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

Sir Derf

Mentor
Edit - found error, see later post

So, what about that Odds of getting or building a Level 3 Piece in n Draws....

Was as the corrected list above was, 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 32
  • or getting a 4th 1 with no 2s or 3s
Here is what I think the table is

Draws
(n)
(x)3(1x)3(11x)3(111x)3(2x)3(12x)3(2x)2(21x)2(11x)2(111x)2(111x)1Total
n
Cumul
1 - n
1
15.00%
15.00%
15.00%
2
2.25%
6.00%
4.50%
9.00%
21.75%
36.75%
3
0.34%
1.80%
2.40%
1.35%
3.60%
2.70%
7.20%
4.80%
24.19%
60.94%
4
0.05%
0.41%
1.08%
0.96%
0.30%
1.62%
0.61%
3.24%
2.16%
1.92%
2.56%
14.91%
75.84%
5
0.01%
0.08%
0.32%
0.58%
0.06%
0.49%
0.12%
0.97%
0.65%
1.15%
0.38%
4.81%
80.66%
6
0.00%
0.02%
0.08%
0.22%
0.01%
0.12%
0.02%
0.24%
0.16%
0.43%
0.06%
1.36%
82.02%
7
0.00%
0.00%
0.02%
0.06%
0.00%
0.03%
0.00%
0.05%
0.04%
0.13%
0.01%
0.35%
82.37%
8
0.00%
0.00%
0.00%
0.02%
0.00%
0.01%
0.00%
0.01%
0.01%
0.03%
0.00%
0.08%
82.45%
9
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
0.00%
0.02%
82.47%
10
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
82.47%
11
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
82.48%

Something is wrong here, but I can't yet see what it is. Generically, it doesn't make sense that this doesn't eventually accumulate to 100%, but I have a more specific cross-check that is failing. Pulling from this table, the odds of getting a 3 on the first try is 15%, as expected, and the odds of getting the first 3 on the second try is 2.25%+6.00%+3.50% = 12.75%, also as expected. However, the combined odds of getting a
1st 3 on the third try appear to sum to 0.34%+1.80%+2.40%+1.35%+3.60%=9.49%, when the expected is 10.84%, off by 1.35%. I suspect either or both of my (11x)3 and (12x)3 column, but at the moment I can't spot the error. I'm posting this as is, knowing that this is flawed, both as a continuing record of my thought process, and in the faint hope that someone who is interested might puzzle this out before me. I'll continue looking into this and get back later.

I don't know about anyone else, but INNO is sure giving me a lot of entertainment out of this, and I haven't had the chance to actually start playing this yet.
 
Last edited:

Sir Derf

Mentor
Well, I found the 'error' I had identified above, but I'm left with trying to figure out what this means, and what to do...

My missing 1.35% in the 10.84% chance total of "getting your first 3 on the third pick" is from the 1.35% chance of getting the sequence 223, which I have discounted in this table, because I have already deemed the initial draw of 22 to be a successful 3, and so this 1.35% is actually a partial continuing outcome of the 9.00% chance that I already accounted for.

This still doesn't feel right, but probability is weird. Our brain is naturally wired for some calculations. We can intuit additive and linear (multiplicative or percent) relationships, and are OK at parabolic approximations, at least where trajectories under normal gravity are concerned; however inverse relationships (1/x), geometric growth (n^x, power series, compound interest) and conditional probabilities are not things that come naturally to us. Gut instinct can easily be wrong in these circumstances. Just look at how difficult dealing with "The Birthday Paradox" or "The Monty Hall Problem" is, and you will see what I mean.

I'm queasy over this. Some might say that this 'goes against common sense' or 'looks illogical'. But at the moment, this is what the math appears to be saying, and absent finding the error in the math, that's what I'm going with. I'm not throwing it out because I'm queasy. I'm going to ruminate on this for a while, to either find a math flaw, find how I'm asking the wrong question, or come to understand how this can be the correct answer.

At the moment, this is my Douglas Adams '42' moment...
 

Sir Derf

Mentor
So, I finally got around to looking into the above Odds of building a Level 3 Piece, and found an issue. There is a 12th possible way to build a Level 3, and it turns out it is the 2nd most likely combination; what I would describe as getting a 2nd 1 after 1 2 with no 3s.


So, what about that Odds of getting or building a Level 3 Piece in n Draws....
  • 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 32
  • or getting a 2nd 1 after 1 2 and no 3s
  • or getting a 4th 1 with no 2s or 3s
Here is what I think the updated table is

Draws
(n)
(x)3(1x)3(11x)3(111x)3(2x)3(12x)3(2x)2(21x)2(11x)2(111x)2(12x)1(111x)1Total
n
Cumul
1 - n
1​
15.00%​
15.00%​
15.00%​
2​
2.25%​
6.00%​
4.50%​
9.00%​
21.75%​
36.75%​
3​
0.34%​
1.80%​
2.40%​
1.35%​
3.60%​
2.70%​
7.20%​
4.80%​
9.60%​
33.79%​
70.54%​
4​
0.05%​
0.41%​
1.08%​
0.96%​
0.30%​
1.62%​
0.61%​
3.24%​
2.16%​
1.92%​
4.32%​
2.56%​
19.23%​
89.76%​
5​
0.01%​
0.08%​
0.32%​
0.58%​
0.06%​
0.49%​
0.12%​
0.97%​
0.65%​
1.15%​
1.30%​
0.38%​
6.11%​
95.87%​
6​
0.00%​
0.02%​
0.08%​
0.22%​
0.01%​
0.12%​
0.02%​
0.24%​
0.16%​
0.43%​
0.32%​
0.06%​
1.69%​
97.56%​
7​
0.00%​
0.00%​
0.02%​
0.06%​
0.00%​
0.03%​
0.00%​
0.05%​
0.04%​
0.13%​
0.07%​
0.01%​
0.42%​
97.98%​
8​
0.00%​
0.00%​
0.00%​
0.02%​
0.00%​
0.01%​
0.00%​
0.01%​
0.01%​
0.03%​
0.02%​
0.00%​
0.10%​
98.08%​
9​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.01%​
0.00%​
0.00%​
0.02%​
98.10%​
10​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
98.11%​
11​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
98.11%​


This looks better, but I'm still suspicious that it appears to plateau at 98.11 instead of approaching 100% (I have more rows than I copied, it didn't budge) I'll keep looking.

With that said, I'm looking at a <2% missing, so I feel semi-confident saying you have just over 95% chance of that you will have or be able to build a Level 3 Piece in 5 Draws from the Cup.
 

Sir Derf

Mentor
And, I found a typo in my formula. This grid looks matched common sense, so I have much lower concern with these numbers.

So, what about that Odds of getting or building a Level 3 Piece in n Draws....
  • 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 32
  • or getting a 2nd 1 after 1 2 and no 3s
  • or getting a 4th 1 with no 2s or 3s
Here is what I think the updated table is

Draws
(n)
(x)3(1x)3(11x)3(111x)3(2x)3(12x)3(2x)2(21x)2(11x)2(111x)2(12x)1(111x)1Total
n
Cumul
1 - n
1​
15.00%​
15.00%​
15.00%​
2​
2.25%​
6.00%​
4.50%​
9.00%​
21.75%​
36.75%​
3​
0.34%​
1.80%​
2.40%​
1.35%​
3.60%​
2.70%​
7.20%​
4.80%​
9.60%​
33.79%​
70.54%​
4​
0.05%​
0.41%​
1.08%​
0.96%​
0.30%​
1.62%​
0.61%​
3.24%​
2.16%​
1.92%​
4.32%​
2.56%​
19.23%​
89.76%​
5​
0.01%​
0.08%​
0.32%​
0.58%​
0.06%​
0.49%​
0.12%​
0.97%​
0.65%​
1.15%​
1.30%​
1.54%​
7.26%​
97.03%​
6​
0.00%​
0.02%​
0.08%​
0.22%​
0.01%​
0.12%​
0.02%​
0.24%​
0.16%​
0.43%​
0.32%​
0.58%​
2.21%​
99.23%​
7​
0.00%​
0.00%​
0.02%​
0.06%​
0.00%​
0.03%​
0.00%​
0.05%​
0.04%​
0.13%​
0.07%​
0.17%​
0.59%​
99.82%​
8​
0.00%​
0.00%​
0.00%​
0.02%​
0.00%​
0.01%​
0.00%​
0.01%​
0.01%​
0.03%​
0.02%​
0.05%​
0.14%​
99.96%​
9​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.00%​
0.01%​
0.00%​
0.01%​
0.03%​
99.99%​

Better than 95% chance that you will have or be able to build a Level 3 Piece in 5 Draws from the cup.


Unless people express interest, I think I'm not going to attempt the equivalent computations for Levels 4 through 6 Pieces. While I think I have the kinks worked out to be able to build the computations for them, the shear number of ways that you can build these larger pieces is growing rapidly. I'll extend a few guesses with no justification, but I'd say 95% chance for Level 4 with at least 6 Draws, Level 5 with at least 7 Draws, and Level 6 with at least 8, 9, or maybe 10.
 
Last edited:

Sir Derf

Mentor
Just a few scribbles on Level 6 pieces.

All the other Levels, your earliest chance at success is with a single Draw from the Cup, from 40% down to 5%; for Level 6, your earliest chance at success is with a double draw, requiring 2 5s, a 0.25% chance.

After that, drawing in 3 requires either some combination of 2 5s and anything at 0.7125% or some combination of 2 4s and a 5 at 0.15%, for a Total of 0.8625, and a Cumulative chance in 2 or 3 draws of 1.1125%.

After that, it gets both better, by having more possible winning combinations, and worse, by having individually smaller and smaller odds on each combination.

On the plus side, as opposed to Levels 1-4, where you have an ever diminishing but still possible chance of never being able to build your goal piece, if only because you might constantly draw larger than desired Pieces (like Level 5s), when your goal is a Level 5 or 6 piece, you are ultimately guaranteed to eventually be able to build your target in a finite number of draws. For a Level 5 piece, you are 100% guaranteed to be able to build one by 16 Draws; the worst case would be drawing 15 1s, at which point whatever you draw will give you a 5. Similarly, for a Level 6 piece, you are 100% guaranteed to build one in 32 draws. Keep in mind, the odds of ending up in these worst case situations are tiny, 10^-17 and 10^-41, respectively, and you will have hit the 50% and 95% expectation levels way before that, but it's nice to know that these will eventually happen if you can wait it out.
 

Sir Derf

Mentor
Having computed the odds of drawing/building a Level 1, 2 or 3 Piece, this is another path to an approximation of the cost of a Piece.

Level 1 Piece
Draw (n)CostOdds you'll pick a 1 first on the nth draw
1440.00%
2824.00%
31214.4.0%
4168.64%
5205.18%
6243.11%
7281.87%

Average cost 8.94

Level 2 Piece
Draws
(n)
CostTotal for
n Draws
1430.00%
2837.00%
31219.50%
4168.37%
5203.27%
6241.21%
7280.43%
8320.15%
9360.05%
10400.02%

Average cost 8.98

Level 3 Piece
Draws
(n)
CostTotal
n
1415.00%
2821.75%
31233.79%
41619.23%
5207.26%
6242.21%
7280.59%
8320.14%
9360.03%

Average cost 11.67
 

Sir Derf

Mentor
Level PieceAverage Cost from 100 DrawsAverage Cost from probability to build 1
14.008.94
25.608.98
38.5011.67
412.67
520.00
640.00

The first cost is a bulk estimate - ignore useless draws, use all possible pieces to make the as many of the target as possible.
The second cost is an individual estimate - include the cost of unused pieces as you try to build a single target.

Again, these are Semi-Pointless Math. I earlier mused that the first column were probably overestimates, as the cost for Level 6 Pieces included the overly costly building of a Level 6 Piece out of 32 Level 1 Pieces for a cost of 128 Chips. Likewise, the second column is also an overestimate, because it simultaneously assumes you are starting with nothing, but also includes you drawing Pieces you aren't going to use, which would probably then be initially available for the building of later Pieces.
 

Sir Derf

Mentor
I would love to get some feedback from Beta players on actual gameplay, even if it is just impressions and feelings. My numbers seem to say that Level 6 Pieces are hard and costly to build, even more so after the change (removing the 2% chance at getting one from a draw).
 

Herodite

Senior Forum Moderator
Elvenar Team
@AutumnWolf Best thing to do is to read through the Info here, of course this Info could change when it comes over to the Live Servers so is never written in Stone :D

Kind Regards

Herodite
 

Sir Derf

Mentor
Been away for a few.

Reread @Jackluyt's file.

I see that there was info about the rewards and odds form a/the Lucky Draw card... Something seems off... If I am reading it correctly, 1) it totals 95%, and 2) the last set appears to read 15% chance each on L5Tool, L5Die or... Chips, not L5Figure.

Does anyone have information on the recipes that showed up? What were the combos asked for, how often did they come up? Did they come up across all three offer slots, or were they different per slot?

And, did the 12 offers appear to appear equally across the three offer slots, or was there some segregation between the slots?
 

Silly Bubbles

Illusionist
Does anyone have information on the recipes that showed up? What were the combos asked for, how often did they come up? Did they come up across all three offer slots, or were they different per slot?

And, did the 12 offers appear to appear equally across the three offer slots, or was there some segregation between the slots?

There's some more information on trades and the slots here:

I don't have any more information on trades costs and related patterns yet. At this moment, I'm thinking of recording the trade offer cost details as they keep coming up and see what I can make out of it.
 
I'm quoting a player (Karvest) from the Beta Forum, probably answers some of your questions:

There are 105 out of 234 different offers that require lvl6 item (35 of each type).
The best for grand prize/league ones are those giving 2 lucky draws with 20% chance. First one appears in middle slot and have 24 different combinations of items (21 of them require level 6 item), second appears in the bottom slot and have 10 different combinations (9 with lvl6 item).
You can always refuse an offer that you can't fulfill, and get better one.
 
Last edited:

sunrae

Soothsayer
I would love to get some feedback from Beta players on actual gameplay, even if it is just impressions and feelings.
I played on Beta and won all the set buildings plus 2 extra ones. My strategy was very simple - go for the most red counters. I won several lucky draws which included level 6 Pieces, free dwarf chips(quite a lot) and some random Pieces. I did not re-roll as I thought that was a waste of chips so I did a lot of melding the pieces together to gain the ones needed. I was very lucky I know but just to say getting the set without paying diamonds is possible. The lucky draws are the thing to go for I reckon.
I did love all the troops I won in the 2nd place and it's great that they are a more regular feature in the events. I struggled in the beginning to get to grips with it but after a couple of days I really enjoyed this mini game. I was pleased they dropped the 5 chips needed to 4, the only real frustration was we didn't get many chips from doing the quests which I thought was mean, but the lucky draw wins sorted that.
 

Jackluyt

Shaman
Been away for a few.

Reread @Jackluyt's file.

I see that there was info about the rewards and odds form a/the Lucky Draw card... Something seems off... If I am reading it correctly, 1) it totals 95%, and 2) the last set appears to read 15% chance each on L5Tool, L5Die or... Chips, not L5Figure.

Does anyone have information on the recipes that showed up? What were the combos asked for, how often did they come up? Did they come up across all three offer slots, or were they different per slot?

And, did the 12 offers appear to appear equally across the three offer slots, or was there some segregation between the slots?

Thanks for pointing out the error - fixed now!

295825425_10221299170289401_2480761602522377643_n.jpg
 

OldHag

Scholar
What about the dwarf offers that you have all the pieces for, but don't want to accept the trade. One of my offers currently only has a tick to accept the trade, the discard button disappeared when I had all the items it asks for.
Will I get the chance to discard that particular trade if/when I use some of the pieces needed?

p.s Thanks as always, @Jackluyt :)

forget it, I've found out you can decline the trade if you use some of the pieces on another trade offer.,
 
Last edited:

Sir Derf

Mentor
Wait, what? An Offer is undeclinable if you have all the pieces to pay for it? No, no, no, no, no.... I have to wait to decline an offer, wait to have the 30 minute cooldown, wait to get a new offer that I might like, all because I have the pieces already?
 

Sir Derf

Mentor
Also, thank you to those who responded to my earlier question, but that wasn't what I was asking for... I know what the Offers are (the lists of potential rewards and odds)... I was asking for information on the Recipes (the piece combinations needed to accept an Offer)

It would be helpful to decide whether to accept or decline a recipe/offer combo if you have an idea what possible future recipes a given offer might be presented with.
 

Sir Derf

Mentor
I played on Beta and won all the set buildings plus 2 extra ones. My strategy was very simple - go for the most red counters. I won several lucky draws which included level 6 Pieces, free dwarf chips(quite a lot) and some random Pieces. I did not re-roll as I thought that was a waste of chips so I did a lot of melding the pieces together to gain the ones needed. I was very lucky I know but just to say getting the set without paying diamonds is possible. The lucky draws are the thing to go for I reckon.
I did love all the troops I won in the 2nd place and it's great that they are a more regular feature in the events. I struggled in the beginning to get to grips with it but after a couple of days I really enjoyed this mini game. I was pleased they dropped the 5 chips needed to 4, the only real frustration was we didn't get many chips from doing the quests which I thought was mean, but the lucky draw wins sorted that.
Reroll does not use chips. Reroll recharges when you collect 5 Triumph Gems (progress for Grand Prizes); you don't use them up when you reroll.
 

OldHag

Scholar
yes and no, each time you have a piece of a trade offer, it's ticked green, if all 3 are ticked green you can either accept that offer or take another trade that would use one or more pieces from your unwanted trade, then you can decline it.
There's a lot of waiting if you decline all your offers, you may or may not like what you get next. :)
I'm looking for offers that have an ok chance to win some lucky tickets.
 

Sir Derf

Mentor
The more pieces you have, the more likely you will match a recipe. And then not be able to decline that offer.

Sooooo, if I have all the pieces to match with all the offers, but I don't like any of the offers, I can't decline any of them? I have to either combine or delete pieces until I break a recipe?
 
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