3x3: Relative Probabilities Method

There is a statistical flaw in pure chance games like this you can take advantage of to increase your odds if you are patient.

While not as glaring and hugely beneficial to exploit as a true bias or abnormality that skews the outcome to favor certain numbers (such as would be the possible case with a roulette wheel), it can still be useful.

Here's the deal:
The flaw lies in the fact that you can observe winning rings without playing. This is pretty much like counting cards at a blackjack table, only much easier (you know the size of the shoe and the beginning odds). If you were to stand and watch a blackjack table with at least one empty seat and then choose when to sit down and play a hand you would be able to skew the relative odds in your favor for that hand. It's not perfect, but try it in a casino if you need help finding the exit .

In GW no one is going to stop you.
Here is a graph of the per round average wins for each ring in 3x3.


I counted the 3 ring as the one closest to the barker on the podium but that really doesn't matter.

What you do is observe without playing, counting which rings, especially corner rings have had a win (not a 15 ticket but a 25,40,55 ticket win).

Then, after an obvious corner ring which has had less wins then the others becomes known to you, you play it. Stay until a win hits and move off the ring. Rinse and repeat.

Very slow, but if, for example, you play the high probability corner ring relative to the round at the right time you can get the odds of a win from 1:9 to about 1:3 or 1:4, which translates into 30 tickets to play, win of 55 tickets, net gain of 25 tickets per round you do this.

It requires patience... Lots of patience. However, I've had a run of about 6 hours now with a net ticket gain of 8.33 tickets per play.

YMMV,
John

If I'm reading this right, what you're proposing is analagous to watching 50 coin flips land on heads. By your reasoning, the 51st would have a higher probability of landing on tails, right?

However, this is contradictory to the basic premise of probability. Each "toss" or in this case, winning ring, is independent of the last toss, so you can never truly "predict" which ring is going to light up next, unless Anet has a crappy algorithm that you can predict.

It's a noteworthy effort, however, I don't think that just because a ring has flickered less in one round, that it will be more likely to flicker in the next

This is assuming, of course, that the draws are purely random. If they must fulfill a certain quota per round (5 rights, 5 middles, 4 lefts, etc...) then your theory should work.

Also, I'm curious to know how many samples you took for that graph, and what basis you used. Realistically, with a huge amount of samples, the center ring should be highest in sheer number of wins per round. It has a 5/9 chance of winning as opposed to the sides' 4/9 chance and the corners' 3/9 chance.

I took samples for about half an hour or so I wasn't really watching the clock or I would have stopped . I wrote a little tcl/tk app with 9 squares (like a calculator) so I could click the corresponding square for each win on my laptop while playing on my PC. I had something like 3000 plays in my raw tsv output file. I took the arithmetic mode for each ring across my dataset for the graph. I think that's right as opposed to median or mean.

What I'm presuming here is that each round (From when the barker describes the game to when he does so again) is using the same seed value. Each round consists of 20 or 21 plays, I forget.

It seems to hold relatively true, it seemed that in a given round, each corner was getting about 3-4 hits. But maybe not. With card counting you have a mathematical change in probability as the size of the shoe is depleted of certain cards allowing you to select opportune moments. It seemed like this was occurring in the 3x3 though I have only circumstantial evidence to support that, as you said, if it's random then the only relevant sample size is every play from the very first to the last and you'll get the straight ratio of odds as expected.

It really boils down to the algorithm and whether a round is more akin to a shoe of blackjack or not. I think it loops with the barker's spiel about the game (paltry 10 tickets, etc). But I could have gotten lucky. I found that I was getting to the point where I could hit a 55 ticket win within 3 or 4 plays each time and sometimes on the 1st play.

I'll do a larger sample in a bit and a newer graph, which should show if there is an per round bias or not.

- John

This may help, wasted 2 hours the first day it showed up in shing jea. I stopped after I found out that it has 5 levels...

After 479 rounds/hits

rings like this:
1--2--3
4--5--6
7--8--9

Full hits that the rings got: the full payout:
1: 46
2: 56
3: 48
4: 68
5: 62
6: 63
7: 51
8: 53
9: 32

Attempt to make a graphical showthingy:

46 -- 56 -- 48
68 -- 62 -- 63
51 -- 53 -- 32

To break even, you should have been in a circle that had more than 53 hits. Only 4 would give a profit. 5 of them gave a loss.

I have reason to believe that it is not completely 1/9 chance random.

Instead of doing what you seemed to do, which seems to be standing there where there were less hits, I went where people were winning.
I actually gained tickets that way.

What if it isn't random? What if there are patterns? What if full hits are triggered by something?

I noticed that the winning rings were populated by talkative people and that the losing rings were the home of those who were truly afk.

During the time that I kept track of the hits, I noticed that no ring loses only 1 time in a row. It loses or wins at least 2 times in a row. I've seen times where the same ring won 4 times, one time even 5 times in a row.

This all could be coincidence. But ot could be that there is not some randomising algorithm that is used here. It could be a game of patterns or triggers with rewards for the actives and punishments for the inactives (from what I've seen).

Anet could have a good reason for this.
The rich can afford to go afk and sink their money. But the poor will try a few times and then abandon it. But if they notice that they're gaining, they'll try to stick around longer, gain more tickets... = gold.
So in a way, these games could be designed to take from the rich and give to the poor.

But all I have is 479 hits and some things I remember that I saw. I still have no proof for anything. Still, the hits may be of help to you or something, dunno X.x

Your numbers are all perfectly in line with a fair game, given how many samples you have. As for you noticing that squares are losers twice or more in a row, that's typcially to be expected since that's mainly how the probabilities of winning are. For example, corner squares lose twice for every one win on average. So obviously, what you're noticing is just what's usually expected.

Until someone records like 10,000 outcomes accurately and notices a statistically relevant discrepancy, this game can only be considered perfectly fair.

And everything that Lasareth said is true, you're presuming that the probability will shift toward those rings which haven't occurred in a while which is a common fallacy and the reason why a lot of people lose money gambling I think, though, that the OP's graph is meant to show actually WINNING though, not "not losing" if you get what I mean; he's recording which ring was picked but not also which rings were adjacent.

Nothing that a computer does is random. Computers use psuedo random number generators to make "random" numbers. If implemented well, it should be almost as good as random (it should not be too hard if you want 1/9 chance of random). However, in computers, there are many implementations of psuedo random number generators (PRNG) that are not very random. For example, some computer security people analyze how viruses spread, because many viruses select IP addresses at "random" and attempts to infect them. Many times, the virus cannot generate certain ranges of IP addresses or end up hitting certain ranges much more often, because it's not easy to generate truely random numbers from 1 to 4 billion.

In normal probability, if you flip a coin 100 times, and you get 100 tails, the next coin flip isn't more likely to be heads. It's independent of the previous flips, it's still 50% chance heads or 50% chance tails. However, in computers, there is always some correlation. The numbers are being produced from a written algorithm. The correlation may be so small that we can barely get any information from it, or it can be a strong correlation that we can keep track of and actually win more.

Considering that programmers work long hours and debugging well takes forever, it's definitely possible that the PRNG is not implemented to be very random. It's a minor detail, and it may be "good enough" and the ANET released it (not that it is a bad thing, if they fully test everything, the dragon festival update would never come out). Note that many patches have bugs in them, such as the pet deleting and face changing bug on the Dragon Festival update. So, yeah, it is quite possible that the "randomness" is not perfectly random.

and all probability says that 6 full houses in a row is statistically impossible but I couldn't get out of Texas Holdem that night to save my life! (true story and I certainly wasn't cheating =P)

I notice that every couple of hours certain rings get more attention than others, not just total winning but the semi winning as well. I went in with about 2000 tickets and within 2hrs had no tickets... *shrugs* And yes we had that many losses in a row... Never had I been on such a sucky circle in the game lol.

Yeah but they're not supposed to lose twice for every win =/
They're supposed to lose 8 times for every win. =X

edit: also, in my results, the corners are the only ones who lose money, the sides and center gain it X.x

I tried thsi game a couple times and it seems like there is a pattern of some kind. It seems like for one whole round, there would be a certain circle that makes a lot of tikets (the first time, i just went to the center circle with only 10 tickets and i had 100 by the end of the round), then the next round, that same circle loses a ton (by the end of the next round i literally had 0 tickets, yet i stayed in the center). After that i started changing cirlces every 4 picks or so. Also, it seemed to me that usually, once it did one corner, then it would usually do the other corners with 1 or 2 other circle in between, then it would do the other 4 outer ones, once again with 1 or 2 other circles in between.

For example (using Don Zardeone's grid thingy)

1--2--3
4--5--6
7--8--9

if it did 1, then it would do somthing like 3, 9, 7, 5
Then it would do 8, 2, 6, 9, 4
then it would go back to the corners, and then do the other 4, and keep doing a similar patern.

Using this, i would step back and look at which ones were used so far and then go on the one that wasn't.
For example, if it alredy did 2, 4, and 6 recently, then i would stand on 8 and within a round or 2, usually i would get tickets for the one i was standing on. It seemed like i was getting tickets, but after a while, i got bored of this and decided to stop.

BTW I only did the ticket circle game on the first day of the event and i spent like 10 minutes after losing those 100 tickets i won to figure this out. It might be more random now and not nearly as predictable so don't get mad at me if this doesnt work, but it DID SEEM to work for me, very slowly tho, untill i got bored of the ticket game and went off to the dragon arena. Maybe I just happened to get lucky those times but o well. Hopefully someone can use this and maybe figure out a way to get tickets every game or somthin (assuming that is possible )

O and also, it seemed taht the center, which had a ton of afk people, almost never got the tickets, at least compared to the other rings. And it seemed like the rings with very few people, but the people were acually talking, instead of being afk, would get teh tickets more often.

I hope this can help someone that wants to make profit of the tickets like i do, or at least maybe give them ideas that help them. If not, o well, I found something interesting to do (at least untill it started reminding me of school somehow, which made it get boring) and i tried. Thats all that matters for me, somthin to do, and i tried.

If you mean that just by standing in the center and sides, then it didnt work for me. All that happens is I either A) win a lot, then suddenly lose all my tickets, or B) lose all my tickets right away. I dont think just standin in one circle wins anything in the long run...

Final Verdict:

I went back and used my hacked together program to record results from about 5000 plays. 5016 plays to be exact. Each round consists of 19 plays and takes about 3 minutes. I spent about 13.5 hours gathering this. While probably not statistically as accurate as 10k or more would have been... The results were pretty damning. After 264 rounds, I took the frequency of each winning ring and calculated that as a ratio against the total number of plays.

If everything is purely random the probability of a ring winning is 1:9, 1/9 or .1111 (with a little bar over the ones to indicate it's repeating).

The resulting ratios from the observations were from .08 to .13. No specific type of ring was favored (corner, side, center). I also observed no noticeable difference among people who were actively chatting, moving or otherwise as to winnings.

I think these results are consistent with a decently random game of chance.
The only way to win at this game is to be lucky. My original post was speculating along the lines of the gambler's fallacy and indeed completely contrary to probability & statistics (though very tempting) and based on erroneous assumptions regarding the underlying algorithm.

The basis for the 3x3 ring game (and most likely the others as well) is a decent PRNG with a sufficient level of entropy to be able to avoid any noticeable bias.

If anyone wants to repeat the experiment:

You will want/need (I did it on Linux but I've done this list for Windows, all apps are equivalent or Windows versions of the same app used):
Vim http://www.vim.org
MS Excel (I used gnumeric)
ActiveState Perl (I used plain old Perl)
+ TK module: http://www.activestate.com
RLPlot: http://rlplot.sourceforge.net/

And here's the ugly script for recording your data with (modified to a Windows ActiveState location of perl):

---Cut---

#!C:\Perl\bin\perl.exe
use Tk;

open(RESULTS, "> 3x3-results.csv");
print RESULTS "Play, Winning Ring\n";
my $mw = MainWindow->new;
$mw->title("3x3 Recorder");
$mw->Button(-text=> "1", -command => sub { $plays++; print RESULTS$plays.","."1\n"; })->grid(-row => 0, -column => 0, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "2", -command => sub { $plays++; print RESULTS$plays.","."2\n"; })->grid(-row => 0, -column => 1, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "3", -command => sub { $plays++; print RESULTS$plays.","."3\n"; })->grid(-row => 0, -column => 2, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "4", -command => sub { $plays++; print RESULTS$plays.","."4\n"; })->grid(-row => 1, -column => 0, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "5", -command => sub { $plays++; print RESULTS$plays.","."5\n"; })->grid(-row => 1, -column => 1, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "6", -command => sub { $plays++; print RESULTS$plays.","."6\n"; })->grid(-row => 1, -column => 2, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "7", -command => sub { $plays++; print RESULTS$plays.","."7\n"; })->grid(-row => 2, -column => 0, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "8", -command => sub { $plays++; print RESULTS$plays.","."8\n"; })->grid(-row => 2, -column => 1, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "9", -command => sub { $plays++; print RESULTS$plays.","."9\n"; })->grid(-row => 2, -column => 2, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Button(-text=> "Done", -command => sub { close (RESULTS); exit })->grid(-row => 3, -column => 0, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Label(-text=>"Plays:")->grid(-row => 3, -column => 1, -ipadx => 3, -padx => 4, -pady => 4);
$mw->Label(-textvariable=>\$plays)->grid(-row => 3, -column => 2, -ipadx => 3, -padx => 4, -pady => 4);
MainLoop;

---Cut---

That was a fun timesink. Do check out RLPlot if you want a easy to use graphing tool that's free and multiplatform.

- John

Whoops. Double posted.