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Topic: Net Melee Balance Mod: ALL ABOARD (Read 39791 times)
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jaychant
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I guess I just don't understand how probability works.
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Resh Aleph
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Rottem Tomatoes
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The probability for resurrecting once is 0.75.
Yes, if by "resurrecting once" you mean "resurrecting at least once", which I suppose is the intuitive interpretation of those words. The number in my table is the probability for resurrecting exactly once, which is a stricter interpretation.
Cedric's table has the correct "at least" probabilities (though he didn't do tildes, which might awake the wrath of the Gods of Mathematics...... or something).
Edit: By the way, I just learned how to find the "averages" mathematically. For vanilla UQM, the expected value for the first failure is 1 / 0.5 = 2, meaning 1 resurrection. For the mod:
0.2625*1 + 0.219375*2 + 0.147469*3 + 0.078427*4 + 0.031672*5 + 0.008974*6 + 0.001504*7 + 0.000079*8 = 1.680729 (approx.)
A nice exercise in probablity, this has been. 
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« Last Edit: May 25, 2009, 08:53:36 pm by Resh Aleph »
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Marines on Maulers and limpets on Earthlings / Bright Podship plasma and warm Kohr-Ah death rings /
Shofixti Scouts doing gravity whips / These are a few of my favorite ships! © meep-eep
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Resh Aleph
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I believe you, I just don't understand why.
Because, while 0 resurrections and 1+ resurrections indeed have the same chances, when you do get 1+ resurrections, you have a fairly good chance of getting more than just 1. So while the weight of the 1+ resurrections group is the same as 0's, its "center of gravity" is higher than 1, which raises the average a bit from 0.5.
Why is it exactly 1? Well...
Let's list all possible results for a match. I choose to represent each result as the number of the first resurrection attempt that fails. So 1 represents a match where the first resurrection fails (meaning 0 resurrections), 2 represents a match with a single resurrection, and so on.
The possible match results are 1, 2, 3, 4, 5, ...
Their corresponding probabilities: 1/2, 1/4, 1/8, 1/16, 1/32, ...
It turns out that if you want the average result over a large number of matches (the so-called expected value), you simply sum all possible results multiplied by their chances. Makes sense. Let's do it then:
1*(1/2) + 2*(1/4) + 3*(1/8) + 4*(1/16) + 5*(1/32) + ... =
= 1*(1/2)1 + 2*(1/2)2 + 3*(1/2)3 + 4*(1/2)4 + 5*(1/2)5 + ...
Now, for reasons beyond me, it holds that for all -1 < p < 1,
p + 2p2 + 3p3 + 4p4 + 5p5 + ... = p / (1-p)2.
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UPDATE - proof:
For all -1 < p < 1 it holds that
1 + p + p2 + p3 + p4 + p5 + ... = 1 / (1-p)
(Just your everyday geometric series.) Now, differentiate both sides as functions of p:
0 + 1 + 2p + 3p2 + 4p3 + 5p4 + ... = 1 / (1-p)2
And multiply both sides by p to get the equation. Q.E.D.
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In our case p = 1/2, so we get (1/2) / (1/2)2 = 2.
So the average result (first-failed-attempt) is exactly 2, making the average number of resurrections exactly 1. Crystal clear now, isn't it?
By the way, the calculation for the mod is simpler:
1*0.2625 + 2*0.219375 + 3*0.147469 + 4*0.078427 + 5*0.031672 + 6*0.008974 + 7*0.001504 + 8*0.000079 = 1.680729
The match results I used here are the number of successful resurrections, not the first failed one. So the average resurrection count is approximately 1.680729.
(Talk about thread derailment...)
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« Last Edit: May 26, 2009, 09:57:36 pm by Resh Aleph »
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Marines on Maulers and limpets on Earthlings / Bright Podship plasma and warm Kohr-Ah death rings /
Shofixti Scouts doing gravity whips / These are a few of my favorite ships! © meep-eep
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Cedric6014
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In other words, just toss a coin a few times
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Shiver
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Aaaaaaanyway... Back on topic, I have a bug to report. The mod seems to crash quite often when playing Dreadnought vs. cyborg (happened once vs. cyborg Broodhome and then again vs. cyborg Terminator). I know the mod is designed for PvP games, but cyborg mode is still useful for basic practice.
I had that crash, but it was a long time ago and hasn't happened to me since I applied something that might possibly fix it. I played a bunch of games against the cyborg and it isn't crashing at all. I don't think that's a cyborg-related bug, at any rate.
Oh, and my fighters seem to crash into DOGIs and die. Is that supposed to happen? 
Yes. DOGIs and marines will smash a fighter apart if they get close to them.
Alephresh: Are you playing v1.10? Have you got the effects package working properly? What color are those Ur-Quan fighters?
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« Last Edit: May 28, 2009, 05:59:18 pm by Shiver »
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jaychant
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Another reason for playing against the cyborg is there just never seems to be someone (active) at #uqm-arena. I've gone there at least 5 times in the past week, and was never able to play a game with someone. 
I have noticed that when a Chenjesu finishes off a Dreadnought, the game often crashes (usually when the photon shard actually hits), but I have also noticed this in vanilla UQM and it has been happening ever since I made my stupid mod, so it doesn't look like it's really a bug in the balance mod.
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Gekko
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Another reason for playing against the cyborg is there just never seems to be someone (active) at #uqm-arena. I've gone there at least 5 times in the past week, and was never able to play a game with someone.
00:15 -!- jaychant [n=julian@adsl-75-45-186-9.dsl.sfldmi.sbcglobal.net] has joined #uqm-arena
00:16 < jaychant> Hey Elvish_Pillager, how about a game?
00:17 < jaychant> OK, roflcat, are you here?
00:17 < jaychant> How about you Gekko?
00:18 < jaychant> AmonX?
00:18 -!- jaychant [n=julian@adsl-75-45-186-9.dsl.sfldmi.sbcglobal.net] has left #uqm-arena []
00:20 < Gekko> ... I was going to play with him
23:06 -!- jaychant [i=4b2dba09@gateway/web/ajax/mibbit.com/x-275131b01af3446e] has joined #uqm-arena
23:07 < jaychant> Shiver_ I don't suppose you're here?
23:08 < jaychant> OK then... AmonX, Gekku, TheMisterCat?
23:09 < jaychant> Oh well...
23:09 -!- jaychant [i=4b2dba09@gateway/web/ajax/mibbit.com/x-275131b01af3446e] has quit [Client Quit]
23:27 < Shiver_> If he won't read the topic, I can't help him
13:47:15 -!- Topic for #uqm-arena: Welcome to The Ur-Quan Masters netplay arena. Activity in this channel is low these days. If you're looking for a game, ask and wait at least 10 minutes. || Visit http://wiki.uqm.stack.nl/Netplay_howto for information about connecting to other players. || Problems with netplay? The tutorial at http://www.gekko.frud.biz/uqmtutorial/ may solve your problem.
I was going to play with you a few days ago, but didn't make it in time. It's not like we are staring at our irc clients, just waiting for games 
Stay there a bit longer next time.
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« Last Edit: May 29, 2009, 12:53:56 pm by Gekko »
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