Tervigon Preggo Goodness

[thehorrorchord]

had a game the other day, and my tervigon consistently spawned out 11-12 terms a turn for a whopping 46 termys by end game. pretty good. luckily they were all getting cut down from dark eldar fire, so i had enough models each turn.

anyone else have any epic tervigon spawn numbers?

[wisdomseyes1]

3 and 18

3 on the last turn of the game. 18 on the last turn of the game. I can't remember any of my games where I spawned more than once.

[1b2a]

I have had the rumored 6 5 4 spawn one time on turn one and slightly less the next two turns but never anything better.

[osirisjdu]

told my friend first time i used it that the best i could get and not run out was 15 with 4-5-6. rolled it first turn.
mentioned the odds of that happening again. rolled 4-5-6
said odds are i should run out next turn. 6-6-6.
he hates the thing now.

[lostminds]

3 tervigons in one game spawned 15 each per turn for 5 turns... and to top it all off it was an objective game.

Usually they stop spawning on 2nd turn for me...

[coredump]

Jul 28, 2012 19:05:31 GMT osirisjdu said:

said odds are i should run out next turn. .

[anal retentive math geek = ON]

Actually the odds are the same every turn. the odds for making it another turn were no worse on turn 3 then on turn 1. Like flipping a coin. If you flip and get 5 heads in a row, that 6th flip is till 50-50.

[=OFF]

(ah, who am I kidding, I can never really turn it off.)

[maine]

I ran the math on Tervigons recently. If we assume that >5 spawns is counted as 5 spawns, and the Tervigons survive 5+ turns, the odds are as such:

1 Tervigon:

Spawns	Exactly	Equal or More
1	44%	100%
2	25%	56%
3	14%	31%
4	8%	17%
5+	9%	9%

1 Tervigon will spawn, on average, 2.2 broods/game, of average 11 Gaunts each.

2 Tervigons, the math gets a bit trickier, but it can be done; here we assume >10 is as good as 10

Spawns	Exactly	Equal or More
2	20%	100%
3	22%	80%
4	18%	58%
5	14%	40%
6	9%	26%
7	9%	17%
8	4%	8%
9	2%	4%
10+	2%	2%

2 Tervigons will spawn an average of 4.4 broods/game, of avergae 11 gaunts each.

3 Tervigons will spawn an average o 6.5 broods/game.

Coredump: If you really want to get pedantic, perhaps you should go into the a difference between discrete random variables and continuous random variables. There is a difference between 'likelihood' and 'probability'. The probability of any one roll never changes, but the likelihood of a continuous streak reduces with each subsequent roll. It seems to me you know people are talking about likelihood, and in reality are being critical of their choice of grammar...

Edit: My original math used used some rounded numbers, and the original Tervigon odds were slightly off (was using .42 instead of .4444); I increased the precision and re-ran (to 4 total decimal points).

[acmemyst]

Maine: I've recently been doing the same, and couldn't quite figure out the variance on the total number of Gants spawned for one Tervigon over the course of a game (i.e., all the information for the complete distribution). Any suggestions?

As an aside, the thing about continuous streaks in terms of gaming is of course that "whatever happened, happened". Which is to say, it is more useful to consider the odds of getting any particular roll on your next throw, and this is obviously not influenced by what happened before. That being said, I very much had the urge to post the same remark as coredump on my initial reading osirisjdu's post

[Edit] Also, I'm not quite sure if your math is correct, actually. I got the same figure (.42) on the odds that you run dry after one roll, when solving it analytically. However, bruteforcing the numbers through code gave me .44, and I can't figure out what I'm doing wrong in either case. Just throwing that out there.

[maine]

acmemyst: I had a bad input value (I had .42 originally, I'm not sure where I got that value). Re-ran my program with .44, and updated the values above, also using more precision on the input values.

I wrote up a Python program to calculate the number of spawns using recursive functions.

import math

numTervigons = 4

tervigonStopOdds = .4444
tervigonContinueOdds = 1.0 - tervigonStopOdds

def pmf(k,n): return math.factorial(n) / (math.factorial(k) * math.factorial(n-k))
def pm(k,n,p): return pmf(k,n) * math.pow(p,k) * math.pow(1.0-p,n-k)

numSpawns = {}
numSpawnsOccurences = {}
def Turn(turnNum, spawns, odds, numProducing):
  if numProducing == 0 or turnNum > 6:
    numSpawns[spawns] = numSpawns.get(spawns, 0) + odds
    numSpawnsOccurences[spawns] = numSpawnsOccurences.get(spawns, 0) + 1
  else:
    spawns += numProducing
    for i in range(numProducing + 1):
      newOdds = odds * pm(numProducing - i, numProducing, tervigonContinueOdds)
      Turn(turnNum + 1, spawns, newOdds, numProducing - i)

Turn(1, 0, 1.0, numTervigons)

for spawns,odds in numSpawns.iteritems():
  print "%d = %f" % (spawns,odds)

sum = 0
for spawns,odds in numSpawns.iteritems():
  sum += spawns * odds

print "Average result = %f" % sum

totalCount = 0.0
sum = 0.0
for spawns,count in numSpawnsOccurences.iteritems():
  sum += spawns * count
  totalCount += count

mean = sum / totalCount

sumDiffSq = 0
for spawns,count in numSpawnsOccurences.iteritems():
  sumDiffSq += math.pow(spawns - mean, 2) * count

popStdDev = math.sqrt(sumDiffSq / totalCount)

print "StdDev = %f" % (popStdDev)

Edit: Updated using probability mass rather than manually computed odds, supports unlimited numbers of Tervigons.

Fun fact: 5 Tervigons can produce an average of 10.9 broods in 6 turns.

[acmemyst]

Heh, I was just about to comment on those hardcoded magic numbers

Also.. Eeeewww, Python. Needs moar C/C++!!1!
Seriously though, looks good

Anyway, any thoughts on how to compute the variance/standard deviations for this?

[Major Chrispy]

AAARGH!!! THE MATH! IT BURNS!!!

Seriously looking at it just gave me a headache o.o''

[maine]

Jul 28, 2012 22:16:27 GMT acmemyst said:

Heh, I was just about to comment on those hardcoded magic numbers

Also.. Eeeewww, Python. Needs moar C/C++!!1!
Seriously though, looks good

Anyway, any thoughts on how to compute the variance/standard deviations for this?

Languages are tools, and the more tools one has in their toolchest, the better they will be at their job. Python is excellent for rapid prototyping and scripts. The majority of my work I do in C++, but Python is very handy for short one-offs and small tools.

I've added computation of the standard deviation to the post with the source.

Tervigons	Avg Broods	StdDev
1	2.18	1.81
2	4.37	2.71
3	6.55	3.5
4	8.77	4.24

That was a useful exercise, and helps give context to the previous data. Averages can be misleading. 1 standard deviation means that while 2 Tervigons will produce an average of 4.4 broods/game, there is a reasonable chance they will produce many more broods. If you go by the previous chart, 1 in 4 games should see 6 broods produced.

[acmemyst]

Jul 28, 2012 23:22:03 GMT maine said:

Jul 28, 2012 22:16:27 GMT acmemyst said:

Heh, I was just about to comment on those hardcoded magic numbers

Also.. Eeeewww, Python. Needs moar C/C++!!1!
Seriously though, looks good

Anyway, any thoughts on how to compute the variance/standard deviations for this?

Languages are tools, and the more tools one has in their toolchest, the better they will be at their job. Python is excellent for rapid prototyping and scripts. The majority of my work I do in C++, but Python is very handy for short one-offs and small tools.

I know, and couldn't agree more. I'm aware that this is exactly one of Python's strong points. It was just meant as banter; I have this ongoing campaign of praising C/C++ to heaven and back, even when context would say I'm wrong.

That was a useful exercise, and helps give context to the previous data. Averages can be misleading. 1 standard deviation means that while 2 Tervigons will produce an average of 4.4 broods/game, there is a reasonable chance they will produce many more broods. If you go by the previous chart, 1 in 4 games should see 6 broods produced.

Yeah, that's why I was inquiring. If it wasn't almost 2 AM over here I'd do this myself (blatantly stealing your code), but any chance you could make a table of the variance/std on the average number of Gants also? Would appear to be useful to figure out how much models you'd reasonably need given the number of Tervigons in your collection.

PS. It seems that your code never fills numSpawnsOccurences, but that's probably just a slight copy/paste slip-up?

PPS. Welcome to the Hive

[maine]

Jul 28, 2012 23:46:29 GMT acmemyst said:

PS. It seems that your code never fills numSpawnsOccurences, but that's probably just a slight copy/paste slip-up?

You are correct, just a copy/paste issue. Fixed.

Regarding 3d6 Standard Deviation:

en.wikipedia.org/wiki/File:Roll_of_3d6.svg

Mean = 10.5, StdDev = 2.958.

While these numbers are useful for determining a 'most likely maximal number of Gaunts needed', the one thing we can't take into consideration is casualty loss. This is so variable I don't think it's possible to factor in.

Anyway, asuming (Mean+StdDev(1)) broods of (Mean+StdDev(1)) Termagants (13.458) produced:

(Mean) is using the Mean Broods/Tervigon * Mean Termagants/Brood (10.5)
(Mean+StdDev) is using Mean+StdDev Broods/Tervigon * Mean+StdDev Termagants/Brood (13.458)

Tervigons	Termagants (Mean)	Termagants (Mean+StdDev)
1	23	54
2	46	95
3	69	135
4	92	175

A fairly clear progression here:
Mean = 23 Termagants per Tervigon
Mean+StdDev = Start with 54, add ~40 per Tervigon.

....

We can math it out all day, but progression is fairly linear: 2 Tervigons will produce, on average, twice as many Gaunt broods as 1. 3 will produce 3x as many, and so on.

Unless you intend to never lose a Termagant to enemy fire, you are probably safe bringing 30 Termagants for your first Tervigon, and 20 more for each additional Tervigon.

... and all our math has seriously deviated from the original point of the thread!

[coredump]

Someone should have a link to the last time we did this. Would let you compare results.

IIRC, the mean per Terv was about 23 and the median was about 17.

Which was funny, since 17ish is a local minima...