Devourer Bias

[kev]

I've had a similar experience regularly enough that it seems unlikely to be coincidence.  In my gravity/aether deck I often have more aether than gravity and pests seem to take disproportionately from gravity.  I've considered playing three phase shields in one turn to get aether down to zero so that gravity can build.

[danieldubois]

While it is not in gameplay, in the bazaar/deck construction, Aether is the last color in the list.  If internally Aether is an edge condition, I would check the code for some potential off-by-one bugs when it picks random numbers (such that it's effectively picking 1-11 instead of 1-12).

[zanzarino]

This happens because devourers randomly pick an element - not a random quantum.

That means that if you have two types of quanta stored:
50 aether quanta
1 fire quantum

There is a 50% chance they will steal the fire quantum. Even if it is only 1 quantum.

If they steal aether quanta you are not even going to notice; that's why it feels like they are picking on your mark element: it is often used to "splash" quanta and devourers will often keep that quanta storage at zero.

Intended.

[danieldubois]

To a casual observer with experience in studying human psychology, what you have hypothesized sounds very probable, i.e., that this is a cognitive bias.  People are intuitively terrible with randomness, the brains sees patterns where one does not exist, occum's razor, etc.  If I were programmer and people came to me with these complaints, I would roll my eyes and just assume exactly what you have.

That said, anyone who plays fractal/hope versus Decay can easily see something is amiss.

I took the trouble to document my latest game of that matchup just now.  It was very disappointing because Decay filled up his board with RoL tokens, and never put more than 2 devourers into play, but it was still results I expected to see.  BTW, usage of that word is notable.  To be random means it defies predictability.

Column 1 is which turn it is.
Column 2 is the aether quanta I had at the end of the turn before clicking done, and the amount of aether quanta I gained from end of turn, separated by an arrow.
Column 3 is the light quanta I had at the end of the turn before clicking done, and the amount of light quanta I gained from end of turn, separated by an arrow.
Column 4 is the number of devourers Decay had at the end of his turn.
Column 5 is the aether quanta I had at the end of Decay's turn, and the amount of aether quanta I had after he did his end of turn drain effects, separated by an arrow.
Column 6 is the light quanta I had at the end of Decay's turn, and the amount of light quanta I had after he did his end of turn drain effects, separated by an arrow.


turn   aether+gain(b->e)   white+gain(b->e)   devos   aether-loss(b->e)   white-loss(b->e)
1      3->8            0->1            1      8->8            1->0         
2      0->5            0->10            1      1->0            10->10
3      1->6            10->20            2      6->6            20->18
4      6->11            18->27            2      11->10            27->26
5      10->15            26->35            2      15->13            35->35
6      13->18            27->35            2      18->18            35->33
7      0->5            33->48            2      5->5            48->46
8      5->10            46->60            2      10->9            60->59
9      6->10            59->72            2      10->10            72->70
10      10->14            70->83            2      14->14            83->81
11      14->18            81->94            2      18->17            94->93
12      17->21            93->106            2      21->21            106->104
13      21->25            104->118         2      25->25            118->116
14      25->29            116->129         2      29->28            129->128
15      28->32            128->140         2      32->32            140->138
16      32->36            138->149         2      36->36            149->147
17      36->40            147->157         2      40->39            157->156

So, in this game 8 aether quanta was drained.  And 24 light quanta was drained.

I'm not well-versed enough in confidence intervals and standard deviation to conclusively say how wrong this is, but I believe it to be statistically significant.

In my experience, this was actually slightly atypical.  Normally the ratio of light mana drained goes much larger.  In games where more devourers get into play, I will commonly see 5-1, 6-0, etc. turns.  I don't see vice-versa.  I think with a bigger sample size, the results would be even more glaring.

If I get a chance and I'm at home, and this matchup comes up, I'll pull up camtasia and stick a video on youtube, and I expect to see similar bias.

PS: For the sake of science I probably should have held off on my RoL/Fractal until he did his first fractal, but hey, I wanted to win!

[dragonhuman]

I had a ton of quantum in each pool and the enemy had 7 devourers (or whatever a row is)
they didn't take a single point of time quantum from me (which was my mark) which suxed cause I had more time than I needed and could've used the other quantums

[Kurohami]

It's weird how I generates 7 life quanta every turn and they get sucked dry every turn while my aether quanta is almost left alone to pile up although I have a lot less aether pillar. The aether quanta was only needed for fractal while the life quanta is for playing stuff, but the devourers only like life quanta, and I don't get to play anything.

[danieldubois]

I did it again to drive the point home, and because I have more time than sense:

turn   aether+gain(b->e)   white+gain(b->e)   devos   aether-loss(b->e)   white-loss(b->e)
1      1->5            0->3            0      5->5            3->3
2      5->9                3->6                0      9->9            6->6  he kills all three of my RoLs - Oops!
3      9->13            6->6            1      13->13            6->5
4      13->17            5->5            1      17->16            5->5  got another RoL, but I'm waiting for him to fractal 1st, for science
5      16->20            5->5            1      20->20            5->4
6      20->24            4->4            2      24->23            4->3
7      0->4            3->8            2      4->4            8->6  bah, not waiting any longer
8      4->8            6->10            3      8->8            10->7
9      0->4            7->14            4      4->4            14->10
10      2->7            2->8            4      7->5            8->6
11      6->12            6->12            4      12->11            12->9
12      0->6            9->20            6      6->5            20->15
13      5->11            2->14            6      11->8            14->11
14      8->14            12->25            6      14->11            25->22
15      0->6            9->22            6      6->3            22->18  7 is getting drained now?!?
16      3->9            5->18            6      9->7            18->13  off-screen devourer?!?
17      7->13            0->13            6      13->12            13->7
18      0->6            7->22            6      6->4            22->17  trading in last fractal for two rols, since my 13 white per turn is more like 8
19      4->10            4->18            6      10->7            18->14
20      8->15            1->15            6      15->12            15->11
21      13->21            11->25            6      21->19            25->20
22      19->26            0->13            6      26->22            13->10  (I went for thudnerbolt/miracle here, instead of dragon #5, 3 misses on dusk /sad)
23      23->32            10->22            6      32->29            22->18   (crap, 3 misses again, I'm going to get decked)
24      29->38              5->17?      Whew, no super Dusk with 0 cards left in deck!

So 35 aether drained, 66 light drained.  Again, I'm a bit suprised it was that "close".  Apparently, I was under the influence of some cognative bias myself, more inclined to notice the laege imbalanced 6:0 turns, and less inclined to notice the common 3:3, despite being aware of the tendency to do just that.

Nevertheless, notice as in my previous trial, aether "won" over life (was drained harder) precisely twice out of >17 turns, whereas light 24 times.  That's like flipping a coin 26 times and only seeing two heads.  Or, if you prefer to look at each individual drain event, rather than on a per turn basis (which is probably a better idea as this gives a better sample size), it was 43 versus 88.

Wikipedia has an article on checking whether a coin is fair (http://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair).  We'd have to plot the curve of

f(r) = 131! / (43!*88!) * r^43 * (1-r)^88

between r's of .45 or .55, and then find the area under it.  I can't figure out how to do that, but a rough guess would be to assume a straight line between f(.45) and f(.55), and get the area of the trapezoid

Using http://www.math.sc.edu/cgi-bin/sumcgi/calculator.pl:
f(0.45) = 131! / (43!*88!) * r^43 * (1-r)^88 = fac(131) / (fac(43)*fac(88)) * 0.45^43 * 0.55^88 = 0.00131392106344201
f(0.55) = 131! / (43!*88!) * r^43 * (1-r)^88 = fac(131) / (fac(43)*fac(88)) * 0.55^43 * 0.45^88 = 1.57329936547103e-07 = 0.000000157329936547103

A = 1/2 * h * (a+b)
A = 1/2 * (0.55-0.45) * (f(0.45)+f(0.55))
A = 0.5 * 0.1 * (0.001314) = 0.0000657

Odds of this being a fair coin are about 0.00657 percent.  Better than one in a million, but not by much!

PS:   I win a Pest and a Drain.

[danieldubois]

Game #3: 15 aether drained, 39 light drained.

[Artois]

Game #3: 15 aether drained, 39 light drained.

Yup there does appear to be a bias.  I have experienced the similar, with Fractal/Hope v. Devourer.

[Jumbalumba]

I just wanted to post that 'r' that danieldubois couldn't understand what is is actually the probability of getting a certain outcome. Not sure which it is in this case, i.e., I'm not sure if r is actually the probability of taking aether quanta or light quanta.

131! is too big and I can't be bothered at the moment to find out where to calculate it.

[Demagog]

131! = 847158069087882051098456875815279568163352087665474498775849754305766436915303927682164623187034167333264599970492141556534816949699515865660644961729169613882287309922474300878212776434073600000000000000000000000000000000

I happen to be one of those people that can calculate extremely large numbers in a very short amount of time.





Just kidding. http://world.std.com/~reinhold/BigNumCalc.html

[danieldubois]

danieldubois couldn't understand

Excuse me?  I said I couldn't figure out how to get the area under the curve, i.e. the integral of that function over a range.  I never said I didn't "understand" anything.