Surprise attack bonus

[rah]

YES, THERE IS A SURPRISE BONUS AGAINST A HUMAN PLAYER. We tested it early this morning. Thanks Baron O.

I'll post the results of the test later today after a little sleep.
The evidence will prove it beyond a shadow of doubt.

RAH

[ottok]

But how big is calculated by level!

[DrSpike]

Originally posted by rah
YES, THERE IS A SURPRISE BONUS AGAINST A HUMAN PLAYER. We tested it early this morning. Thanks Baron O.

I'll post the results of the test later today after a little sleep.
The evidence will prove it beyond a shadow of doubt.

RAH

Good. Did you do 50 repititions? If so I'll do some trickery when you post the results and derive the most likely specification for the bonus.

[Baron O]

dr spike

we ran 30 simulations
warrior vs warrior on surprise either total suprise and after treaty 30-0

warrior vs phalanx no surprise 0-30


on the various ends of the spectrums, rah has #'s on other permentations. but inital data on surprise warrior vs phahlax the warrior did win occsionally. most of the time on surprise it did at least take phalanx to red most of the time.

rah will post the results later. i just got up earlier than he did

[Baron O]

dr spike

i was too tired to run 50 simulations

[DrSpike]

Yeah well evidently 30 is enough to say there is a bonus, but pinning down the most likely specification for the bonus we could use a little more.

But I went ahead with 30......though bear in mind 30 observations is the bare minimum necessary to invoke the central limit theorem (which underpins my distibutional assumptions).

H0: bonus is 85%
H1: bonus is greater than 85%

The null was rejected in this test. For those interested I derived the proportion of expected wins under a bonus of 85% from the formulae in the combat thread, and derived the variance of the sample estimate with 30 repititions. I then normalised the estimated proportion and tested against a N(0,1) distribution.

H0: bonus is 90%
H1: bonus is greater than 90%

This time the null is just accepted.

Unfortunately given the extreme nature of the sample results I cannot go any further. With 50 repitions it would be clearer......we must consider now the possiblity that the bonus is 100%.

With 50 repititions a 50-0 score would lead to the second test above being rejected.......and just one loss would give me some additional statistical traction.

20 more please guys.

[DrSpike]

Originally posted by Baron O
but inital data on surprise warrior vs phahlax the warrior did win occsionally

More exact figures here would also yield some statistical traction. I await Rah's awakening with interest.

[Baron O]

dr spike

i think you will have a netter perspective after rah posts the other data, i am game for 20 more but mrs rah probably won't let that happen today.

[DrSpike]

Of course those with any statistical skill can probably see that if the bonus is 100% warrior-warrior can ultimately prove nothing, because the test statistic asymptotically approaches infinity as the expected proportion approaches 1!

/me worries what Rah's reaction will be if he is told warrior v warrior tests are inconclusive.

It is still worth going to 50 before we cross that bridge though.

[Baron O]

dr spike

are you a mathamatician, or a closet math freak?

this is just for my curiosity

[rah]

Test condition
30 repititions all attacks from and to hexs with no defensive bonus.

First set of fifteen rounds. Four attacks per round in the order below.
warrior on warrior surprise
15 wins 0 loses 4 vet promotions
warrior on warrior control
6 wins 9 loses 5 vet promotions
made peace
warrior on phalanx surprise
3 wins 12 loses 8 vet promotions
warrior on phalanx control
0 wins 15 loses 4 vet promotions

Second set of fifteen rounds. Four attacks per round in the order below.
warrior on phalanx surprise
6 wins 9 loses 8 vet promotions
warrior on phalanx control
0 wins 15 loses 6 vet promotions
made peacewarrior on warrior surpise
15 wins 0 loses 9 vet promotions
warrior on warrior control
5 wins 10 loses 8 vet promotions

It appears that after making peace the second surprise round has similar results to the initial surprise attacke.

SO warrior on warrior surprise 30 wins to ZERO loses.
Quite convincing proof of a surprise bonus, especially when you consider that in the control it was only 11 wins to 19 loses.

for the warrior on phalanx surprise it was 9 wins to 21 loses. Not that unsimilar to the control of warrior on warrior.

It would seem to have it be 30 to zero it would have to me more than 50% . It was the opposite of the control for warrior vs phalanx 0 wins to 30 loses. So it leads me to believe that it's closer to 100% , but I'll let the statisticians prove just what it is.

And when given time, I'll do more testing to add data so the actual amount of the bonus can be more acurately determined.

THERE IS A SURPRISE BONUS AGAINST HUMAN PLAYERS.



Thanks Baron O for you help.

RAH

[DrSpike]

Originally posted by Baron O
dr spike

are you a mathamatician, or a closet math freak?

this is just for my curiosity

Nah, I'm an academic economist, but I specialise in applied empirical work.

[DrSpike]

Hmm the initial phalanx results suggest is lower than 100%, but a null of 'bonus is 100%' cannot be rejected given the sample size.

Based on the warrior data so far the range 90% - 100% is likely, though the phalanx results are indicating slightly lower. 20 more tests on warrior v warrior with surprise bonus and 20 more warrior v phalanx would pin things down further.

For practical play the conclusion is as we expected though: surprise attack when you can, and cry when you see you are going to get surprise attacked.

[War4ever]

well done guys......well done!

[rah]

Now that we've got a save, it won't take as long to get another 20 results. There's also a river near the area we selected so we can try some attacks on that too.