@Brobb, I am glad you are pretty passionate on this topic. I keep pretty good records, and am not looking to assign blame to anything, just trying to increase my win percentage… which this raid strategy did. As for the coin toss percentages, I used Bernoulli trials to do the math… if you can come up with a better binary tree solver to predict percentages of random events, good for you.
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A Bernoulli tree won’t work here, because we’re not interested in the chance of ten sequential heads in ten tosses (which is the result you’ve calculated) but in any ten sequential heads in a hundred tosses. One can’t cheat through that in any way I know - you’ve just gotta build the formula (which I can’t face doing just now). (Maybe I’ll get excited and do it later.)
And here’s the problem with your raid ‘strategy’ improving your results: if an activity goes badly, then you stop doing it for a while, then it goes normally, then you have not achieved anything. Because we always expect it to go normally - that’s why we call it normal.
What you’re experiencing is just mean regression. Your behaviour is typical of gamblers, who try to ride hot streaks and break cold streaks, but what you’re experiencing is just randomness. People are built to be silly like that - all of us. Got a lucky hat? I do. (It’s not really lucky, but I can’t help believing it is.)
I hope none of this is offending you. You’re obviously not an idiot and I do feel passionately about this stuff.
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Phooey… now I just want to figure it out, because I think that I am right. If you google “problems with random number generators” you will get a litany of responses including many well respected institutes dumping a lot of money into making / getting a truly random number generator. To quote someone in stack overflow,
“An algorithm for truly random numbers cannot exist as the definition of random numbers is: … There are better or worse pseudorandom number generators(PRNGs), i.e. completely predictable sequences of numbers that are difficult to predict without knowing a piece of information, called the seed.”
Most software calls on a hardware based RNG or a built in “Pseudorandom number generators”. I have had tile selection, hero summons, and chest rewards have all occurred after I lost “connection” and the results appeared when I restarted the game. The tile selection makes me think that the logic for section is in the app and not the server, because the battle continues while the “Wi-Fi” symbol is showing. If the RNG call is on my iPhone, I think that it is an algorithm as there doesn’t appear to be a hardware random number generator on board. As such SG is using an algorithm (which isn’t random) and the basis of my original point. Note that these algorithms can be quite good.
Edit… bummer, I accidentally erased this post thinking i was responding to the following one… I think i restored it back.
We’re reasonably familiar with PRNGs around these parts - I get the impression more than a few forum contributors have worked with them. If you read up in the thread you may even come across some discussion of them, The point is that a decent RNG is just not necessary here. A totally predictable sequence with a relatively fast periodicity would work absolutely fine.
I’m open to hearing arguments to the contrary. Why do you think using a high quality RNG would be necessary? How would it help anything?
Edit: I’ll give you a starting point. Why not just use the first thousand digits of Pi, repeated?
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Thanks for the banter, but I believe that we are in the weeds and either way it is irrelevant to the original post and I need to actually work today. Also, I don’t want anything changed so at the end of the day, I don’t have a dog in the race. Furthermore, no one’s data suggests that the initial boards are anything other than some level of random and in no way filled based on player hero choices.
I was talking with a co-woker and he pointed out that you get a lot more gems in map fights than raids… My response, well yes, only the initial board is random, all the rest have player interactions making them un-random. Map fights tend to last longer than raids (for me at least).
One silly inconsequential side note, the initial board is not truly random as it is specified to not have any 3+ color sequences.
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Hey guys…
I really like that I started a long discussion like this and obviously we have a lot of experience in different ways and from my perspective there is a need to adress this somehow to S&G
I still experience a major shift of stones into the color i DONT have in the raid team.
This is why I go even more risky now and i am currently using my titan teams with 3 colors of a kind corresponding to the tanks’ color.
And this efffects in even more extrem situations. in 6 out of 10 fights 4 of my heores are killed before any of my strong color heroes is loaded. But if i get 6 stones in the color i easily win.
So anyhow I still don’t believe that the colors are random as this is too obvious or - i somehow see a point in the randomizer is really really bad - there is some bugs in coding.
It would be great to have a concrete statement by S &G. Does anyone know how to get this?
Sure…read up. Post #36 in this same thread. Stones' colour distribution is NOT random - MASTER Board Conspiracy - #36
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Fair enough on all counts. (I think you’ll find that we also talked through the likely mechanism for avoiding opening board matches, btw, in this very thread.)
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I liked you ideas on this but wanted to add the idea of just storing all the acceptable opening boards and then picking one… That is, until I calculated the number of possible opening boards.
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Agree with you.
Several posts mention the server generates the starting board to prevent “move zero” combo/ cascades.
Pseudo random may be a feature not a bug
One reason you get combo/ cascades of 15+ is because random boards, and pseudo random boards, have matches already ( “move zero” matches ), so when you fill in a large negative section of the current board repeatedly, it tends to keep generating one, or more, auto matches. This is okay if the pseudo randomness is low since they want the endorphin rush/ strategy of trying to trigger combos/ cascades by creating the largest amounts of negative space on the current board to keep you playing. Gryphonkit, my wife, is very good at reading match 3 boards and setting up combo/ cascade several moves in advance.
This would also explain why many starting boards have a dominant color, no matter how you generate it, it is easier to get a locked board by breaking up a board of a solid color with imperfections of the other four color. Or for a truly random board, observer bias remembers all the dominant color starting boards since you are most likely to remember the first and last board of a combat. While a hugely dominant color is unlikely with a truly random starting board, though not exceedingly rare, that is not what is required here as long as the dominant color has a decent pseudo randomness.
Thank you for confirming this.
I suspected as much. Since I prefer summoning from legendary training when I have 15 finished and extra low cost when I have 48 finished. Seems a waste to store them on the server before I remove the finished heroes from the camps.
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Wow, you have incredible self-control—you only look at your TC20 outcomes once a month? That’s like opening your Christmas presents on Epiphany.
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I read your posts with interest, followed by the somewhat highbrow debate with @Brobb that followed. Bernoulli trees. Impressive. I like sharing space with smart people.
Can’t help thinking, however, that there’s are lot of mixing of factors going on in this whole thread. A lot to work through… but let me try stumble along in my plain old simple-thinking way. (I have 3 years of Maths, but still wouldn’t dream of using a Bernoulli tree in anger).
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It doesn’t matter how ‘pure’ the PRNG is… as long as it’s vaguely random. The trick is to make it impractical to reliably predict the next number in sequence. Any RNG has the chance of creating oddball combinations… and the longer you look (i.e. the more data you cover), the more oddball combinations you’ll find. Brobb covered this. I think the ‘pureness’ of the RNG is largely non-relevant, within limits. (e.g. @Brobb: I don’t agree with using digits of Pi for your ‘Randomness’. You are probably less likely to get oddball sequences of long consecutive streaks with that… because there is a fundamental ‘pattern’ inherent in it. Such may well (is likely to) make the possibility of long repeating sequences less likely than properly random data (or even vaguely representative PRNG data). This would make it inappropriate because of its ‘biased’ distribution of data.
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Your reasoning of more 4* and 3* ascension items in April after nothing in march is based on too little data. You’ll probably find that what you got in March was reasonably bad luck… but quite possible to happen, followed by reasonably good luck in April. The system selects AGAINST drawing 4* and 3* (low probability), so you expect a chance of getting no reward, but may be reasonably low. Maybe your ascension rate in April was only slightly higher than normal? Did you compare the number of chests, Titans, Level of Titans, Events, Orbs, etc you pulled in April versus March? A small variance in these factors could make a significant difference to the outcome.
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The opening board cannot be truly Random. It can’t even be close. It needs to be designed to not result in immediate matches when fully produced. (This has been discussed in this thread - I even posit a reasonable algorithm to produce such - above). This will make it more likely than ‘pure’ random to produce some paucity in colours, because depending on the situation it is in, it may be limited in the colours it is ‘allowed’ to select to prevent a match from occurring. This is ENTIRELY SEPARATE to the tiles that are produced to back-fill when you start making matches. These can be more truly random. But even then, as soon as you start matching tiles, all bets are off, because the player is heavily influencing the distribution based on their team set-up and/or play style. If you don’t have yellows on your team, you don’t play those tiles, so they stack up. If you triple on blue, you’re likely to play blue matches as or when you spot them instead of just patiently letting them accrue… and so on. As a result, the player’s actions in causing colour surpluses or droughts is far more of a factor than the RNG.
If you’re writing random number generators that need to be of a high spec, I’d be interested to see the outcome in using them to make opening boards (and then correlating that to doubling or tripling up on a colour… you’ll probably find plenty will produce non-ideal opening and a non-trivial number will produce really RUBBISH openings. The difference is a human only has to experience this a mere HANDFUL of times to make a big deal of it.
If 1 person out of 100 (say) who is reading the forums experiences a run of 3 or 5 of these over a 1 or 2 week period (which isn’t unreasonable to expect) they post, and get a lot of confirmation bias going on by others who remember ‘some’ instance of similar happening to them at some point in time (not necessarily closely related in time to the one the person reported). So a few reasonably isolated instances of it occurring over the WHOLE FORUM READING PLAYER BASE may well make it appear as being far more widespread than what it is.
D a m n… I could go on… but I’m sure the reader (whoever you are) is probably losing the will to live at this point.
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Great post, well thought out.
Before you dump on the value of using part of Pi as a crappy sort of PRNG, however, I’d point out that so far the digits have no discernible pattern to them. (Though in fairness up till last month we had only checked the first 22,459,157,718,361 of them. (That’s about 22 and a half trillion.))
They also include some pretty cool ‘oddball sequences’. Even within our arbitrary first thousand digits, we see six consecutive nines starting at digit 762. (That’s a pretty famous sequence for Pi geeks. [Blushes.])
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D a m n… I regret now only learning the first 50.
My argument was purely on ‘logical’ grounds without grounding of knowledge of pattern analysis done on the digits of Pi. Will be an interesting subject. (I do recall that it has a sequence of 0 to 9 within it at position 17,387,594,880 (Edit… I looked this up after the fact… in an interesting article - here.))
My ‘gut’ is that you’ll get such sequences more often in a random set… but really have absolutely no basis for that. I’ll go with ‘Mahamagoobrie’.
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It helps that I just spent $100 USD on elemental summons chasing Delilah ( which I did not get ) . So I am set for 4* & 5* heroes to level for months.
@Brobb Are you seriously going to tell me that there is no difference between 7.14 and 6.88? I agree there’s no effective difference in the other colors, but for blue tiles, there very definitely is a noteworthy difference.
There was also absolutely no need to be so condescending. You don’t see what I’m pointing out? Fine. I don’t know how, but fine. Just disagree like an adult and move on. Your tactics make it effectively impossible to have an objective discussion with you.
I don’t think you need a degree in statistics to see that averages of 7.14 and 6.88 are functionally equal over a sample of 254 opening boards. Maybe I’m wrong - maybe that’s not blindingly obvious.
I don’t think you need a degree in statistics to see that if your triple colour (purple) shows “no effective difference” (your words) over the sample then any case for non-random boards is totally undermined. Maybe I’m wrong - maybe that’s not blindingly obvious.
I don’t think you need a degree in statistics to read the actual words that @Kahree began his post with:
Actually, there’s no way I’m wrong there - that’s certainly blindingly obvious.
So, first you misinterpreted the blue tile data. (Let’s give you the benefit of the doubt and say you didn’t understand it.) Then you ignored the purple tile data. (By your statement you obviously understood it, so let’s give you the benefit of the doubt and say you… um… forgot it?) And then, to top it all off, you drew from the post precisely the opposite conclusion to that its author plainly stated in the body of the post itself. (Benefit of the doubt… err… I’m struggling here… maybe you had some sort of seizure?)
I’m not suggesting any mendacity is at play here. What we see is just confirmation bias at work. Faced with a post that strongly suggests there is no board bias, you systematically misinterpreted both the data and the text to conclude that it is saying there is some board bias. That is awe inspiring to me. It’s an example that is almost unbllievable in its perfection.
Rest assured, there was nothing condescending in my previous post. For the avoidance of doubt: my tone remains one of joyous amazement that anyone can so blithely embrace confirmation bias. You’re an incredible example.
And you don’t like my “tactics”? What tactics? The tactics of pointing out the incredibly bleeding obvious? I’m not sure you need to be any kind of tactician to do that, and if you find it difficult to have an “objective” discussion when the incredibly bleeding obvious is pointed out, then maybe it’s not really an “objective” discussion that you’re trying to have.
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My intellectual honesty means I need to challenge you on this… really just because it’s interesting.
You are correct in this if you are dealing with a system in which fractions have meaning. The problem is with E&P there isn’t a concept of ‘6.88 tiles on a board’ (obviously). So the interesting thing is that to arrive at an average for Blue of above 7 for 1 scenario and below 7 for the other, means that more boards under the 6.88 scenario must have produced less than the ‘normal’ distribution of tiles for blue on a 35 tile board, while for the above 7 it means that on average more than the ‘normal’ distribution of blues occurred.
This is even more significant for the purples. 1 is only .02 above the normal and the other only .1 below, but the difference is that more boards under the .1 below must have produced 6 or fewer tiles while the +.02 means more boards yield above normal 7 for purple. So even though the mathematical differences are small, it’s the fact that they straddle the ‘watershed’ whole number 7 that (to my mind) makes the difference a bit more significant. (A difference of 7.3 versus 7.1 to my mind is less noteworthy in average game outcome than the ‘smaller’ difference of 7.1 versus 6.9 because the latter straddles the watershed.)
The conspiracy theorists will love this, and say ‘SEE?!?’.
But I do not post this to give them any succour. The sample set is small. Very likely a repeat of the experiment will produce very different colours straddling the watershed number of 7 in the different scenarios.
And consider this: In the 6.88 blue scenario, who is to say that we didn’t have the majority of games opening with 8 blues (say) but a minority of them opening with only 2 (say). This would draw the average down to under 7, but the net effect would be that you would still have been better off with blues for the most part. Really @Kahree should be reporting Median and not Mean for the results to be more meaningful.
So really, it’s an ‘academic’ argument. I’m more than satisfied from Kahree’s post that the distribution of opening tiles is not being ‘tampered with’ by SG.
Model it on a spreadsheet. Correlate opening board colour counts with doubling up of colour (remembering to avoid matches in your opening board of course - algorithm above if you want it). I can almost guarantee you it won’t take you long to find runs of 250 simulations producing correlations of doubled colour having lower instance of that tile on average. (But of course there will be plenty of other 250 simulation sets that show the opposite). The trick is… if I’m trying to ‘prove’ my conspiracy theory, I’ll select the 250 simulation sets that support my theory and disregard the rest (confirmation bias) and show this to the world and say ‘SEE’. (This is why science has peer review by the way). Naturally you’d then conclude that it’s not SG who are causing opening boards to have paucity of your doubled hero colour, but THE VERY UNIVERSE ITSELF. (Rumbles of thunder).
Love this topic. So interesting.
P.S.) Liked your post due to its intellectual content, and not in any way to encourage your (sometimes) callous handling of the person who has the misfortune of being the focus of it.
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You’ve illustrated here why the it’s not so important what side of the ‘threshold’ seven tile expected return the mean falls on. I wouldn’t lose too much sleep over that. I would have been a bit put out if median had been reported instead of mean - the former is less valuable than the latter for our purposes, even over a small sample size (especially when it’s highly likely, even over a sample of only 254 boards, that the median in both instances is 7) but I certainly agree that it would have been nice to have both.
“Callous”? Moi? I thought I was quite sensitive and caring with the poster. I tried to assume the best of them. Do you think I failed?
You don’t know the median is 7… you’d need to see the individual data points to determine it.
So in my (lots of blue ‘8 or more’ and few ‘2 or less’) scenario, the mean would be under 7, but the median would be above 7. This is significant and I think a better representation of the average game ‘outcome’.