Turn 76, 1000BC

[Krill]

Originally posted by notyoueither


There's also diplomacy, Krill. This isn't online MP.

AC could decide to screw with us, sure. Have you seen there tech? Metal casting, meditation, fishing, alphabet, AH, IW...and a stupid neighbour. But if they pissed us off, what are they left with? An incompetant ally in nana and Vox who literally will not be around for long. Against a possible 3 civ tech alliance they would not stand a chance, and they know it. They need us as much as we need them.

[Krill]

As I see it if the first strikes become more likely to hit the more damaged the archer becomes, no? So as the odds tend towards a 50/50 in your sim they actually are better for us? So I take it from you sim that we need 4 hits from the first 2 skirms to have a 50/50 chance in your sim, but in reality we only need 3 hits from teh first 2 skirms to haev the 50/50?

[notyoueither]

I can't say that. I was not counting hits. -0.04 is 1 hit?

However, you can see how odds break if the first guy does less, and that it is very difficult if they are not 1.4 or less for the 3rd attack.

[Krill]

yeah, that is why I said it was difficult to sim it with 3 skirms. It is easier to throw away 2 skirms and then check the odds. If odds are bad, then don't throw away the third, which ought to be materazzi due to position. If odds are good move in for the kill

[Solomwi]

As I understand them, first strikes work just like any normal round, except that the unit with the first strike doesn't take any damage if it loses that round. The relevant questions I see are (as always, any correction on game rules and such is most appreciated):

1. Will we get a first strike round?

According to the combat article on CFC, the number of possible first strike rounds is determined by comparing first strike chances of the two units. If one has more, it gets the difference in first strike chances. Also, they say the math on whether a first strike chance turns into a first strike round is about 50%. Since the archer has one and the skirmisher 1-2, I take that to mean that sometimes the archer and skirm will cancel each other out, and sometimes the skirm will get a single FS chance.

2. What effect will a first strike round have if we do get it?

Our chance to hit will be the same as our chance to win any other round (so yes, they should become more likely to hit *if* we get the FS round, as the archer takes damage). So, either we won't hit, meaning nothing changes, or we will, meaning it simply counts as one of the rounds we need to win. If it doesn't hit, effectively you can add one to the rounds the archer will need to kill our skirm, since he'll have to win that round, then however many more to inflict 100 HP of damage. If it does hit, you can effectively subtract one from our rounds needed in "real" combat. Either way, the effect is for the gap to decrease by one. I leave the effect that has on overall odds of winning the battle to those with better statistical knowledge than mine.

The uncertainty of getting that round is one reason I didn't try to factor the first strikes into the sim, though the main one is that if it happens, the round plays out just like any other, except for the skirm not taking damage. It can therefore be accounted for by the sim through simply counting it as one of our needed rounds and recognizing that a loss won't count toward the archer's needed rounds.

NB: The odds I gave, and that the spreadsheet gives, are for individual rounds, not for the overall battle. Sorry if that confused anyone.

[notyoueither]

More accurate to sim it, I think. No factors forgotten. I'd like to do another 50, but I do not have the hour and a half or 2 hours to do it.

[Krill]

Easiest way to sim it is to look for cut off points. which seems to be that 1.4 health left on the archer before the last skirm attacks.

[Krill]

siming it out now from nyes sime, and it confirms that we need 4 hits from teh first 2 skirms for greater than 50% odds. If we get 3 hits from teh first 2 skirms then we have odds of about 41%

[Krill]

Yeah, but Solomwi, look at it this way; as the archer tends towards 50% health it's strength drops such that the potential free strike is more likely to hit than miss, if we get it. Effectively this means that the 50/50 chance we have of winning the final battle IF the archer is down to half helth is actually about 80% according to the ingame combat calc.

[Solomwi]

Originally posted by notyoueither
More accurate to sim it, I think. No factors forgotten. I'd like to do another 50, but I do not have the hour and a half or 2 hours to do it.

No doubt, but I haven't even tried the Worldbuilder out yet, and your save wasn't up when I whipped out the spreadsheet. Now that it is, I plan to run a few trials to add to the data. Also, never hurts to have a second tool to apply.

Oh, and not forgotten, but deliberately omitted.

[Blake]

Combat simulation gives 60% odds,

This is the one I used and I believe it to be accurate.

http://c4combat.narod.ru/c4c.htm

The main limitation is it doesn't take first strike chances, the odds with ignoring the FSC = 59.2%, with 1 First Strike = 72%, if you average those you get 65%. So it's safe to say we have 2/3 odds.

Yes, but I'd still think about risking it if Blake or someone else can convince me that winning 40 turns earlier has a substantial impact on our chances of winning the game.

I think that overall it will improve our chances of winning the game, it means we can put our economy into high gear sooner, and may allow us to grab a wonder.

The question is all about diplomacy.

The thing I feel we must do is send AC and maybe Banana heads up, probably before sending the save on. So they are the first to know (ok along with Vox).
This goes whether we win or lose the fight.

The points to stress if we win is that we need to discuss wonder builds, since the Storm is no longer tied up with a military campaign. We may declare that we will (continue to) support AC in their effort to get the Great Library, assuming that they are indeed pursuing that wonder.

If we lose (other than a flawless loss first battle+abort) we should still send a heads up, we should stress that the time line for the demise of Vox has not really changed significantly and that their archers pose zero threat to our Axemen, just that Vox have slightly more liberties when it comes to getting units out.
We would also want to note that Vox have trained a Settler, which they may send North, with the (implied?) suggestion that a military unit may be able to snag a free worker.

[Solomwi]

50 trials, 31 wins, 62%.

   Odds for 1st skirm attack are 0.08
 1 Strength after 1st skirm attacks
O2 Odds for second attack
 2 Strength after 2nd attack
O3 Odds for 3rd attack
 3 Strength after 2nd attack

         1       O2      2       O3      3     Result
1	3.0	0.8	3.0	0.8	2.2	Fail
2	2.2	10.4	2.2	10.4	0.5	Fail
3	2.2	10.4	1.8	42.1	0.0	Win
4	2.6	3.2	2.6	3.2	1.8	Fail
5	1.8	26.6	1.4	81.4	0.0	Win
6	2.2	10.4	2.2	10.4	1.4	Fail
7	1.8	26.6	0.0			Win
8	2.6	3.2	1.4	82.3	1.4	Fail
9	3.0	0.8	3.0	0.8	2.2	Fail
10	2.6	3.2	2.6	3.2	1.4	Fail
11	3.0	0.8	3.0	0.8	2.2	Fail
12	1.0	89.8	1.0	89.8	0.0	Win
13	0.7	99.0	0.0			Win
14	1.8	26.6	1.4	81.4	0.0	Win
15	1.8	26.6	0.0			Win
16	2.2	10.4	1.8	41.2	1.8	Fail
17	1.4	80.0	0.0			Win
18	1.4	80.0	1.0	96.7	0.0	Win
19	2.2	10.4	1.4	81.4	0.0	Win
20	3.0	0.8	2.2	10.4	1.4	Fail
21	2.6	3.2	2.2	10.7	2.2	Fail
22	2.2	10.4	0.5	99.5	0.0	Win
23	2.6	3.2	1.4	82.3	0.0	Win
24	3.0	0.8	2.6	3.2	2.2	Fail
25	2.2	10.4	0.1	100.0	0.0	Win
26	2.2	10.4	1.4	81.4	0.0	Win
27	1.8	26.6	1.4	81.4	0.0	Win
28	2.6	3.2	1.8	42.0	0.4	Fail
29	1.8	26.6	1.4	81.4	0.0	Win
30	3.0	0.8	1.4	80.0	0.0	Win
31	1.8	26.6	1.8	26.6	0.0	Win
32	1.8	26.6	1.4	81.4	0.0	Win
33	1.0	89.8	0.0			Win
34	3.0	0.8	3.0	0.8	2.6	Fail
35	2.2	10.4	1.4	81.4	0.4	Fail
36	1.0	89.8	0.0			Win
37	3.0	0.8	3.0	0.8	1.4	Fail
38	3.0	0.8	1.8	26.6	0.5	Fail
39	2.6	3.2	2.2	10.7	1.4	Fail
40	1.8	26.6	0.9	97.0	0.0	Win
41	2.6	3.2	0.5	99.9	0.0	Win
42	1.0	89.8	0.0			Win
43	2.6	3.2	0.9	97.0	0.0	Win
44	2.2	10.4	1.0	96.7	0.0	Win
45	2.2	10.4	1.4	81.4	0.0	Win
46	1.8	26.6	1.8	26.6	0.0	Fail
47	2.2	10.4	1.8	41.2	0.0	Win
48	1.4	80.0	0.0			Win
49	1.4	80.0	0.0			Win
50	1.8	26.6	0.0			Win

Note that most odds corresponding to 1.8 are 26.6%, but there's a 42% and a 41.2%. That's the difference between 61, 59 and 60 HP, respectively. Not that we have much room to manipulate it, but I found that jump point illustration interesting. I'll break my results down similar to what nye did in a little bit.

[Solomwi]

Based on strength after first attack:

0-1.8: 19/20, 95%
2.2: 8/12, 67%
0-2.2: 27/32, 84%
2.6: 3/9, 33%
0-2.6: 30/41, 73%
3.0: 1/9, 11%
2.6-3.0: 4/18, 22%

Thus nye's suggested decision point looks to hold up for my data, as well.

Based on strength after second attack (40 entries due to 10 winning on the second attack):

<1.4: 8/8, 100%
1.4: 10/12, 83%
0-1.4: 18/20, 90%
1.8: 3/7, 42%
0-1.8: 21/27, 78%
>1.8: 0/13, 0%

Again, there looks to be a clear decision point, this time at 1.4. O3 at 2 = 1.4 (maybe it's just because it's late, but I found that funny) ranges from 80-82.3%. The next highest O3 is 42.1%, so that in itself is telling. Though I might argue "in for a penny, in for a pound" at 1.8, leaving the more strategically placed forest skirm to menace them might still have enough of an effect to warrant breaking off the attack. Above 1.8 and we're just wasting him, it seems.

[vmxa1]

I have no objection, lets see if we can get this done and start making some real progress.

[Arrian]

Thanks to everyone who put in the effort to back up the 60/40 odds. I'm comfortable with my original proposal:

Attack with the skirm on the cow. If we damage Donegeal (even a little), continue.

A 60% shot is too good to pass up. Hell, we'd have to seriously consider a 40% shot, no? Take it.

Attack.

-Arrian