| Odds on Last Movement |
Thu, 07 May 2009 16:26  |
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Has anyone done any statistical analysis to determine what the odds are on having last movement when there is less than 20% difference in mass?
The Stars engine is supposed to make up to a 15% random adjustment in mass to allow near equal weight ships an equal chance. I expected to see a small advantage in say a 10% lighter ship but I couldn't pick it up in a quick simulation. If the 15% random function was a binomial or bell curve, there should be a significant difference. Even if it is a coin toss, I would expect a bigger difference on a weight reduction.
Has anyone done any analysis on this? I am curious to figure out at what point the mass makes a difference on the probability of who moves last.
The Universe is usually not fair.
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| Re: Odds on Last Movement |
Fri, 08 May 2009 07:51  |
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| Micha wrote on Thu, 07 May 2009 16:49 |
AlexTheGreat made a study and an excel sheet about this, I don't know if he has a link to the sheet somewhere, or if it's on Stars!wiki ...
He might pick up your post or you could send him a mail/PM ...
mch
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I don't have it in an uploadable place right now but I'll look into that possibility over the next couple of days.
If you want it urgently send me an email to mcdonaldjk at bigpond dot com.
Also Gible, if you want it for the Wiki it's not a problem.
To give you a quick idea, if the heavier ship is exactly 10% heavier than the lighter one then the chances of the heavier ship moving last is 23.35%.
[Updated on: Fri, 08 May 2009 07:58] Report message to a moderator
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| Re: Odds on Last Movement |
Sun, 10 May 2009 22:45 |
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Thanks to the information provided by AlexTheGreat and some additional effort confirming the data I think I can answer my own question.
| Stars Player Guide |
Each part tokens move in order from heaviest to lightest with a margin of +/-15%.
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Knowing that there was up to a 15% adjustment factor wasn't enought to calculate the probability unless I had an idea on how the randomizing was done.
- It could be binomially calculated (e.g. Mass less 15% plus 1% up to 30 times for each coin flip that was heads).
- One shot binomial: 15% is added subtracted subtracted or no change to the mass depending on a random variable.
- It could be calculated based on a Normal distribution.
- Or the 15% randomness could be calculated based on equal chance of hitting any percentage between -15% and + 15% (i.e. equal Mass -15% + 30% * Rnd). This is sort of the way that planet enviroments are determined.
In AlexTheGreat spread sheet, the formulas are based on the 4th way.
Being a natural skeptic I thought it would be best to run some tests to show whether that calcution is about right. This was not an easy matter but I have reasonable results. I will put them up in a separate follow-on message.
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| Re: Odds on Last Movement |
Mon, 11 May 2009 00:55 |
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To get a better idea of the odds of last move I put together a simulation. With one race I produced a 320KT BB with a weak range 3 weapon and 2 1/4 speed and the race other I produced six different BB with weak range 1 guns, speed of 1 1/4. The 6 ship designs had mass of equal to 320KT less 3%, 5%, 7%, 10%, 15% and 20%. The idea is to look at battles and see the last movement on each of the 16 move segments of each battle as the range 3 ship tried to move away and the range 1 ship tried to close.
I arranged for 15 battles of each design and only looked at the last move of each sequence. That should give me 16 x 15 or 240 data points for each design. 240 x 6 designs = 1440 battle moves to evaluate. 
I only completed about 1072 of the 1440 evaluations (before losing my mind) 
Unfortunately, there is at least one issue with this evaluation. One of the movement choices is not to move at all. When stars chooses that, no movement is recorded and the battle simulator does not even indicate a movement for that token. Despite this issue, I think I got reasonable results:
Odds of Lighter Ship Moving First:
2% Observed 69% Predicted* 56%
5% Observed 64% Predicted* 63%
7% Observed 74% Predicted* 71%
10% Observed 84% Predicted* 79%
15% Observed 90% Predicted* 89%
20% Observed 97% Predicted* 97%
* Predicted by equations from AlexTheGreat
Except for the 2% case, the observed results follow closely the expected results.
I have some charts and graphs if anyone is interested.
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| Re: Odds on Last Movement |
Mon, 11 May 2009 01:24 |
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| DenHam wrote in an email on Mon, 11 May 2009 17:10 |
Here is my spreadsheet and graph. It includes results from 1072 battle simulation last moves. I used movement of 1 1/4 with range 1 guns for the lighter ship and 2 1/4 with range 3 guns for the heavier ships. This seems to provide the best simulation for last moves. I ignored first moves. See my post for more information.
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How exactly does having different speeds help?
[Updated on: Mon, 11 May 2009 01:25] Report message to a moderator
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| Re: Odds on Last Movement |
Mon, 11 May 2009 02:15 |
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| gible wrote on Mon, 11 May 2009 01:24 |
| DenHam wrote in an email on Mon, 11 May 2009 17:10 |
Here is my spreadsheet and graph. It includes results from 1072 battle simulation last moves. I used movement of 1 1/4 with range 1 guns for the lighter ship and 2 1/4 with range 3 guns for the heavier ships. This seems to provide the best simulation for last moves. I ignored first moves. See my post for more information.
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How exactly does having different speeds help?
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I think Denham was trying to determine whether or not BS made a difference.
I was pretty sure that I had the odds calculation right when BS was equal but in my email to Denham & yourself I included a disclaimer (as shown in your Wiki entry on MoveLast) whereby I suspected that BS would make no difference but that I had not confirmed that suspicion to date.
BS 2.25 v 1.25 is a good choice for the comparison since it means that the faster ship always has more movement potential than the lighter one.
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| Re: Odds on Last Movement |
Mon, 11 May 2009 05:15 |
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| AlexTheGreat wrote on Mon, 11 May 2009 18:15 |
| gible wrote on Mon, 11 May 2009 01:24 |
| DenHam wrote in an email on Mon, 11 May 2009 17:10 |
Here is my spreadsheet and graph. It includes results from 1072 battle simulation last moves. I used movement of 1 1/4 with range 1 guns for the lighter ship and 2 1/4 with range 3 guns for the heavier ships. This seems to provide the best simulation for last moves. I ignored first moves. See my post for more information.
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How exactly does having different speeds help?
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I think Denham was trying to determine whether or not BS made a difference.
I was pretty sure that I had the odds calculation right when BS was equal but in my email to Denham & yourself I included a disclaimer (as shown in your Wiki entry on MoveLast) whereby I suspected that BS would make no difference but that I had not confirmed that suspicion to date.
BS 2.25 v 1.25 is a good choice for the comparison since it means that the faster ship always has more movement potential than the lighter one.
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No, I don't think he was, otherwise he'd have used more than two different speeds, surely. That's what I couldn't understand, since(this study aside) how battle speed is turned into battleboard moves is fairly well understood already.
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| Re: Odds on Last Movement |
Mon, 11 May 2009 10:18 |
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[quote title=gible wrote on Mon, 11 May 2009 01:24]| gible wrote |
How exactly does having different speeds help?
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You are right that the speed was set to be 2 1/4 versus 1 1/4 always giving the heavier ship exactly 1 extra move in each sequence. The thinking was that in an open battlefield using the extra move the range 3 ship will move to range 2 if it has the last move, and that the range 1 ship will move to range one or zero if it has the last move.
Beleive it or not Range 2 versus Range 3 does have the same obvious dynamics because the range 3 ship will almost always move into within range 2 range.
One of the issues with using 16 moves in each battle is that the lighter range 1 ship will at some point corner the heavier ship. When cornered, no move will improve the heavier ships position. In this case the results might be a little skewed since the heavier ship might choose not to move at all. If I had a lot of free time, a more careful analysis would exclude all "cornered" move sequences.
Two times there was a move sequence where neither ship moved at all. I had to exclude that from the data.
The Universe is usually not fair.
That would be too easy.Report message to a moderator
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