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Dawn of the Phoenix
- Thread starter anonglitch
- Start date
Silly Bubbles
Necromancer
I'm sorry but I'm tired of repeating and explaining the same thing over and over, also handling the other stuff is not very pleasant to me. If you're interested in a different approach, you can read my original post and leave it or take it, all up to you. Personally, I'll give it a go as I don't have anything to lose and hopefully a lot to gain. Fingers crossed 
SkyRider99
Immortal
It seems to me that you are both correct. Just in a slightly different aspect.
Sir Derf
Adept
I really dislike that I have to constantly do the math to test out your assertions, that's not really the way burden of proof is supposed to go, but I do likes me some semi-pointless math...
Odds of getting bonus chests for 112 chest players opening 44 chests
| # of Bonus Chests | Odds | Cumulative Odds | Total Feathers |
|---|---|---|---|
0 | 10.47% | 10.47% | |
1 | 24.24% | 34.71% | |
2 | 27.43% | 62.14% | |
3 | 20.21% | 82.35% | |
4 | 10.90% | 93.25% | |
5 | 4.59% | 97.84% | |
6 | 1.57% | 99.41% | |
7 | 0.45% | 99.86% | |
8 | 0.11% | 99.97% | |
9 | 0.02% | 99.99% | |
10 | 0.00% | 100.00% | |
11 | 0.00% | 100.00% | |
12 | 0.00% | 100.00% |
Odds of getting bonus chests for 77 chest players opening 64 chests
| # of Bonus Chests | Odds | Cumulative Odds | Total Feathers |
|---|---|---|---|
0 | 0.12% | 0.12% | 192 |
1 | 0.84% | 0.96% | 198 |
2 | 2.93% | 3.89% | 204 |
3 | 6.74% | 10.63% | 210 |
4 | 11.42% | 22.05% | 216 |
5 | 15.22% | 37.27% | 222 |
6 | 16.63% | 53.90% | 228 |
7 | 15.31% | 69.22% | 234 |
8 | 12.12% | 81.34% | 240 |
9 | 8.38% | 89.72% | 246 |
10 | 5.12% | 94.84% | 252 |
11 | 2.79% | 97.64% | 258 |
12 | 1.37% | 99.01% | 264 |
13 | 0.61% | 99.62% | 270 |
14 | 0.25% | 99.86% | 276 |
15 | 0.09% | 99.96% | 282 |
16 | 0.03% | 99.99% | 288 |
17 | 0.01% | 100.00% | 294 |
Winning a 3rd 112 chest is at 82.35% accumulated odds, and earns a total of 232 Feathers, 11 GPs. Similarly, 81.34% accumulated odds opens 8 77 chests and earns 240 Feathers, 12 GPs.Winning a 4th 112 chest is at 93.25% accumulated odds, and earns a total of 248 Feathers, 12 GPs. Similarly, 94.84% accumulated odds opens 10 77 chests and earns 252 Feathers, 12 GPs.Winning a 5th 112 chest is at 97.84% accumulated odds, and earns a total of 264 Feathers, 13 GPs. Similarly, 97.64% accumulated odds opens 11 77 chests and earns 258 Feathers, 12 GPs.Winning a 6th 112 chest is at 99.41% accumulated odds, and earns a total of 284 Feathers, 14 GPs. Similarly, 99.62% accumulated odds opens 13 77 chests and earns 270 Feathers, 13 GPs.Winning a 7th 112 chest is at 99.86% (or nearly 1 in 1,000 times) accumulated odds, and earns a total of 300 Feathers, 15 GPs (and a second Phoenix base). Similarly, 99.86% accumulated odds opens 14 77 chests and earns 276 Feathers, 13 GPs.
I give. Making me work out the math for you, you are correct. Most of the time, typical strategy will give me more total feathers and Grand Prizes; rarely, your strategy will give you more feathers and Grand Prizes. While typical strategy gives 'higher odds at higher payouts', your approach does give the "highest odds of the highest payouts".
And if you are happy with trying to maximize the unlikely, you are welcome to it. You will, once in a while, outperform the typically professed strategy, but don't fool yourself into overstating how often that will occur. Your "hopefully a lot to gain" isn't really all that much and doesn't really happen that often. For me, I'll maximize the likely, earn 1 or more Grand Prizes than you 49 out of 50 times, and pat you on the back at besting me by almost assuredly only a single Grand Prize, oh, about once every 5 years.
BTW, if we say "a lot to gain" is an outcome where you get 3 more Grand Prizes, that's takes place when you win 11 bonus 112 chest SE in 44 picks and get 18 Grand Prizes vs. 19 bonus 77 chest SE in 64 picks and get 15 Grand Prizes, and that happens at the 99.999886% cumulative odds, the proverbial 1 in a million. That's a lot of hope.
Edit: And this is why I publish my work. So when I make a mistake, it can be discovered that much easier.
While I trusted my work, as surprising as it seemed, something was still nagging at me....
In my previous post, I had stated that I first worked with 129 vs. 77, but it was too close to call, so shifted to 112 vs. 77, remember... Well, the math I worked out above I computed with the at least some of the data for the 129 chest, that the chest paid out 500 SE, not 100 SE. So, the real numbers are much, much worse... I'm not even sure if the curves still cross over. I'm busy with stuff at the moment, so only have time to post this retraction. I'll come back later with the correct data.
Last edited:
Sir Derf
Adept
1) The original original assertion was publicly posted for all to see, and if it needs correcting, that correction should be publicly posted for all as well.
2) This is a public forum, and the conversation is on topic and within the rules. If you think it is 'nicer' to not read it..... um, then don't read it?
2) This is a public forum, and the conversation is on topic and within the rules. If you think it is 'nicer' to not read it..... um, then don't read it?
Killiak
Artisan
Yeah see, you already made your point. Several times over. Both of you.
Right now you two are having a discussion about who can shout the other guy down via rehashed "I AM RIGHT"-posts all the time, in some sort of looping 'akshually'-meme. So really, it would be lovely if you can just duke it out between the two of you, via PM's, who has the biggest e-peen and then post the result in a single post.
And yes, there is an option is for everybody to block you or report all your posts so that a mod can go and tell you to give it a rest. I mean, we can do that, if you prefer? Over time though, your forum experience is going to be a lonely one. So please, let it rest already. Sjeesh.
Sir Derf
Adept
Politely @Killiak , then you're not reading closely enough. Having done the math (albeit incorrectly), I was completely willing to accept that @Silly Bubbles was correct in his claim that his strategy would give the "highest odds at the highest payout". Rather than "shouting down the other guy", I have been attempting to weigh both propositions , and thought I had argued his case so well that I was admitting defeat and that the other guy was technically correct (although probably way overestimating how correct he thought he was).
I would further think that most people would probably skip reading a few posts before going the block route. This isn't my first foray into semi-pointless math, after all. As to reporting to a mod... I mean... are the posts off topic? Are they personally insulting? If you bother to read them, are they purely repetitive, or is there the gradual addition of new and relevant information? Some people are liking some of the posts, so I would venture a guess to say that not everyone has the same feelings about them that you do.
I would further think that most people would probably skip reading a few posts before going the block route. This isn't my first foray into semi-pointless math, after all. As to reporting to a mod... I mean... are the posts off topic? Are they personally insulting? If you bother to read them, are they purely repetitive, or is there the gradual addition of new and relevant information? Some people are liking some of the posts, so I would venture a guess to say that not everyone has the same feelings about them that you do.
Sir Derf
Adept
Anyway...
So, the earlier where I said it was computed for a 112 chest (gives 4 feathers, 22% chance of 100 bonus SE), who could open 44 chests if they started with 5,000 SE, was actually a horrible mish-mash, and was instead computed as if a 129 chest (gives 5 feathers, 5% chance of 500 bonus SE) was also able to open 44 chests, and not the 38 he should have been. So, it was more like comparing a 77 chest to a 129 chest while giving the 129 chest a 30 feather head start. Let's do this correctly...
So, the earlier where I said it was computed for a 112 chest (gives 4 feathers, 22% chance of 100 bonus SE), who could open 44 chests if they started with 5,000 SE, was actually a horrible mish-mash, and was instead computed as if a 129 chest (gives 5 feathers, 5% chance of 500 bonus SE) was also able to open 44 chests, and not the 38 he should have been. So, it was more like comparing a 77 chest to a 129 chest while giving the 129 chest a 30 feather head start. Let's do this correctly...
Sir Derf
Adept
Correct odds of getting bonus chests for 112 chest players opening 44 chests
Odds of getting bonus chests for 77 chest players opening 64 chests
Median outcome for the 112 chest is around 9 bonus successes, about 208 total feathers, 10 Grand Prizes
Median outcome for the 77 chest is around 6 bonus successes, about 228 total feathers (20 more, so higher payout), 11 Grand Prizes.
99.07% chance for the 112 chest is 16 bonus successes, 232 total feathers, 11 Grand Prizes.
99.01% chance for the 77 chest is 12 bonus successes, 264 (32 more, an even higher-er payout) total feathers, 13 Grand Prizes.
15 Grand Prizes for the 112 chest is at a whopping 34 bonus successes out of 44 chests, 25 more than expected, with an accumulated odds so low, excel wouldn't go that low (less than 1 in a trillion).
15 Grand prizes for the 77 chest is at 18 bonus successes out of 64 chests, 12 more than expected, with an accumulated odds of 99.9990%, or one in 1 hundred thousand.
| # of Bonus | Odds | Cumulative Odds | Bonus SE | Extra Chests | Extra Feathers | Total Feathers | Grand Prizes |
|---|---|---|---|---|---|---|---|
0 | 0.00% | 0.00% | 0 | 0 | 0 | 176 | 8 |
1 | 0.02% | 0.02% | 100 | 1 | 4 | 180 | 9 |
2 | 0.13% | 0.16% | 200 | 2 | 8 | 184 | 9 |
3 | 0.53% | 0.69% | 300 | 3 | 12 | 188 | 9 |
4 | 1.54% | 2.22% | 400 | 4 | 16 | 192 | 9 |
5 | 3.46% | 5.69% | 500 | 5 | 20 | 196 | 9 |
6 | 6.35% | 12.04% | 600 | 6 | 24 | 200 | 10 |
7 | 9.73% | 21.77% | 700 | 6 | 24 | 200 | 10 |
8 | 12.69% | 34.45% | 800 | 7 | 28 | 204 | 10 |
9 | 14.31% | 48.76% | 900 | 8 | 32 | 208 | 10 |
10 | 14.13% | 62.89% | 1000 | 9 | 36 | 212 | 10 |
11 | 12.32% | 75.21% | 1100 | 10 | 40 | 216 | 10 |
12 | 9.55% | 84.77% | 1200 | 11 | 44 | 220 | 11 |
13 | 6.63% | 91.40% | 1300 | 12 | 48 | 224 | 11 |
14 | 4.14% | 95.54% | 1400 | 13 | 52 | 228 | 11 |
15 | 2.34% | 97.88% | 1500 | 14 | 56 | 232 | 11 |
16 | 1.19% | 99.07% | 1600 | 14 | 56 | 232 | 11 |
17 | 0.55% | 99.63% | 1700 | 15 | 60 | 236 | 11 |
Odds of getting bonus chests for 77 chest players opening 64 chests
| # of Bonus | Odds | Cumultaive Odds | Bonus SE | Extra Chests | Extra Feathers | Total Feathers | Grand Prizes |
|---|---|---|---|---|---|---|---|
0 | 0.12% | 0.12% | 0 | 0 | 0 | 192 | 9 |
1 | 0.84% | 0.96% | 150 | 2 | 6 | 198 | 9 |
2 | 2.93% | 3.89% | 300 | 4 | 12 | 204 | 10 |
3 | 6.74% | 10.63% | 450 | 6 | 18 | 210 | 10 |
4 | 11.42% | 22.05% | 600 | 8 | 24 | 216 | 10 |
5 | 15.22% | 37.27% | 750 | 10 | 30 | 222 | 11 |
6 | 16.63% | 53.90% | 900 | 12 | 36 | 228 | 11 |
7 | 15.31% | 69.22% | 1050 | 14 | 42 | 234 | 11 |
8 | 12.12% | 81.34% | 1200 | 16 | 48 | 240 | 12 |
9 | 8.38% | 89.72% | 1350 | 18 | 54 | 246 | 12 |
10 | 5.12% | 94.84% | 1500 | 20 | 60 | 252 | 12 |
11 | 2.79% | 97.64% | 1650 | 22 | 66 | 258 | 12 |
12 | 1.37% | 99.01% | 1800 | 24 | 72 | 264 | 13 |
13 | 0.61% | 99.62% | 1950 | 26 | 78 | 270 | 13 |
14 | 0.25% | 99.86% | 2100 | 28 | 84 | 276 | 13 |
15 | 0.09% | 99.96% | 2250 | 30 | 90 | 282 | 14 |
16 | 0.03% | 99.99% | 2400 | 32 | 96 | 288 | 14 |
17 | 0.01% | 100.00% | 2550 | 34 | 102 | 294 | 14 |
Median outcome for the 112 chest is around 9 bonus successes, about 208 total feathers, 10 Grand Prizes
Median outcome for the 77 chest is around 6 bonus successes, about 228 total feathers (20 more, so higher payout), 11 Grand Prizes.
99.07% chance for the 112 chest is 16 bonus successes, 232 total feathers, 11 Grand Prizes.
99.01% chance for the 77 chest is 12 bonus successes, 264 (32 more, an even higher-er payout) total feathers, 13 Grand Prizes.
15 Grand Prizes for the 112 chest is at a whopping 34 bonus successes out of 44 chests, 25 more than expected, with an accumulated odds so low, excel wouldn't go that low (less than 1 in a trillion).
15 Grand prizes for the 77 chest is at 18 bonus successes out of 64 chests, 12 more than expected, with an accumulated odds of 99.9990%, or one in 1 hundred thousand.
Sir Derf
Adept
Sorry for the false computations and erroneous conclusion earlier. The curves do not cross. The 77 chest is superior to the 112 chest at every equivalent step, from the absolute worst outcome of getting no successful bonuses, to the median outcome, to the wildly unlikely outcome. You don't get better if you luckily win more bonuses. Focusing on maximizing the rate of Bonus SE, ignoring the relative Costs and Feather benefits is not a successful strategy.
Since I was willing to admit I was wrong when the math appeared to bear you out, I can only hope that you will be willing to do the same when the correct math shows that I am right.
(Wow, I never knew that there were both character and time limits on postings... My original was over 10,000 characters, and in the gradual paring down into smaller pieces, I hit limitations on placing posts too quickly.)
Since I was willing to admit I was wrong when the math appeared to bear you out, I can only hope that you will be willing to do the same when the correct math shows that I am right.
(Wow, I never knew that there were both character and time limits on postings... My original was over 10,000 characters, and in the gradual paring down into smaller pieces, I hit limitations on placing posts too quickly.)
Silly Bubbles
Necromancer
If you prefer it, I don't have to post at all. As I said, this is getting ridiculous anyway and obviously not many people care.
Silly Bubbles
Necromancer
Please don't involve me in an argument that you have with someone else and also if you read at least some it, you would realise that I have the same problem as you do. I'm tired of it as much as you are. Sometimes, I'm sorry that I tried to help, at the end I become target.
Killiak
Artisan
I have been, actually. But this reaction just proves my point. It's a "Nu-uh, I am right", just worded differently.
One example, to keep the length of this down:
You think comparing another person's stance in a discussion to a Flat Earther is flattering? If that was supposed to be comedy, I assure you that 'the funny' bit of that didn't come across very well. Straight up insulting and demeaning.
Also, the same people who like some of your posts also like some of mine. If you want to measure anything by likes, Facebook is probably a better location to do so.... and that doesn't say much.
Anyway, I don't know what I was thinking with my post. From my perspective and personal opinion, there is a massive need to always be right on your end, so of course you would not let it rest even when asked. Of course you would tell me "nuh-uh".
I'll just take the only option left to me. I'm sure you'll write some reply on how I am wrong, but guess what? I won't see it anymore!
@Silly Bubbles
Sorry if it came across as such mate, nothing against you.
Sir Derf
Adept
Oh no, a thread on a forum on the internet contained a discussion/argument on a topic that I'm not personally interested in... this never happens...
"Nu-uh, I am right", just worded differently.... well yeah, that's how persuasive argumentation works. But key to this is, I believe, that the "worded differently" is having different ways of explaining why I'm right, or why you're wrong, or as a great philosopher said "Argument is an intellectual process. Contradiction is just the automatic gainsaying of anything the other person says."
Humor is subjective, and not everyone likes every attempt. I will point out that the analogy was explicitly comparing the argument style and not the person. It is unavoidable that stating someone's logic is bad can lead to the inference that the person is bad. Not what I said.
Would not let it rest, even when asked... Yes, when asked. Again, this is kinda how conversation and argumentation works. Yes, anyone can stop a discussion at any time, but you're actually faulting me for responding when directly asked? " I still haven't seen any calculations that proves the solution I gave wrong.", so I gave calculations... "What if I don't care about feathers per chest but just purely about winning additional currency?", so I expanded and more directly addressed the question. I do apologize at posting incorrect analysis and then correcting, but hey, nobody's perfect...
Yep, you're right, I did write some reply on how I think your arguments, your statements, were wrong. Forum, conversation, funny that...
@Killiak @Silly Bubbles nothing against either of you.
"Nu-uh, I am right", just worded differently.... well yeah, that's how persuasive argumentation works. But key to this is, I believe, that the "worded differently" is having different ways of explaining why I'm right, or why you're wrong, or as a great philosopher said "Argument is an intellectual process. Contradiction is just the automatic gainsaying of anything the other person says."
Humor is subjective, and not everyone likes every attempt. I will point out that the analogy was explicitly comparing the argument style and not the person. It is unavoidable that stating someone's logic is bad can lead to the inference that the person is bad. Not what I said.
Would not let it rest, even when asked... Yes, when asked. Again, this is kinda how conversation and argumentation works. Yes, anyone can stop a discussion at any time, but you're actually faulting me for responding when directly asked? " I still haven't seen any calculations that proves the solution I gave wrong.", so I gave calculations... "What if I don't care about feathers per chest but just purely about winning additional currency?", so I expanded and more directly addressed the question. I do apologize at posting incorrect analysis and then correcting, but hey, nobody's perfect...
Yep, you're right, I did write some reply on how I think your arguments, your statements, were wrong. Forum, conversation, funny that...
@Killiak @Silly Bubbles nothing against either of you.
Almondum
Spellcaster
Hello guys,
I tried to read bits of all the 7 pages during my lunch break, but there just wasn't enough time.
I am glad that you have reached a conclusion regarding the chests. At present, I always try to open a 77 chest, but sometimes it is not present and I open the 112.
I am mostly following a table from a Google docs that is about the event. Beside the 77 chest, are the other chests in the list in the correct order (77, 129, 112, 46, etc).
Thank you!
Almondum
I tried to read bits of all the 7 pages during my lunch break, but there just wasn't enough time.
I am glad that you have reached a conclusion regarding the chests. At present, I always try to open a 77 chest, but sometimes it is not present and I open the 112.
I am mostly following a table from a Google docs that is about the event. Beside the 77 chest, are the other chests in the list in the correct order (77, 129, 112, 46, etc).
Thank you!
Almondum
Jake65
Sage
Random thought on the value of a fed Twilight Phoenix, perhaps a different angle on the previous discussion/comparison:
The 5% troop recovery happens too quickly for me to check the numbers but essentially the total troops recovered during the 12 hours come at the cost of one pet food. 1650(?) spell fragments.
Seems like a bargain to me
The 5% troop recovery happens too quickly for me to check the numbers but essentially the total troops recovered during the 12 hours come at the cost of one pet food. 1650(?) spell fragments.
Seems like a bargain to me
Pauly7
Magus
I was reminded that I never got around to posting this RNG oddity on the forum:
In my baby city I don't really do the events, because there is no point. On this one I'd literally completed one quest before I'm stopped due to not having workshops. Anyway, since then I've been collecting my daily bonus, etc. The other day I took my handful of event currency to try my luck. I opened the 129 chest 4 times and won 500 SE 4 times. This seems virtually like winning the National Lottery. A chance of 0.000625%, I think.
On balance, I would rather have won the lottery though.
In my baby city I don't really do the events, because there is no point. On this one I'd literally completed one quest before I'm stopped due to not having workshops. Anyway, since then I've been collecting my daily bonus, etc. The other day I took my handful of event currency to try my luck. I opened the 129 chest 4 times and won 500 SE 4 times. This seems virtually like winning the National Lottery. A chance of 0.000625%, I think.
On balance, I would rather have won the lottery though.