior over the first day or two and adjust your choices and recipe pickiness accordingly.


Interesting, interesting...

 

[SkyRider99]

My Semi-Pointless Math Sense is definitely tingling

Nice. It may be advisable to not try climbing tall buildings, or to shoot web from your hands though.

Your choice of spandex day wear is up to you.

 

[Jake65]

Your choice of spandex day wear is up to you.

There's a comment on another thread about being able to use our own avatars.
Spandex might be the reason why we can't

 

[Silly Bubbles]

This is what I got so far (based on what I've read) and I might be completely wrong as it's just based on what others said so please correct me if I am. It looks like that the cheapest way is not to combine any pieces and wait for trade offers that need the pieces you won from cups. Assuming that the cost of trade offers varies between all different types of pieces. It might involve checking every half an hour for new trade offers after I reject them. This might not be a huge problem if I want the main prize but it will a problem to get specific daily prize as I have only 24 hrs and reroll is unpredictable. I will either need to combine pieces to match the trade offers or accept trade offers that I'm not fully happy with. Either way it's going to be much harder to get specific daily prizes.

 

[Deleted User - 61610]

Balancing changes

Dear Human and Elves,
Based on your feedback we have made the following changes in our event balancing, effective today:

• The costs for using cups has decreased from 5 to 4 Dwarven Chips.
• Cups will not spawn tier 6 Game Pieces anymore, as we don't want players ending up stuck with pieces you can't disassemble.

We're looking forward to hearing your feedback on these changes!

Kind regards,
Your Elvenar Team

 

[Silly Bubbles]

It seems that Beta forum has taken on another complicated calculation to get the cost of each piece. To me the true cost of each piece is what it actually cost me rather than what it could've cost me. Oh well, here we go again. It looks like I might have to post some overcomplicated math calculations so people actually read and understand my posts.

 

[Deleted User - 849326167]

This is what I got so far (based on what I've read) and I might be completely wrong as it's just based on what others said so please correct me if I am. It looks like that the cheapest way is not to combine any pieces and wait for trade offers that need the pieces you won from cups. Assuming that the cost of trade offers varies between all different types of pieces. It might involve checking every half an hour for new trade offers after I reject them. This might not be a huge problem if I want the main prize but it will a problem to get specific daily prize as I have only 24 hrs and reroll is unpredictable. I will either need to combine pieces to match the trade offers or accept trade offers that I'm not fully happy with. Either way it's going to be much harder to get specific daily prizes.

I agree with your analysis and conclusions. Not only by reading the beta forum, but also by making some calculations. Going for the set is doable with a consistent time-costing approach (one has to refuse lots of trades), but going for a specific daily price is way more difficult. Unless one accepts lots of bad trades. And from the information I gathered from iDavis and Jackluyt's websites there are lots of bad trades ...

And don't worry I do understand your post. But I don't need the calculations, I have done them myself (did cost me a few hours though).
But explaining those calculations here. That is a nightmare. I'm not looking forward to do that.

 

[Sir Derf]

Just to put to text what might be buried in the linked documents...

You have an inventory space of 5x9=45 spaces for game pieces. Assuming you keep balanced between the three piece types, Figures, Tools and Dice, that's 15 spaces per type.


Yeah, ultimately, a game piece, as you play, will have cost what you used to make it. Yes, you will make a more accurate accounting of your game play if you keep track of it. And if you keep track of it, your actual average cost will make for a good estimate of your potential future cost. At a minimum, some people might like to have starting estimate of game piece costs before they start playing...


And, I have to have a little chuckle at the change INNO made, that cups will no longer give Level 6 pieces... "...as we don't want players ending up stuck with pieces you can't disassemble..." You're stuck with a piece if you don't take offers that use that piece; if you don't take offers that use Level 5 pieces, well, you'll be stuck with those; if you don't take offers that use Level 4 pieces... Also, don't want people stuck with pieces you can't disassemble; but, you can't disassemble any of the pieces, whether it was Level 6 or any other Level.

Recomputations in the style I posted earlier coming soon with the new 4 Chip cost and no-Level-6 cup percentages coming.

 

[Sir Derf]

So, INNO adjusted from 5 Chips per Cup to 4, and moved the 2% chance at a Level 6 Piece all the way back to increase Level 1 from 38% to 40%. Here are some recomputations for approximate relative values. These are not definitive; your milage will vary. If anything, these are probably over-valued, as for example, most people won't build Level 6 pieces using massive numbers of Level 1 pieces. So take this as a rough relative worst-case estimate, and not mathematical gospel truth.

Spoiler: Semi-Pointless Math (tm)

400 chips = 100 picks
40 Level 1
30 Level 2
15 Level 3
10 Level 4
5 Level 5
----------
100 Pieces

40 Level 1 Pieces costing 160 Chips, 160/40 = 4 Chips per Level 1 Piece.



40 Level 1 Pieces costing 160 Chips -> 20 Level 2 pieces
30 Level 2 Pieces costing 120 Chips

Total, 30+20 = 50 Level 2 Pieces costing 120+160 = 280 Chips, 280/50 = 5.6 Chips per Level 2 Piece.


40 Level 1 Pieces costing 160 Chips -> 20 Level 2 pieces
30 Level 2 Pieces costing 120 Chips + 20 Level 2 Pieces -> 25 Level 3 Pieces
15 Level 3 Pieces costing 60 Chips

Total, 40 Level 3 Pieces for 340 Chips = 8.5 Chips per Level 3 piece


40 Level 1 Pieces costing 160 Chips -> 20 Level 2 pieces
30 Level 2 Pieces costing 120 Chips + 20 Level 2 Pieces -> 25 Level 3 Pieces
15 Level 3 Pieces costing 60 Chips + 25 Level 3 Pieces -> 20 Level 4 Pieces
10 Level 4 Pieces costing 40 Chips

Total, 30 Level 4 Pieces for 380 Chips = 12.67 Chips per Level 4 Piece


40 Level 1 Pieces costing 160 Chips -> 20 Level 2 pieces
30 Level 2 Pieces costing 120 Chips + 20 Level 2 Pieces -> 25 Level 3 Pieces
15 Level 3 Pieces costing 60 Chips + 25 Level 3 Pieces -> 20 Level 4 Pieces
10 Level 4 Pieces costing 40 Chips + 20 Level 4 Pieces -> 15 Level 5 Pieces
5 Level 5 Pieces costing 20 Chips

Total, 20 Level 5 Pieces for 400 Chips = 20 Chips per Level 5 Piece


40 Level 1 Pieces costing 160 Chips -> 20 Level 2 pieces
30 Level 2 Pieces costing 120 Chips + 20 Level 2 Pieces -> 25 Level 3 Pieces
15 Level 3 Pieces costing 60 Chips + 25 Level 3 Pieces -> 20 Level 4 Pieces
10 Level 4 Pieces costing 40 Chips + 20 Level 4 Pieces -> 15 Level 5 Pieces
5 Level 5 Pieces costing 20 Chips + 15 Level 5 Pieces -> 10 Level 6 Pieces

Total, 10 Level 6 Pieces for 400 Chips = 40 Chips per Level 6 Piece

Level	Max Count/100 pick (Pieces/500 Chips)	Cost (Chips)	New Cost/Piece (Chips/Piece)	Old Cost/Piece (Chips/Piece)
1	40	160	4.00	5.00
2	50	280	5.60	6.93
3	40	340	8.50	10.38
4	30	380	12.67	15.00
5	20	400	20.00	22.11
6	10	400	40.00	31,82

 

[Silly Bubbles]

I agree with your analysis and conclusions. Not only by reading the beta forum, but also by making some calculations. Going for the set is doable with a consistent time-costing approach (one has to refuse lots of trades), but going for a specific daily price is way more difficult. Unless one accepts lots of bad trades. And from the information I gathered from iDavis and Jackluyt's websites there are lots of bad trades ...

And don't worry I do understand your post. But I don't need the calculations, I have done them myself (did cost me a few hours though).
But explaining those calculations here. That is a nightmare. I'm not looking forward to do that.

That’s great that you double check me, nothing’s worse than when one person's bad recommendation that harms the game spreads like Covid.

Personally, I’m a strong believer in common sense and logic first and math second so I’m not calculating things yet but I will. I’m still missing more info on what pieces are used in trade offers like are there any patterns, what odds each piece has in appearing etc.

 

[Sir Derf]

What odds each piece has of appearing has already been documented, both the original percent chances from drawing in the cup, and the newly changed values. You can find them in @Jackluyt document, linked to early in this thread, or in the beginning of some of my math posts that you probably ignore...

Common Sense & Logic vs. Math... Love that compare and contrast... If Common Sense is something distinct enough from Logic to bear being mentioned separately, that makes me suspicious of the validity of whatever gets deemed 'common sense'. I mean, if a concept isn't logical, what does that leave? And then to consider Logic also separate from and better than Math. In what way is logic separable from math, or math separable from logic? Logical statements, logical thinking, all have mathematical representations. Most logic, when reduced to its simplest form, is basically Boolean Math; that is, math performed using only two values. I think you're really devaluing the speculation involved in the use of provided probability tables for computing compound events and projecting average results...

 

[Sir Derf]

For those who might find this interesting, here's a slightly different speculative set of computations.
For those who don't find this interesting, here's a post to skip.

I have no Game Pieces, but I want a Level x Piece. How many Draws from a Cup might it take to get naturally?

Level 1 - 40% chance.

Draw (n)	Odds you'll pick a 1 first on the nth draw	Odds you'll pick at least one 1 in n draws
1	40.00%	40.00%
2	24.00%	64.00%
3	14.4.0%	78.40%
4	8.64%	87.04%
5	5.18%	92.22%
6	3.11%	95.33%
7	1.87%	97.21%

Level 2 - 30% chance

Draw (n)	Odds you'll pick a 2 first on the nth draw	Odds you'll pick at least one 2 in n draws
1	30.00%	30.00%
2	21.00%	51.00%
3	14.70%	65.70%
4	10.29%	75.99%
5	7.20%	83.19%
6	5.04%	88.24%
7	3.53%	91.76%

Level 3 - 15% chance

Draw (n)	Odds you'll pick a 3 first on the nth draw	Odds you'll pick at least one 3 in n draws
1	15.00%	15.00%
2	12.75%	27.75%
3	10l.84% 10.84%	38.59%
4	9.21%	47.80%
5	7.83%	55.63%
6	6.66%	62.29%
7	5.66%	67.94%

Level 4 - 10% chance

Draw (n)	Odds you'll pick a 4 first on the nth draw	Odds you'll pick at least one 4 in n draws
1	10.00%	10.00%
2	9.00%	19.00%
3	8.10%	27.10%
4	7.29%	34.39%
5	6.56%	40.95%
6	5.90%	46.86%
7	5.31%	52.17%

Level 5 - 5% chance

Draw (n)	Odds you'll pick a 5 first on the nth draw	Odds you'll pick at least one 5 in n draws
1	5.00%	5.00%
2	4.75%	9.75%
3	4.51%	14.26%
4	4.29%	18.55%
5	4.07%	22.62%
6	3.87%	26.49%
7	3.68%	30.17%

 

[Sir Derf]

Apologies. While the following technically computed exactly what it said it was, the implication was that these were partial probabilities, computing the odds of one way to build a higher valued piece. Instead, they improperly included the odds of other successful combinations, and actually counted some combinations many, many times over, such that the numbers were large overestimations of their intended purposes. Better values will be added in a later post.

But I want a Level 6 Game Piece, and you can't get that directly... Well, you're gonna have to draw some combinations.....

What are the odds of getting 2 Level x Pieces from the Cup in n draws (Getting one in n-1 and the second on the nth?)

Looking above at the odds to get a single Level 5, you can begin to get a sense on the difficulty to get two Level 5s... Apologies for the formatting, I copy/pasted from Excel, then hand entered a few...

Draw (n)	Odds you'll get a second 5 on the nth draw	Odds you'll get only 2 5s in 2 to n Draws
2​	0.2500%​	0.25%​
3​	0.4750%​	0.73%​
4​	0.6769%​	1.40%​
5​	0.8574%​	2.26%​
6​	1.0181%​	3.28%​
7​	1.1607%​	4.44%​
8​	1.2864%​	5.72%​
9​	1.3967%​	7.12%​
10​	1.4927%​	8.61%​
11​	1.5756%​	10.19%​
12​	1.6465%​	11.84%​
13​	1.7064%​	13.54%​
14​	1.7562%​	15.30%​
24	1.8603%	33.92%
34	1.5981%	51.23%

But, you can also build a 5 from two 4s...

Draw (n)	Odds you'll get a second 4 on the nth draw	Odds you'll get only 2 4s in 2 to n Draws
2​	1.0000%​	1.00%​
3​	1.8000%​	2.80%​
4​	2.4300%​	5.23%​
5​	2.9160%​	8.15%​
6​	3.2805%​	11.43%​
7​	3.5429%​	14.97%​
8​	3.7201%​	18.69%​
9​	3.8264%​	22.52%​
10​	3.8742%​	26.39%​
11​	3.8742%​	30.26%​
12​	3.8355%​	34.10%​
17	3.2943%	51.82%

And a 4 from two 3s...

Draw (n)	Odds you'll get a second 3 on the nth draw	Odds you'll get only 2 3s in 2 to n Draws
2​	2.2500%​	2.25%​
3​	3.8250%​	6.08%​
4​	4.8769%​	10.95%​
5​	5.5271%​	16.48%​
6​	5.8726%​	22.35%​
7​	5.9900%​	28.34%​
8​	5.9401%​	34.28%​
11	5.2114%	50.78%

And a 3 from two 2s...

Draw (n)	Odds you'll get a second 2 on the nth draw	Odds you'll get only 2 2s in 2 to n Draws
2​	9.0000%​	9.00%​
3​	12.6000%​	21.60%​
4​	13.2300%​	34.83%​
5​	12.3480%​	47.18%​
6​	10.8045%​	57.98%​

And lastly, a 2 from two 1s...

Draw (n)	Odds you'll get a second 1 on the nth draw	Odds you'll get only 2 1s in 2 to n Draws
2​	16.0000%​	16.00%​
3​	19.2000%​	35.20%​
4​	17.2800%​	52.48%​

Edit: Change the final column headers from "Odds you'll get at least 2 xs in n Draws" to "Odds you'll get only 2 xs in 2 to n Draws"

 

[Silly Bubbles]

I’m still missing more info on what pieces are used in trade offers

What odds each piece has of appearing

I hope you can see the misalignment.

I still haven't give up, maybe once in not so distant future my posts will get properly read and even understood.

Common Sense & Logic vs. Math... Love that compare and contrast... If Common Sense is something distinct enough from Logic to bear being mentioned separately, that makes me suspicious of the validity of whatever gets deemed 'common sense'. I mean, if a concept isn't logical, what does that leave? And then to consider Logic also separate from and better than Math. In what way is logic separable from math, or math separable from logic? Logical statements, logical thinking, all have mathematical representations. Most logic, when reduced to its simplest form, is basically Boolean Math; that is, math performed using only two values. I think you're really devaluing the speculation involved in the use of provided probability tables for computing compound events and projecting average results...

Actually, you can calculate all sorts of nonsense using perfectly correct math. Eg three elves times three orcs equals 9 cakes.
So just because you can calculate something doesn't necessarily mean that it needs to be calculated or that it does make sense. Yes, you can make complicated correct calculations but that doesn't mean that the result is needed or useful or make sense to a specific situation. What's the point in calculating distance to the Moon when you're deciding what to buy in a local shop.

 

[Sir Derf]

I thought I was addressing your next phrase, "...what odds each piece has in appearing", which I assumed meant "appearing when you draw from a cup", and not "appearing in the offer recipes". I do try to read and understand the posts I respond to; apologies if I inferred a meaning you did not imply, and if I was not clear on what my antecedent was.

As to your mathy response.... 3*3=9 in unitless pure math. I agree "three elves times three orcs equals 9 cakes" would be nonsense (unless, in some bizarre world elves and orcs are units of distance and cakes are units of area, or some such similar uniting.) So, have any of my computations, in any of my postings, mixed units in a nonsensical way? No? Then why are you bringing up this perfectly correct but completely unrelated objection? Let me save you the effort and point out several other, equally inapplicable complaints in advance...

• Conclusions are unreliable if you divide by zero at any step in the process ( I haven't, as far as I know)
• Statistics don't lie, but liars use statistics (I use statistics, yes, but am I lying...)
• Never go against a Sicilian when death is on the line (regardless of our genealogies, I don't think Elvenar is life-threatening)

As to your last question, I was going to rephrase it in terms of several of your earlier questions, but I think that would be cross-thread posting and the mods would probably frown on it...

In the mean time, I'll continue posting my on-topic musings. As with any other post, by any other user, in any other thread, those who find it useful can read them, those who don't can skip them. That's how a forum works.

 

[Sir Derf]

Spoiler - As with many of my musings, I might think I know where they will end up, but I won't really know until I get there. This went in an unexpected direction, but hey, we learn from mistakes.


But I really, really, really really, really want a Level 6 Piece. I can hope for 2 5s, and have to pick up to 34 times and still only have a 51.23% chance at success. What about the other combos, you know, a 5 and 2 4s, or something crazy like 16 1s?

Well, let's try something simpler... How about the odds of getting any of the building blocks for a Level 3 Piece?

So, we want the odds of...

• getting a 1st 3 with no 2s or 1s
• or getting a 1st 3 after 1 1 and no 2s
• or getting a 1st 3 after 2 1s and no 2s
• or getting a 1st 3 after 3 1s and no 2s
• or getting a 1st 3 after 1 2 and no 1s
• or getting a 1st 3 after 1 2 and 1 1
• or getting a 2nd 2 with no 3s or 1s
• or getting a 2nd 2 after 1 1 and no 3s
• or getting a 1st 2 after 2 1s and no 3s
• or getting a 1st 2 after 3 1s and no 3s
• or getting a 2nd 1 after a 1 and a 2 and no 3s
• or getting a 4th 1 with no 2s or 3s

Simpler? Seems pretty complex to me, having to combine 1211 different possibilities. Yeah, but consider, if this is how complex it needs to be just to handle all possible ways to achieve a Level 3, consider what it would take for Level 4, then Level 5, and then Level 6.

Why does it have to be this complex? Because, we don't want to end up counting the same winning combination multiple times.

And, having written this, I now see that my earlier post alleging to compute odds of getting pairs, implying it was a part of the odds to make the target Piece, is wrong for exactly this reason.

Because, in my attempt to compute "Build a 3 out of 2 2s", I was forgetting about those pesky 1s and 3s. When I computed the odds of 2nd 2 on the third draw, I was forgetting that the ignored card might be a 3; When I computed the odds of 2nd 2 on the fourth draw, I was forgetting the either, or both cards might be a 3, or that both could be a 1. I wasn't counting odds of "only being able to make a 3 out of 2 2s." While implying I was being selective, I was actually being inclusive, and inclusive multiple times over.


So, I made an earlier mistake. I'll correct it shortly.

Edit - and I made a mistake in this one, counting a condition twice.

 

[Sir Derf]

Okay let's go simpler.....

What are the odds of getting or building a Level 2 piece in n Draws.

Similar to the above, we want the odds of

• getting a 1st 2 with no 1s
• or getting a 1st 2 after 1 1
• or getting a 2nd 1 with no 2s

Here is what I think the table is:

Draws (n)	(x)2	(1x)2	(1x)1	Total for n Draws	Cumulative for 1 to n Draws
1​	30.00%​	---	---	30.00%​	30.00%​
2​	9.00%​	12.00%​	16.00%​	37.00%​	67.00%​
3​	2.70%​	7.20%​	9.60%​	19.50%​	86.50%​
4​	0.81%​	3.24%​	4.32%​	8.37%​	94.87%​
5​	0.24%​	1.30%​	1.73%​	3.27%​	98.14%​
6​	0.07%​	0.49%​	0.65%​	1.21%​	99.34%​
7​	0.02%​	0.17%​	0.23%​	0.43%​	99.77%​
8​	0.01%​	0.06%​	0.08%​	0.15%​	99.92%​
9​	0.00%​	0.02%​	0.03%​	0.05%​	99.97%​
10​	0.00%​	0.01%​	0.01%​	0.02%​	99.99%​

Nearly 95% chance that you will have or be able to build a Level 2 Piece in 4 Draws from the Cup.