Ruben Schlüter
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"Why yes, OF COURSE I CAN'T HIT ANYTHING WITH MY F***ING CRUISERS WHILE YOUR CARRIER HITS EVERY SINGLE TURN! GAAAAAAAAH!"

Ever got that feeling in TI? You might be unlucky - or someone with selective perception, but aside from the constant feeling that the dice hate me (which I know they do, by the way), I was wondering if I couldn't do some more fundamental "research" on this topic. Generally, I'd rather look at the "early" combats, that is juicy opportunities that might present themselves during the first three, four rounds.

So I sat down and did some programming, for starters just for ground combat, cause that's the easiest case (only equal units, so no "preference" in sacrificing order, and you'll usually not retreat - don't know if it's even possible...).

So here are the first results, and I will detail them out further as they come in (I use 1,000,000 combats as a base, so simulation takes a while on my 2.5 year old machine).

Reference case:
Attacker lands one GF, defender has one.

Attacker wins: 411,538
Defender wins: 588,462
Defender still has his ground force: 411,587

So what is the effect of a +1 bonus on the attacking side (Sardakk N'orr player)?

Attacker wins: 483,115
Defender wins: 516,885
Defender still has his ground force: 310,208

Okay, so one GF doesn't seem to be enough, really. So how about two?

Attacker lands two GF, defender has one.

Attacker wins: 868,399
Attacker has both ground forces on the planet after invasion: 543,480
Attacker has one ground force on the planet after invasion: 324,919
Defender wins: 131,601
Defender still has his ground force: 92,338

Now that looks good, right? How does the +1 shift this?
Attacker wins: 925,227
Attacker has both ground forces on the planet after invasion: 598,637
Attacker has one ground force on the planet after invasion: 326,590
Defender wins: 74,773
Defender still has his ground force: 44,893

Yee-haw, >90% chance for the taking! Not bad, not bad at all.

Okay, now as everything worth doing is worth overdoing, how about three attacking groundforces vs. only one defending?
Attacker wins: 982,204
Attacker has three ground forces on the planet after invasion: 606,312
Attacker has two ground forces on the planet after invasion: 331,746
Attacker has only one ground force on the planet after invasion: 44,146
Defender wins: 17,796
Defender still has his ground force: 12,400

Well, okay, that settles that question. But wait - will three be enough versus two defenders?
Attacker wins: 811,816
Attacker has all three ground forces on the planet after invasion: 284,656
Attacker has two ground forces on the planet after invasion: 351,502
Attacker has only one ground force on the planet after invasion: 175,658
Defender wins: 188,184
Defender still has both ground forces: 55,265
Defender still has one ground force: 100,406

Wow, that looks pretty decent, I'd say. But two on two will be a problem, right? Right...
Attacker wins: 464,869
Attacker has two ground forces on the planet after invasion: 205,811
Attacker has only one ground force on the planet after invasion: 259,058
Defender wins: 535,131
Defender still has both ground forces: 204,648
Defender still has one ground force: 257,758

tl;dr

If you go for ground combat, take at least one GF more than the defender has (that is if both roll vs. 8). Largest surprise to me was that 3 vs. 2 will win >80% of times.

Now what else would be interesting? Take bombardment into account? Compare the basic chances vs. the chances when playing a morale boost card? Or go directly for space battles?

I'll take your suggestions. Or make up my own mind and keep you posted.
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Jan Ozimek
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Must resist M:tG. Boardgames are my methadone :)
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The larger a battle becomes, the less significant a one infantry head start is going to be.
 
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Joey V

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oh this is cool.

now we just need you to program the entire game and settle once and for all, who is more powerful, the L1Z1X or the Yssrasil?

-joey
 
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Ruben Schlüter
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cannibalkid wrote:
oh this is cool.

now we just need you to program the entire game and settle once and for all, who is more powerful, the L1Z1X or the Yssrasil?

-joey


Muahaha. If I could do that, I'd have another job, I guess...

Anyways, I upgraded the simulation today to include offensive bombardment and defensive PDS fire, Shocktroops (incl. promotion), Mechanized Units (including hits), Generals (attacking and defending side), scientists (to improve PDS fire and prevent warsun bombardment)... I will have to do quite some validation (more than 350 lines of code) though, and I have a hard time pinning down the actual outcomes of the battles (if it's more than "planet conquered or not").

Oh, there was a nasty bug in yesterdays code, so the numbers in the OP might actually be wrong. I'll check later...
 
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Ulrich Feindt
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I ran similar simulations earlier this year (only for myself though). I compared some of the numbers and they matched up to about 1000 (as one would roughly expect for one million realizations). However, this could also mean that I have the same bug...

If you want complete ground combat, there is also:
- Duranium Armor (for the MUs)
- Mercenaries
- Fighters (using Graviton Negators)
- Invading with two Generals (N'orr have two of them and the rerolls stack I think)

Also note that there are differing opinions on how the General's rerolls are applied: Some restrict them to GFs, others (like me) allow them for all rolls.
Furthermore MUs can't take PDS or Bombardment hits if playing rules as written.

Lastly, just out of curiosity, what language are you using?
If your computer has multiple CPUs you can increase the overall speed by running multiple simulations simultaneously. I actually took the time to learn how to use parallel processing in Python when I did this but that was on a quad core.
 
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Ulrich Feindt
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As a reference to check some of your results, I did a back of the envelope calculation of the first two cases you simulated and get following probabilities:

Attacker lands one GF, defender has one.

Attacker wins: 41.176% (7/17 to be precise)
Defender wins: 58.823% (10/17)
Defender still has his ground force: 41.176% (7/17)

So what is the effect of a +1 bonus on the attacking side (Sardakk N'orr player)?

Attacker wins: 48.276% (14/29)
Defender wins: 51.724% (15/29)
Defender still has his ground force: 31.034% (9/29)

Calculating 1v1 analytically is very easy, however, because the final decision is always in the last round. As soon as one side can take a hit, this becomes more complicated.
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Marco Bouzada
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Take a look at my 2005 post: http://www.boardgamegeek.com/filepage/12140/ti3-space-combat...

It might be useful
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David Damerell
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Why on Earth would you do this by simulation rather than by straight analysis of probabilities?
 
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Marco Bouzada
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Simulation is better to model complex situations
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David Damerell
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Marco wrote:
Simulation is better to model complex situations


Well, in the sense that sometimes a direct analysis of probabilities is too hard, perhaps. But otherwise it is always better than simulation.
 
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Ulrich Feindt
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True, but the tricky thing with combat in TI3 is that it has no fixed end-point but could in principle carry on forever if nobody hits. So a simulation may seem like the only option.

However, this problem can easily be overcome once one has figured out how this infinite series converges. Over the last few months, I put together some code that can calculate most space battles using that. Maybe I will post it at some point but it is currently not really in a form that could easily be used by someone else.
 
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David Damerell
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Sunchaser wrote:
True, but the tricky thing with combat in TI3 is that it has no fixed end-point but could in principle carry on forever if nobody hits. So a simulation may seem like the only option.


That is hardly an insurmountable barrier - and we can improve on the simulation approach very easily. Consider the very first question in this thread, where it's carefully noted that the attacker keeps their ground force 411,538 times but the defender 411,587 times; would it not be better to notice that since the situation is exactly even, the odds of each ground force surviving must be equal?
 
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Ulrich Feindt
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Yes, and as I said, I did overcome this. However, the solution might not be obvious. Simulations are often much easier to code because you only have to describe what is happening and can let the random number generator take care of the rest.

Regarding symmetry of the OP's first simulation: Pointing out that the odds are equal might be correct but that does not make this more precise. I would assume that the error of those numbers is roughly their square root, i.e. roughly 600 in this case. The difference between those two cases is way within that. So, to me the numbers are basically the same. Note further that both numbers are actually too low by roughly 200 compared to the exact values given in my second post in this thread.
 
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