Odd battle odds

[zsozso]

One thing that really annoys me in CivRev compared to other civ games (like SMAC) is the apparently messed up battle odds relative to the attack/defence strength of the units. For overwhelming ratios it works OK, but for close cases, like 5:4, 12:9, 24:22 and such it seem WAAAY too often the weaker unit wins. In SMAC if you attack at that kind of odds, then you surely get lots of damage but you can still expect to win the battle with a fair probability. But not in CivRev. I do not have precise statistics (maybe I should start running a tally to confirm this), but my gut feeling is that the odds are almost reversed. Well, not exactly reverse, 12:7 still has a better chance to win than 12:10, but at close odds the weaker seems to be more likely to win and the closer the ratio to 1 the more likely. E.g. I do not remember ever winning a battle with 24:22 odds, this seems to be a sure loser.

And it also works the other way around, i.e. if you attack a bit stronger defender, you seem to have a good chance of winning -- and you also get a bonus upgrade or Great General for winning against odds. Maybe that is the reason/rational behind this "feature", they want to give more chance to those bonuses ? After a while of being annoyed by this, I started to rely on this and it seems to pay off: if I see such close odds in my favour, I do not attack , but if I see I am a bit weaker I go ahead.

Apart from ranting about it, I posted this to see if you guys have also noticed this. Or is it only my warped perception ?

[clever id]

While I haven't thought about it that much, I have noticed the close odds = a loss for me. I find close naval battles ALWAYS go in the favor of the CPU.

[snoopy369]

Tally up the battles for yourself - and keep a long list of them, don't just base your opinion on a sample size of ten or twenty. There is a huge tendency for people to notice outliers and forget about common occurrences, and thus consider the outliers to be unreasonably common.

I certainly haven't noticed anything out of the ordinary ... I win slightly more than half my battles when I have slightly more than 50/50 odds, and usually lose battles with worse odds.

[zsozso]

You are right, I need to collect exact stats, I will start doing that and post the results here. However, I do have some data already that is exact:

I played the "Game of the week" on Chieftain (don't laugh!) 6 times over trying to minimize the number of moves to complete it the earliest possible (I'm still only second with 2100BC the best on the leaderboard is 2300BC). In these games I always attack with a horseman against a warrior in a capitol, which works out to 4:2.5 odds on this difficulty level. There are 4 cities to take over in each game, all with the same odds. In every single game the exact same pattern appeared: I won 2 of the attacks and lost the other 2, so I had to follow up with a second horse to take those cities. So, that is 6x4=24 test cases all at the same 4:2.5 odds and 50% losing rate. Straight math odds would suggest over 61% winning chance. OK, this is too little data to draw conclusions, so I'll be back with more data... (famous last words )

[clever id]

Maybe they should have used civilization to teach statistics... I would have done better.

[zsozso]

OK, I got some more significant amount of data tallied up. Looks like my gut feeling was right! I have been recording all attacks in my games where the odds were less than double, i.e. attacker versus defender strength ratio above 0.5 but below 2.0, except for equal values (ratio=1.0) because those seemed to be 50% chance anyway. Here are the stats I have collected:

First the cases where the attacker had (less than 2 fold) advantage:

adv: 79 win: 40(50%) lose: 39(49%)
adv>50%: 25 win: 17(68%) lose: 8(32%)
adv<50%: 38 win: 16(42%) lose: 22(57%)
adv<25%: 15 win: 5(33%) lose: 10(66%)

So what we see on the first line is that the total range (1.0,2.0) has about 50-50 chance, even though you would expect more wins when you have advantage. But it is more interesting when you look at the next 2 lines, that break it down into (1.0,1.5) and (1.5,2.0) sections. When the advantage is above 50% I got twice as many wins than loses, which is about what you can expect, so nothing wrong in that range. BUT, when you look at the less than 50% advantage window I lost more times than won, while it clearly should be the other way around! The problem gets even more obvious and striking for the even narrower slice, when the advantage is less than 25%, then it is TWICE as likely to lose than win! Although the advantage is small, but it is STILL advantage, but the game clearly prefers to award an upgrade or Great General to the defender rather than letting the attacker win as deserved.

Now, let's look at the cases when the defender had advantage:

dis: 37 win: 16(43%) lose: 21(56%)
dis>50%: 5 win: 0(0%) lose: 5(100%)
dis<50%: 27 win: 13(48%) lose: 14(51%)
dis<25%: 13 win: 8(61%) lose: 5(38%)

Again, the full range looks pretty much OK, bit more loss than win, sounds fair for a slightly disadvantaged attack. But when you narrow the ranges down, it gets more interesting: if the disadvantage is more than 50% then you lose, don't even try to attack! But if your disadvantage is less than 50% you have an unexpectedly high 50-50 chance to win (instead of 2/3 loss and 1/3 win). If the difference is even less, the attacker has less than 25% disadvantage, then it has about 2/3 chance to win against odds!

So, what I conclude from the experiment is this:
If the difference in attack/defense strength is more than 25%, then the program uses proper random chance with the correct probabilities for the battle resolution. However, if the difference in less than 25%, then it "cheats", i.e. alters the odds to be much more in favor of the disadvantaged side (either attacker or defender), thus increasing the chance of granting upgrades or Great Generals.

Now, this is officially part of my playing strategy

[Grayson]

very intresting post.

i'd be cool to make the sample size a little larger. Also, did you use just one or two games? or was this spread out over several games? Also, was this just against the AI or was it agaisnt humans on MP??

another intresting factor to add in would be damage. Usually attackers are at a disadvantage early for this with horsemen or knights, since they are composed of only two units (but three to build). defenders can always take none,one or two damage, or be killed.

catapults, tanks, artillary and naval fleets auto heal, so this is an advantage for these attacking units. I also find that these units tend to win more close battles moreso than other units. also, when attacking with a more advanced unit against a less advanced defensive unit, it often seems like the advantage is to the more advanced units even if the battle odds are close.

it seems like some games i win every battle, and others i lose even with the best odds.... but i think it's all in my head and the numbers are closer to the ones you recorded. I think if you sample size was larger, then you'd see a little shift in those closer odds battles where is seems like it's an advantage to be less than 25% of the greater attacking power.

but really really intresting stuff. thanks

[zsozso]

I collected the stats over several games, about 8-10, all against AI -- I think the odds are similar in MP games too, but due to the time limit I am pretty busy during MP game turns so I did not want to spend time on taking notes while playing.

Yes recording damages would be very interesting too, I feel there are some funny probabilities there too.