Luck/Turmoil versus Nothing.

[militarist]

ChrisP, the idea behind taking M3 is connected with one of my previous posts:
"One more interesting question. There is a number of good events which can happen with you theoretically. For example, there are many which require Magic 2 (or at least Magic 2) scale. With Magic lower then M2, you have shorter list of possible good events. Does it mean you will have less good events? Or just it means that you will have the same number of events but from shorter list?"

Edi says that to maximize effect from luck you should take at least magic 2 which switches on many events. The question which is interesting - If I take M2 in comparison with M0, will I have MORE events (as the list of good events is longer), or I will just BETTER events but amount will be the same. It's a big difference. In first case taking M3 could have some sense if you take Luck 3 even in multiplayer. In second - taking M3 adds much less value, as just replaces some cheap cash events by items
which can be worthless.

I didn't see anywhere any mentioning that there is such a thing as basis probability , which is not connected with amount of events possible with current scales.

Answer to this question is also valuable for understanding - what is better - to take one more growth scale of shift luck from luck 0 to luck 1. As luck 1 also switches on some events. And if these events just replace standard events, that the value of such increase is not so dramatic then if taking luck 1 would increase the probability of event by expanding the list of possible events.

[chrispedersen]

Actually, I did an analysis (and posted it) of the events, and death and magic are the two most relevent effects when you turn on luck.

turning on additional events is what I'm talking about in P(eip).
It seems to me there HAS to be an element tied to the province mask. Otherwise +3 luck and -3 Luck would be more likely to have the same values - and they dont.

[thejeff]

Thinking about how inefficient the "check for each possible event in a province" code would be, started me thinking about how else you could do it.

Seriously, you'd have to build a list of possible events for every province you wanted to check, they'd all be potentially different and then generate a random number and check against the probability for that province.
Why go to that trouble when you could just select 1 from the list? But then you'd still have to build the list and you'd always get one, which doesn't seem to match the results. OK, what if you just pick one from the full list and then check to see if it's valid for that province. If it is, great, if not you could give up and have no event or try again a limit number of times.

That seems to be a better mechanism for what chris is proposing, though I'm not sure if it makes any difference in results.

I still think there's some effect we're missing for the number of events, linked to empire size or possibly turn number.

We know some events that are linked to scales, but is there a complete list? Knowing which scale setting had the most and least possible events would help testing this.

[chrispedersen]

Originally Posted by thejeff

Thinking about how inefficient the "check for each possible event in a province" code would be, started me thinking about how else you could do it.

Seriously, you'd have to build a list of possible events for every province you wanted to check, they'd all be potentially different and then generate a random number and check against the probability for that province.
Why go to that trouble when you could just select 1 from the list? But then you'd still have to build the list and you'd always get one, which doesn't seem to match the results. OK, what if you just pick one from the full list and then check to see if it's valid for that province. If it is, great, if not you could give up and have no event or try again a limit number of times.

That seems to be a better mechanism for what chris is proposing, though I'm not sure if it makes any difference in results.

I still think there's some effect we're missing for the number of events, linked to empire size or possibly turn number.

We know some events that are linked to scales, but is there a complete list? Knowing which scale setting had the most and least possible events would help testing this.

But jeff, a lot of this is what I said. Make a list of all available luck events in a province. this is what I call the province mask

now, you could just make a full listing of all eligible events and then roll randomly against the list. number of provinces would then not figure into it at all

The question still becomes - how do you generate the number of times to roll against the list.

Whereas, if you check All of a provinces random events, you would see what we see empirically happening - much more events for luck +-3.

[chrispedersen]

So again, with the same nations, same cbm and the same luck scales 0 0 -3 +3
this time I added +3 order to all nations.

Strong results, again. Over 50 turns:

6,3,26,28 luck events

So the order cancelled out luck, even though luck was suppsed to have a stronger effect.

Personally considering how JK did % chances on magic paths, I feel sure that the addition or subtraction of chance is just added or subtracted from the base chance.

It seems to me, that this give us the base for testing.
Write a mod such that you increase the effect of order until such time as you no longer get any events.


However if you start with p=20, and then deduct 15 for order you'd get about 1/4 the events.

likewise with p=20 and o order +3/-3 luck would give a 41% luck chance - slightly more than doubling.

I again noticed fewer events in the start.

[Finalgenesis]

At least that part is intuitive:

When it says +15% events, it really means +15% events....

That's good to know.

Throw in some magic +3 in there will you :P, that's the next big one I think.

[thejeff]

Originally Posted by chrispedersen

But jeff, a lot of this is what I said. Make a list of all available luck events in a province. this is what I call the province mask

now, you could just make a full listing of all eligible events and then roll randomly against the list. number of provinces would then not figure into it at all

The question still becomes - how do you generate the number of times to roll against the list.

Whereas, if you check All of a provinces random events, you would see what we see empirically happening - much more events for luck +-3.

I think one of us is misunderstanding the other. Probably my fault, since I was describing how I came up with it as much as the theory itself.

Here's how it works under this theory:
First roll the chance of each of the 4 possible events, based on the capital (or pretender?) scales.
For each event generated, pick a random province. In each province pick a random event off the complete list. If the event is not possible, given the provinces scales, terrain and any other conditions, stop. No event happens. (Possibly, reroll a limited number of times.)

Thus, the more events your scales unlock, the more likely you'll actually get an event.
This should get similar effect to checking each possible event in a province with much less work and avoid some of the weirder side effects, such as events earlier in the list being more common than ones later in the list.

You get many more events for Luck +/-3 both do to the increase in chance of generating an event to start with and the increased number of events unlocked. I don't know enough about the number of events possible at different scales to guess how big the second factor is.

Does that make it more clear? Or am I still missing something?


I still think there's more going on. I'm not convinced that number of provinces doesn't play a role. I'll try to test a few more different size nations when I have the chance.
I'm also not sure about the base chances being based on capital scales. Possibly testable using 3L3T and skeptics to hold down capital dominion?

Also terrain plays a role in this. At the very least some events are only possible on land and others in the water. If there are less water events, then you should get less events in water provinces than elsewhere. This may be easier to test than events in different scales since terrain stays consistent and you don't have to worry about dominion spread.

[chrispedersen]

Originally Posted by thejeff

Here's how it works under this theory:
First roll the chance of each of the 4 possible events, based on the capital (or pretender?) scales.
For each event generated, pick a random province. In each province pick a random event off the complete list. If the event is not possible, given the provinces scales, terrain and any other conditions, stop. No event happens. (Possibly, reroll a limited number of times.)

Thus, the more events your scales unlock, the more likely you'll actually get an event.

Ok, we agree on most of this. The difference is that I suggested choosing an event from a tailored list for the province
you suggested pulling a random event and then checking if its applicable. I mentioned that as a possibility as well.

Essentially, logically, this means

Generate # of luck events.
Generate event for each luck event
Randomly choose province.
See if province allows event.

We know that JK likes bit masks, so the last step would just be XORing the event bit mask with the province mask and if true applying the event.

This should get similar effect to checking each possible event in a province with much less work and avoid some of the weirder side effects, such as events earlier in the list being more common than ones later in the list.

I think thats a weekness, because if you take luck -3 and turmoil -3 you are going to get NEVER ENDING hordes of barbarians.

If you take Death 3 and misfortune 3 - you get never ending hordes of plague events.

It can't work this way - because the generation of the event would not generate all these barbarian events, death events.

You get many more events for Luck +/-3 both do to the increase in chance of generating an event to start with and the increased number of events unlocked. I don't know enough about the number of events possible at different scales to guess how big the second factor is.

If you look at the results for Luck 3 vs luck -3, the both should have the same number of events. Luck -3 had 20%(?) more events. The second factor (unlocking events) has to be huge.

Also, if you look at luck 0 vs luck -3 - they are generating 2.5 times the number of events. The luck difference is supposed to be 21% more events - but it is 250%.

I'm also not sure about the base chances being based on capital scales. Possibly testable using 3L3T and skeptics to hold down capital dominion?

Well, I think some useful tests are:

1. Make a mode that increases the order effect. Find out at what level you cease to get luck events.
This will allow us to isolate P(e).

Once you isolate P(e) you can check what effect dominion has. Personally I'm fairly sure that dominion is only relevent to determine the luck scale in a province.

2. Do a check with 1 province. Use turmoil 3 luck -3.
Examine the maxium number of events that occur Turns 1-10, Turns 11-20, 21-30, 30+

I'm pretty sure that you will see 4 events if you capture for 40 turns post turn 30.
And I'm bummed for not getting a single thanks for all these tests!!!

[thejeff]

Originally Posted by chrispedersen

I think thats a weekness, because if you take luck -3 and turmoil -3 you are going to get NEVER ENDING hordes of barbarians.

If you take Death 3 and misfortune 3 - you get never ending hordes of plague events.

It can't work this way - because the generation of the event would not generate all these barbarian events, death events.

You're saying that events do seem to be weighted towards one end of the list? I'd expect that to manifest more as some events being more rare than they should be. Events early in the list will be more common, but only slightly so. To get the effects we see, P(eip) would have to be small enough that it makes it through the whole list fairly regularly, which means that any weighting towards the front of the list would be small. The cumulative effect might be large by the end, but still hard to detect.

If you look at the results for Luck 3 vs luck -3, the both should have the same number of events. Luck -3 had 20%(?) more events. The second factor (unlocking events) has to be huge.



Also, if you look at luck 0 vs luck -3 - they are generating 2.5 times the number of events. The luck difference is supposed to be 21% more events - but it is 250%.

The first seems very weird to me. Without knowing more about how many events are possible at each scale, I'd hesitate to draw any conclusions from it.

The second may not be strange. If the bonus from luck scales is just added to the base chance, then it wouldn't be 21% more events. Assuming 10% base chance for the sake of argument, 21% more events would be 10% *1.21 = 12.1% chance
Straight addition gives you 10%+21% = 31%, a 310% increase.

Well, I think some useful tests are:

1. Make a mode that increases the order effect. Find out at what level you cease to get luck events.
This will allow us to isolate P(e).

Once you isolate P(e) you can check what effect dominion has. Personally I'm fairly sure that dominion is only relevent to determine the luck scale in a province.

2. Do a check with 1 province. Use turmoil 3 luck -3.
Examine the maxium number of events that occur Turns 1-10, Turns 11-20, 21-30, 30+

I'm pretty sure that you will see 4 events if you capture for 40 turns post turn 30.
And I'm bummed for not getting a single thanks for all these tests!!!

Thanks for the tests

I've got a couple of things I want to try as well. I'm not as convinced as you are that number of provinces isn't a factor, so I want to run some tests with the scales I used before on smaller empires.

I'd also like to try something with a water nation, since there should be fewer events available underwater.

I really want a list of events & scales.

[militarist]

"I really want a list of events & scales."

But there is an Edi's DB of events, you can find it easily.