Missile success and failure really needs adjusting!

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Frytner
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Missile success and failure really needs adjusting!

Post by Frytner » Sat Oct 25, 2008 3:45 pm

First off, I would like to congratulate the game design team. Well done!

Kaomaris is a fun game with a lot of potential. I've been telling all my gaming friends about it.

I did want to give you my view as a first timer though as there was one aspect that sucked a lot of the fun out of it for me.

The success/failure of missile strikes is simply too variable - to the point where it makes the game unfair in my humble opinion. You can have two equal forces facing off, each side doing a comparable missile strike (equal EFF and equal numbers etc) and yet have a dramatically disparate result.

There should be a little more predictability for players or at least the range of possible results needs to be reduced.

The game involves quite a bit of planning and predicting what your opponents may or may not do, which can be complex in itself. To then have such unpredictability in missile strikes makes the game simply unfair to players in view.

I'm sure a statistical or mathematical analysis would support me on this but I accept that it really also depends on what you want to achieve with the game. This aspect just seems out of whack with other parts of the game.

There are many ways you could adjust this and I don't profess to have all the answers. One way to reduce this margin would be to have missiles that hit spies or Tech points, when the province has none left, could be re-directed to armies or def, rather than do no damage at all or some variation of this.

I leave it at that.

Cheers,

Frtyner/Rob

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Post by Xarfei » Sat Oct 25, 2008 5:17 pm

This problem exists for as long as I can remember (one of many reasons why I prefer advanced Wok).

I personally agree with Frytner.

I also remeber that people have complained about this before and that any initiative to change the outcome was eventually stopped by the "tradionalists" who insisted keepings things the way they have been from the beginning (arguing that luck will eventually average out...).

I don't really want to get too involved in this discussion since it has been a very long time since I last played standard Wok, but I have just two suggestions (before I get intoxicated).

1) GMs can already (slightly) reduce the variance of the missling outcome by setting (under "expert settings") the minimum and maximum nuber of armies (or spies / tech / def) killed to 3.

2) Maybe one can create more options that would allow GMs to further reduce the luck-factor. E.g. every time misslies are fired, the engine puts the four possible targets in a random order (e.g. Def / Spy / Arm / Tech).
Then the 1st / 5th / 9th .... missile destroys a fixed/random amount of Def, the 2nd / 6th / 10th .... destroyes a fixed/random amount of spies and so on...
This is of course only one possible way to reduce variability, I am sure someone else can think of a better one.

Xarfei

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Post by korexus » Sat Oct 25, 2008 6:08 pm

The first option should really be sufficient. As Xarfei says, GMs can already change the maximum and minimum of each type killed on successful hits. The reason results vary so much is that there are three random factors in a missile attack (hit at all; what you hit; how many you hit) GMs can remove the third entirely if they wish.

We discussed weightings before and they sounded fun, they would also be far more confusing. Then there is the Advanced WoK option of choosing what you want to target in advance.

The reason I added all the GM definable constants in the first place was so the game could evolve. The defaults are mostly those of the original WoK IV engine, but where players have not liked a value games have been played with new values. I feel this is the best way to adapt as it allows us to try out new variants without risking making things worse across the board. Whenever it becomes clear that a new value is preferred, that value can become the new default. (e.g. LEV increases from attacking and from workers.)

That being said, there is also an argument for keeping a high-luck factor. Missiles are great for new players as they give the chance to knock down more experienced people and get a good position in the game. However the fact that they are a risk means that many players will use LEV and TEC workers instead. If they were too predictable, there would be a clear best choice of what to do, which would make games less interesting IMHO.


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Post by Hannibal » Sun Oct 26, 2008 12:36 am

Hi all,

I agree with Frytner. And many of the 20 newbie lobos have said the same thing - they see the appeal of some unpredictability, for excitement and anticipation, but think the luck in missiling, at least, is too great. I agree with Kor that we shouldn't make it TOO predictable.

However, I don't think the first option IS sufficient, ie changing the min-max range if you DO hit.
1) If you change the range on army-hits from 1-5 to, say, 1-4, it lowers the overall effectiveness of missiles at all, changing the balance.

2) Changing it to 2-4 keeps to the same average effect, but IMHO doesn't do enough to avoid the extremes - you could still hit armies 8 times with 10 missiles, and 8 hits would probably, on the odds, still kill as many as 24 armies, the same as the range 1-5 would.

3) Option 1 does nothing for the reverse side of the coin: if you fire 20 missiles, and NONE of them hit armies, then changing the range of armies killed to 2-4 achieves nothing - you still hit no armies ... And if you DO manage just one hit on armies, you avoid it being a kill of 1 army, but also avoid it being a kill of 5 armies ...

I think we have to do something about the chance to hit each type, not just about the range of values if you DO hit, say, armies.

Here's an example (and I've heard of even worse). Kryptus (my son) let me see his TR of yesterday, from his first Standard game. The incoming bombing looked like this:
------ Phase I: Bombing ------
YOUR PROVINCE 45 IS BOMBED!! You have a 18 % chance to detect the source.
Your Spies couldn't locate the Source of the Bombing...
42 missiles are used in the attack.
MISSILE 2 DESTROYS 0.1 DEFENSE!
MISSILE 3 KILLS 1 ARMIES!
MISSILE 4 DESTROYS 0.1 DEFENSE!
MISSILE 5 DESTROYS 0.1 DEFENSE!
MISSILE 6 DESTROYS 0.1 DEFENSE!
MISSILE 8 KILLS 2 ARMIES!
MISSILE 9 KILLS 5 ARMIES!
MISSILE 10 KILLS 5 SPIES!
MISSILE 11 KILLS 2 ARMIES!
MISSILE 12 KILLS 1 SPIES!
MISSILE 14 KILLS 4 ARMIES!
MISSILE 15 KILLS 5 ARMIES!
MISSILE 16 KILLS 3 ARMIES!
MISSILE 19 KILLS 5 ARMIES!
MISSILE 20 DESTROYS 0.1 DEFENSE!
MISSILE 22 DESTROYS 0.1 DEFENSE!
MISSILE 24 KILLS 4 ARMIES!
MISSILE 28 KILLS 5 ARMIES!
MISSILE 29 KILLS 5 ARMIES!
MISSILE 31 KILLS 2 ARMIES!
MISSILE 33 DESTROYS 0.1 DEFENSE!
MISSILE 35 KILLS 3 ARMIES!
MISSILE 37 KILLS 3 ARMIES!
MISSILE 39 KILLS 1 ARMIES!

The "enemy" fired 42 missiles, adjacent, at 50 Kryptus armies. The first 39 missiles killed all 50 armies. Even if the enemy had an eff of 99% (who knows?) those 39M should on average have killed 30A, and left Kryptus with 20A there for the battling phase, but instead wiped out all 50A, destroying any attack-orders.

Note the "runs" of hits-on-armies ...

Of course, Kryptus also missiled back:
>> ORDER 54-49-56 <<
This is a short range attack. Chance to hit is 76 %.
76 vs 0: Missile 1 would destroy tech points but the enemy has none left!
76 vs 61: Missile 2 would destroy tech points but the enemy has none left!
76 vs 67: Missile 3 hits spies but there are none left!
76 vs 79: Missile 4 misses its target...
76 vs 65: Missile 5 hits and destroys 0.1 defenses!
76 vs 40: Missile 6 hits and destroys 0.1 defenses!
76 vs 51: Missile 7 hits and destroys 0.1 defenses!
76 vs 82: Missile 8 misses its target...
76 vs 54: Missile 9 hits and destroys 0.1 defenses!
76 vs 55: Missile 10 hits and destroys 0.1 defenses!
76 vs 72: Missile 11 hits and destroys 0.1 defenses!
76 vs 11: Missile 12 hits and destroys 0.1 defenses!
76 vs 17: Missile 13 hits and destroys 0.1 defenses!

Note the "runs" of hitting def ... Kryptus went on to fire 29M, which on average "should" have killed 16.5A, but only killed 9A.

I think we need to bring results a bit closer to the average, versus both extreme high AND extreme low damage. Bunch up the bell-curve.

One way would be to avoid freak runs. My idea is simple conceptually, dunno how easy to code: You can't hit the same type twice in a row.

So, if you just hit armies, the next hit cannot be on armies. If you just hit Def, then "armies" now have a 1-in-3 chance of coming up (if a hit), not a 1-in-4. If you then hit Tec, then armies AGAIN has a 1-in-3 chance of coming up next, not a 1-in-4. It should bunch up the bell-curve quite a bit, in both directions, ie reducing serial hits on armies AND reducing serial runs of NOT hitting armies. Any mathematicians among us for how much difference it would make? If it didn't make ENOUGH difference, we could change it to "You can't hit either of the types that you hit in the last TWO hits" ...

Or, I could easily go with Xarfei's (2). But we really MUST do something or other, as it really does put off anyone on the receiving end of being bombed too luckily, OR bombing too unluckily.

Han
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Post by Arjuna » Sun Oct 26, 2008 6:38 am

I would agree that missiles are too unpredictable. I've gained and suffered from this in the two games i'm in (i bombed Kryptus last turn - anyone in the game would guess that).

How about a cap of 30% on casualties from missiles? This has the advantage that a player will still have a force to carry out attack orders albeit reduced (the attacker could fire multiple volleys from different provs and each will be limited to 30% of whatever is left - thus overall the loss could be more than 30% - but then there are implications to spreading out too much).

Irrespective of the target force size, missiles despite having a cap, can still do damage proportionate to the size.

Having a cap on numbers favours large armies, but capping the overall %, will balance out irrespective of size and still mean smallish armies can still fight.



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Post by korexus » Sun Oct 26, 2008 7:59 am

I've run some stats. If anyone wants to see the full data, let me know.

Currently: A player with 99 EFF who throws 50 missiles expects to hit 37.13 armies. Under the current system, there is a 90% chance that the true value will lie between 9.19 and 65.06. I agree that this is quite a range, personally I quite like that unpredictability, but anyway...

Under Xarfei's suggestion: The average number of hits remains the same,but the 90% interval reduces dramatically, so that the value lies between 36.75 and 37.5. At this point, we are reducing the luck factor so far, that you may as well say '1 missile = 3/4 * EFF of an army' and do a straight trade.

Han's suggestion is harder to treat statistically, however I could knock up a simulator to try out numbers that way.
A rough description of the results is that, the average will be lower, the extremes will be between those for the current model and for Xarfei's and the curve will be less symmetrical (there are three ways to miss armies, but only one way to hit, so it will still be possible to get 'runs' of misses.

One question to Han before I can do a simulation: Are you counting runs as from hits or from missiles fired? For instance, the first set of missiles you posted ends with
MISSILE 35 KILLS 3 ARMIES!
MISSILE 37 KILLS 3 ARMIES!
MISSILE 39 KILLS 1 ARMIES!
So missile #36 and #38 did not hit armies (they just didn't hit anything else either). Is this a run?


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Post by korexus » Sun Oct 26, 2008 8:44 am

Apologies, I was clearly still half asleep when doing those calculations. Here are (I hope!) the correct numbers.

(Assuming 99 EFF and 50 missiles, with the #armies killed in a successful hit fixed at 3)

Current system:
Mean: 37
90% Confidence Interval: 21 to 53.

Xarfei's suggestion:
Mean: 37
90% Confidence Interval: 35 to 39.

Han's suggestion:
Mean: 30
90% Confidence Interval: 21 to 39.


Discuss!

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Post by Xarfei » Sun Oct 26, 2008 12:12 pm

korexus wrote:
Xarfei's suggestion:
Mean: 37
90% Confidence Interval: 35 to 39.
I also suggested that the number of armies killed per missile could vary (just like it does now).
What if you set it to 2-4 or 1-5?

Xarfei

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Post by korexus » Sun Oct 26, 2008 2:53 pm

That's too many variables to build a simple statistical model, which is why I assumed fixed 3 for each. - It still allows for a general comparison.

I've put together a simulator for the three different methods, you can see it at http://www.gmchris.kaomaris.com/missileform.php, which should allow you to play around with options to your hearts' content. Note that this script just runs the mechanic 10,000 times and reports the results so the numbers may vary ever so slightly from use to use. Making this also highlighted an error in my previous post (It's clearly one of those days). While I had accounted for the reduction in kills from no repeat hits on armies in Han's model, I had not taken into account the extra kills possible from the other three options not being repeatable. This brings the average back into line for all three methods.

Note on reading the results table: The percentages at the top represent how many trials got that many kills or fewer so to discover the chances to kill at least a certain amount, subtract that value from 100.


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Post by Hannibal » Wed Oct 29, 2008 11:39 am

korexus wrote:
One question to Han before I can do a simulation: Are you counting runs as from hits or from missiles fired? For instance, the first set of missiles you posted ends with
MISSILE 35 KILLS 3 ARMIES!
MISSILE 37 KILLS 3 ARMIES!
MISSILE 39 KILLS 1 ARMIES!
So missile #36 and #38 did not hit armies (they just didn't hit anything else either). Is this a run?

Chris.
I deliberately said: " You can't hit the same type twice in a row." So, I did mean the engine taking account of last HIT, not last MISSILE. (I realise that might be harder to code). So, by my lights, your example of missile 37 and missile 39 was not a run if missile 38 hit something that didn't exist, eg Tec, but WAS a run if missile 39 was a miss.

So, from my above two examples of bombing results, in the first example 4,5,6 is a run which wouldn't happen, as is 8,9, as is 14,15,16, as is 28,29, whereas runs 16-19, 20-22, 24-31 and 35-39 are runs if/where only misses intervened, but not runs if the missing missile results were hits on something that didn't exist any more, so that it wasn't reported.

(Side-note: I recommend that forINcoming missiling, the TR should report ALL missile results, not just those that inflict real damage where damage remains to be done - it would have made these posts easier! (and, relevantly, it helps avoid the recipient getting a skewed impression of how effective the bombs on him were, just because the list misses out the missiles which missed, or which hit spies etc when you had none left ...)

I would quite have liked to avoid "runs of misses", in order to narrow the variability of the proportion of misses-to-hits closer to the average ... but I saw that this was not so doable: if someone falls below 66% Eff, then more than half their missiles (even short range) should miss ... so we could not build in that misses cannot repeat in runs, or else they could never be able to reach over 50% of firings being misses! If they were exactly at 66% Eff short range, or 88% Eff long range, they'd be looking at an average around 50% hits-to-misses; if we had "no-repeats-of-missile-misses-results", then we effectively decree that they they can suffer a rate of missile-misses below or up to the mean, but not beyond it/higher missile-misses than the mean ...

So, there are 5 possible results: miss, hitArmies, hitSpies, hitDef or hitTec. I'd leave the miss/hit as is, and just concentrate on the spread of hits if hits are made. That's what I meant.

So, I mean the engine should have to look back at the last HIT, not the last missile, and void the next hit being on the same type as the last hit, such that armies stand a 1-in-3 if they weren't hit on the last hit, but can't come up 2 or 3 or 4 hits in a row.

I see you tweaked your simulation, Kor. For example, you said you had simplified it to hits-on-armies = 3, but the simulation now offers (great) a chance to try 2-4 instead of 1-5, etc. ...

Given the above, is the simulation now "correct" so that I can play around using it? I want to try it with more typical values for number of missiles (31 anybody?!), and for Eff, looking particularly at what % of extreme results we risk (I'm not sure the 90% interval is the most relevant, since that would leave 1 in 10 outside this range ... and with maybe 10-25 bombings per round for maybe 15 rounds, maybe 200 bombing-orders, that would still allow/expect 20 bombing results per game to be "extreme", ie. outside of that range ...?). My aim was not to make it formulaic, but to "bunch up the bell-curve", to nearly-rule-out extremes ... and 20 extremes per game might still be too many?!?

BTW, from the simulator, if I take the 1% column, and the 99% column, their results cover 98% of possible results, right? ie down to getting, on average, only 2%, only 4 per game, "extreme" bombing results outside of that range, right?

Cheers,
Han

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Post by Hannibal » Wed Oct 29, 2008 11:49 am

As to my last paragraph/question, I do realise that most of the maybe 200 bombing-orders per game are using fewer bombs each time than 31 or 50, such that most of the orders, using fewer missiles, stand more risk of an "extreme result". I think people can handle that sending 6 missiles can be more, er, hit'n'miss(!). But for larger strikes, it means only 1-in 50 results lying outside the 1%-99% range? - ie occasional and special and heroic/exciting, rather than happening to somebody or other every turn or every other turn?

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Post by korexus » Wed Oct 29, 2008 7:54 pm

Hannibal wrote: I deliberately said: " You can't hit the same type twice in a row." So, I did mean the engine taking account of last HIT, not last MISSILE. (I realise that might be harder to code). So, by my lights, your example of missile 37 and missile 39 was not a run if missile 38 hit something that didn't exist, eg Tec, but WAS a run if missile 39 was a miss.
Worth checking, the simulator does it the other way right now. It shouldn't make a noticeable difference when EFF is high, but I'll swap the method when I get a moment.
(Side-note: I recommend that forINcoming missiling, the TR should report ALL missile results, not just those that inflict real damage where damage remains to be done - it would have made these posts easier! (and, relevantly, it helps avoid the recipient getting a skewed impression of how effective the bombs on him were, just because the list misses out the missiles which missed, or which hit spies etc when you had none left ...)
That would make the effect of the missiles harder to interpret. The ones which hit would have to be highlighted or a summary given, so the player could evaluate results easily.
I would quite have liked to avoid "runs of misses", in order to narrow the variability of the proportion of misses-to-hits closer to the average ... but I saw that this was not so doable: if someone falls below 66% Eff, then more than half their missiles (even short range) should miss ... so we could not build in that misses cannot repeat in runs, or else they could never be able to reach over 50% of firings being misses! If they were exactly at 66% Eff short range, or 88% Eff long range, they'd be looking at an average around 50% hits-to-misses; if we had "no-repeats-of-missile-misses-results", then we effectively decree that they they can suffer a rate of missile-misses below or up to the mean, but not beyond it/higher missile-misses than the mean ...
I have no idea what you're saying here...
I see you tweaked your simulation, Kor. For example, you said you had simplified it to hits-on-armies = 3, but the simulation now offers (great) a chance to try 2-4 instead of 1-5, etc. ...

Given the above, is the simulation now "correct" so that I can play around using it? I want to try it with more typical values for number of missiles (31 anybody?!), and for Eff, looking particularly at what % of extreme results we risk (I'm not sure the 90% interval is the most relevant, since that would leave 1 in 10 outside this range ... and with maybe 10-25 bombings per round for maybe 15 rounds, maybe 200 bombing-orders, that would still allow/expect 20 bombing results per game to be "extreme", ie. outside of that range ...?). My aim was not to make it formulaic, but to "bunch up the bell-curve", to nearly-rule-out extremes ... and 20 extremes per game might still be too many?!?
There was no simulation before, I was working statistically. This has the advantage of producing the absolute right answer for the model, but the disadvantage of difficulty modeling complicated set ups. Hence the switch. The statistical model was also the reason for the 90% confidence interval. - That falls out neatly as 3 standard deviations, while anything else is tricky to calculate. (Although I think 15 rounds of 15 bombings of an size is probably quite an over-estimate! :P)

Except that the definition of a run is slightly different, the simulator should be fine to play around with. If I discover any other glitches I will post about them.
BTW, from the simulator, if I take the 1% column, and the 99% column, their results cover 98% of possible results, right? ie down to getting, on average, only 2%, only 4 per game, "extreme" bombing results outside of that range, right?
Bingo. However note that players will always remember the times when they were unlucky, no matter how rare they are. :wink:


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Post by Hryllantre » Wed Oct 29, 2008 10:11 pm

My memory is terrible but your right kor I just fired 56 missiles @ 91% and only killled 23 armies!!! - only 2 missiles missed... should've killed 38

I normally get the rotten end of the stick with attacks too and my last turn was no exception...

You have 23 troops at a level of 1.177.
Your PDEF is 10.711
The enemy has 22 at a level of 1.183.
The enemy has a PATT of 9.109

4 attackers remained - not good I would have lots more armies otherwise...

The tool says:-

Attacker wins: 20%
Defender wins: 80%
Average number of attackers
after the end of battle: 1
Average number of defenders
after the end of battle: 6 - that's a swing of 10 armies with a vastly inferior EFF

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Post by Underdog » Wed Oct 29, 2008 11:45 pm

Dameon has returned under a new name? Come on Nick tell everyone it is REALLY you.


For those of you who do not remember him, Dameon had 2 MAJOR problems with WOK4. This was 1 of them the other was the spy player info.
I just couldn't help myself when I saw this thread.
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Underdog is here

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Post by SmashFace » Thu Oct 30, 2008 12:15 am

my thoughts exactly UD, BTW Welcome back, ready for some real wok5 action?
God of WOK

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Post by Hannibal » Tue Nov 04, 2008 1:10 pm

Using Chris's excellent simulator, I've crunched a few options to see the difference. I've taken a more "normal" case than firing 50M at 99% Eff. I've taken a case of firing 30M at 92% Eff, and just looked at the effect on likely kills of armies.

Here are 6 ways the default algorithm could be. ALL of them produce a mean average of those 30M killing 21 armies. We are not here discussing whether to make missiles less or more effective on average, only whether to make the results less VARIABLE-from-the-average-by-luck.

A) Current system, and sticking to hitting 1-5 armies per hit:
Mean avge: 21 armies
90% of results fall between: 7 - 37 armies
98% of results fall between: 3 - 43 armies

B) Current system, but change to hitting 2-4 armies per hit:
Mean avge: 21 armies
90% of results fall between: 7 - 36 armies
98% of results fall between: 4 - 41 armies

C) Xarfei idea*, and sticking to hitting 1-5 armies per hit:
Mean avge: 21 armies
90% of results fall between: 12 - 30 armies
98% of results fall between: 9 - 32 armies

D) Xarfei idea*, but change to hitting 2-4 armies per hit:
Mean avge: 21 armies
90% of results fall between: 14 - 27 armies
98% of results fall between: 12 - 29 armies

E) Han's idea*, and sticking to hitting 1-5 armies per hit:
Mean avge: 21 armies
90% of results fall between: 9 - 34 armies
98% of results fall between: 6 - 38 armies

F) Han's idea*, but change to hitting 2-4 armies per hit:
Mean avge: 21 armies
90% of results fall between: 10 - 32 armies
98% of results fall between: 7 - 35 armies

The above masks the shape of the bell-curve; eg the last example clearly does not mean that the result is equally likely to be anywhere in the 7-35 armies range. What we're debating is how rare to make outcomes that lie outside, or near to, those 98% extremes. So, the difference between a "range" of 3-43 armies and a "range" of 7-35 armies is more than it looks, because results will be more bunched up even between those range-end-values. I think.

I reckon that the 98% line is the most important, because it looks at leaving only 2-4 freak results per game outside of such a range, whereas the 90% line looks at leaving 10-20 freak results per game outside of such a range.

Xarfei's idea produces a narrower and better range of outcomes, but (IMHO) slightly at more cost to the fun? Half of us tend to sometimes go down the TR-page revealing one line after another line, looking to see if the next missile takes out some armies ... Xarfei's idea means that, if your 2nd missile hits armies, you immediately know that only your 6th, 10th, 14th etc missile will hit armies. Han's idea means that you still wonder whether your 4th, 5th, 6th etc missile can hit armies, ie slightly more adrenalin, at the cost of slightly more luck.

I vote for (F). But would accept any of C-F rather than A or B.

Comments and votes? Or a better idea?

*Reminder: Xarfei's idea is that the engine generates the 4 types of hit into a random order, and then any hits follow that same order every 4 hits. Han's idea is that the engine stops a hit being on the same type as the last hit was, such that if you hit something other than armies, then armies then has a 1 -in-3 chance next hit, rather than a 1-in-4 chance; and, on the other hand, that you can't hit armies twice in a row.

Han
There are two ways to write: Short-hand, and Long-Han'ed. ~ Han

"If you can keep your head when all about you are losing theirs"......... it's probably just that you're the last person to appreciate the enormity of the catastrophe about to

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korexus
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Re: Missile success and failure really needs adjusting!

Post by korexus » Sun Nov 16, 2008 6:05 pm

I've implemented Han's suggestion so we can see what happens.

If Standard games start falling over at this point, I probably messed something up...


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Re: Missile success and failure really needs adjusting!

Post by Hryllantre » Fri Nov 21, 2008 7:30 pm

Let's get a game on to test Han's numbers

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