Termagants per Tervigon?

[coredump]

Vectron's math is spot on for average(mean) results. (As you can tell, because it matches what I posted earlier )

Ginger, not really sure what you are trying to say about his approach, so I can't really help you work that out.

The thing to be careful of is that this is *not* a standard (or 'normal') distribution.

The average(mean) is about 23, but that *doesn't* mean that half the time you will get more, and half the time less.
In this case, half the time you will get less than 17 gaunts, and half the time more than 17 gaunts. (This makes 17 the Average(median) ) But because on a few, unusual occasions, you can get 50-60 guants... it brings the overall Average(mean) up to 23ish.


So, when you ask 'how many do I need?', the only way to really answer that is "It depends, how often is it okay if you run out?"

If you want to "never ever ever" run out, then you will need 108 spawning gaunts per tervigon. (plus whatever starts on the board)

But if you are willing to run out 'about half of the time', then you only need 17 gaunts.
I don't remember the numbers exactly, but I believe 25-30 guants puts you in the 'safe' zone 75-80% of the time.

But there are even more mitigating circumstances....
Are you willing to assume some gaunts will die and you can recycle them?
Are you willing to assume some Tervs will die before they are done spawning gaunts?
Will you be running more than 1 terv? more than 2? etc
Are you okay with skipping a turn or two of spawning if needed?

All of these things will let you get away with fewer Spawning gaunts.

[WestRider]

Aug 12, 2013 12:54:00 GMT coredump said:

The spawning math was way mathhammered back with the codex came out. You're assumptions are off, but your end result should be fairly safe.

You have about a 44% chance of getting a double on any particular roll, so you should not get 3 turns in half of your games. But like I said, the mean is 23, the median is only 17; that means you will only get more than 23 about (guesstimating..) about 33% of the time. Extrapolating... I would say more than 30 maybe 10% of the time.

If you want to see the actual numbers, maybe someone here has them bookmarked.

I had it bookmarked, but when the Tactics board was reorganized, it broke the link and I wasn't able to find it again.

[gingerwerewolf]

Aug 13, 2013 14:23:10 GMT coredump said:

Vectron's math is spot on for average(mean) results. (As you can tell, because it matches what I posted earlier )

Ginger, not really sure what you are trying to say about his approach, so I can't really help you work that out.

The thing to be careful of is that this is *not* a standard (or 'normal') distribution.

The average(mean) is about 23, but that *doesn't* mean that half the time you will get more, and half the time less.
In this case, half the time you will get less than 17 gaunts, and half the time more than 17 gaunts. (This makes 17 the Average(median) ) But because on a few, unusual occasions, you can get 50-60 guants... it brings the overall Average(mean) up to 23ish.


So, when you ask 'how many do I need?', the only way to really answer that is "It depends, how often is it okay if you run out?"

If you want to "never ever ever" run out, then you will need 108 spawning gaunts per tervigon. (plus whatever starts on the board)

But if you are willing to run out 'about half of the time', then you only need 17 gaunts.
I don't remember the numbers exactly, but I believe 25-30 guants puts you in the 'safe' zone 75-80% of the time.

But there are even more mitigating circumstances....
Are you willing to assume some gaunts will die and you can recycle them?
Are you willing to assume some Tervs will die before they are done spawning gaunts?
Will you be running more than 1 terv? more than 2? etc
Are you okay with skipping a turn or two of spawning if needed?

All of these things will let you get away with fewer Spawning gaunts.

Ok first of all, Probability in Maths is not my strongpoint, but Ive got a pretty good maths head on my shoulders - so if Im wrong, and you can explain why, please do!

The point I was trying to make is that the chance of not rolling in the next turn is decided this turn. Thus when calculating the chance of how many critters you roll this turn, if you roll at all, then you have obviously passed the previous turns requirements.

What it looked like to me, was that the amount that each turn was being reduced by was 44% of 44%. Making it far lower than I would have expected.

Now either I have been verylucky or my my maths is off, (Probably a bit of both) but Ive been spawning on average 10 Gaunts per Tervigon per turn for about 50% of the turns in my battles. My main opponent almost insists I keep records of this, as he is sure that the mechanic is overpowered and unfair due to him then having to fight off hundreds of points worth of "Free" troops.

If there isnt space here, can someone direct me to the appropriate part of the web for assistance?

Thanks guys.

(And anyway, at the very least I if Im wrong I have more Termagants than I probably need not less!)

[Davor]

This is giving me a chuckle. As I said in another thread, if people are so good with Mathhammer, what the hell are you guys not making money of your mathhammer skills? Go to a casino, race track or what ever and start making money. Some thread in DakkaDakka some guys are arguing saying how good they are and here they are playing with plastic toy soldiers instead of becoming rich LOL.

[coredump]

Davor, I don't know how you are equating being good at math/mathhammer as being able to 'beat' the casinos.

In fact, one of the reasons I *don't* go to casinos is because I am good at Math. See, the casino is also good at math, and they also get to make the rules. Same reason I don't play scratch off lottery tickets.


Ginger:
First, do you understand the difference above when I described Average (mean)(median)(Mode)?

When figuring Average(mean), it is fairly straight forward.
The main thing to realize is there is about a 44% chance of rolling doubles, and thus about a 56% chance you will get to keep going. (It is actually 44.x% and 55.y%, but whatever)

Turn1:
There is a 100% chance that you get to roll on turn 1, and you will get (on average) 10.5 gaunts

Turn 2:
There is a 44% chance that you will already be done, thus a 56% chance that you will get to roll again on turn 2. When you roll again, you get another 10.5 gaunts. *BUT*, this only happens 56% of the time. So to find what you get on average, you will get 56% of 10.5, or an additional 5.88 gaunts.

Turn 3:
You only make it to turn 2 56% of the time, and *of those*, you will only make it to turn 3 56% of the time. So you will only make it to turn 3 (.56*.56=) 31.3% of the time. When you roll on turn 3, you get another 10.5 gaunts, but you only get those 31.3% of the time, so on average, you get an additional 3.29 gaunts.

Turn 4:
Again, you only have a 17.5% chance of getting to roll turn 4. (100% * 56% * 56% * 56% = 17.5%) So, on average, you get an additional (10.5 * 17.5% =) 1.84 guants

Turn 5:
Only a 9.8% chance of getting to roll on turn 5, so only (9.8% * 10.5 =) 1.04 gaunts.

Add this all together, and you get 10.5+5.88+3.29+1.84+1.04 = 22.5 guants per game.


Now, you will obviously never get 1.04 guants on turn 5; you will get 10.5 gaunts; but that only happens once every 10 games.
If you are getting 10 gaunts once every 10 games; that is an average(mean) of getting 1 gaunt per game.
Does that make more sense?



And yes, if you are getting 3 turns of spawning in half of your games, you are way ahead of the expectation. You should be getting passed turn 2 only 30% of the time.
It is almost as likely (about 23%) that you get 10 or fewer gaunts in a game.

[karkacabra]

Aug 14, 2013 8:27:22 GMT gingerwerewolf said:

Ok first of all, Probability in Maths is not my strongpoint, but Ive got a pretty good maths head on my shoulders - so if Im wrong, and you can explain why, please do!

The point I was trying to make is that the chance of not rolling in the next turn is decided this turn. Thus when calculating the chance of how many critters you roll this turn, if you roll at all, then you have obviously passed the previous turns requirements.

What it looked like to me, was that the amount that each turn was being reduced by was 44% of 44%. Making it far lower than I would have expected.

For calculating the number spawned any give turn you're right. But when calculating the average number spawned over several turns of attempted spawning, the probability that one of those spawns will exhaust the Tervigon is a factor in the number of total gants you can expect to spawn.

So if I'll spawn an average of 10-11 gants per turn with a 44% chance to exhaust, then for two turns of attempted spawning, I'll average 16-17 over both turns, because there was a 44% chance that the first spawn exhausted the tervigon and prevented the second spawn entirely. For three turns of attempted spawning, the average is 19-20, because there's a good chance that that either the first or second spawn will exhaust, making the chances that I'll even get a 3rd spawn fairly low, and thus lowering how many you can expect to get out of a third spawn in any given game.

[EDIT] Aaaand coredump beat me to it

That's what I get for idling on a page before responding.

[nameless]

When that calc was completed, it wasn't actually done theoretically, it was done by writing a MatLab code and running 10000 (IIRC) trials (which should be high enough to get theoretical results) and the numbers that coredump is reporting was what the results said.

That thread has gone missing, but you can see a newer version here (with very slightly different results):
thetyranidhive.proboards.com/thread/39869

[coredump]

Right, because while I can find the average(mean) mathematically, I don't know how to determine the average(median) nor average(mode) without running trials. So we are glad it got done.

Well, I am pretty sure I could find the average(median/mode), but it sure seems like a huge pain....

[Davor]

Aug 14, 2013 17:49:30 GMT coredump said:

Davor, I don't know how you are equating being good at math/mathhammer as being able to 'beat' the casinos.

In fact, one of the reasons I *don't* go to casinos is because I am good at Math. See, the casino is also good at math, and they also get to make the rules. Same reason I don't play scratch off lottery tickets.

I said it gave me a chuckle because I was on DakkaDakka reading something about mathhammer and I saw it here as well but way tonned down. So I made a bad comment. Didn't mean anything by it here.

[gingerwerewolf]

Coredump and Karkacabra those are great explanations, thanks for taking the time.

It does make a lot more sense now, and I think Karkacabra has spotted where mentally I was going wrong, I was too focussed on a turn invdividually.

Thanks again!