ackanomic Digest Tuesday, March 02 1999 Volume: 04 Issue: 059 ---------------------------------------------------------------------- From: Eric Plumb Subject: Acka: Decadence Date: Tue, 02 Mar 1999 04:51:22 -0500 (EST) I convert 18 points into whatever amount of Mannna that gives me today. Likewise with A$4. -Hubert Line dancing: Look what happens when cousins breed. ------------------------------ From: K 2 Subject: Re: Acka: Proposal 4106 Date: Tue, 02 Mar 1999 11:06:16 -0500 (EST) #retract 4106 #end I made a small mistake in my calculations; the situation is _much_ worse :-) K 2 JT wrote: > I believe btw that knight and horse need to be two distinct players, so > rufus on rufus isn't valid. I know; but it is the best combination we have - although rAtF on rufus comes close. > However, I seem to recall (and I'd intended > that characteristic tests be more fair than you were portraying). A single characteristic test is quite fair : for two players with the same value for a characteristic they have equal chance of winning and the probability alters as you would expect as the characteristic difference increases. Defeating the dragon, however, requires the multiplication of probabilities generally less than 50% (the dragon has higher stats remember) so: > I'd be interested in how you determined your probabilities. dis-interested parties should look the other way :-) in the (illegal but current optimal case) of rufus on rufus the knight has 50% and 32% of succeeding in eir intelligence and strength tests giving the knight and 16% chance of winning though. (rufus str:13;int:10 vs Dragon str:13;int:14) for rufus as the horse: 32% and 3% in the constitution and wisdom battles. Total chance 0.88%. (rufus con:16;Wis:12 vs Dragon con:18;Wis:20) Chance that both horse and knight win through: 0.14% Then the dragon has a 40% chance of breathing on each of em: 60% chance the knight survives * 60% chance the horse survives = 36% 60% chance the knight survives * 40% change the horse dies * 32% chance of the knight winning a constitution test = 7.68% (36%+7.68%)*0.14% = 0.061% chance of killing the dragon (so I rounded up before :-) Probabilities of winning individual tests were calculated using the central limit theorem - ie by approximating the distribution of the difference in test rolls to a normal distribution of mean 0 and standard deviation SQRT(8.75*2). (the difference of two 3d6 distributions of u=10.5 and s=8.75) where: Vd and Vp = the Dragon's and player's Characteristic Rd and Rp = the Dragon's and player's test roll For the player to win: Vd-Rd <= Vp-Rp Vd-Vp <= Rd-Rp so for a player/dragon combo with equal stats for the player to win: 0 <= Rd-Rp [or 0 >= Rp-Rd which is what I used :-) ] **Brain Wave*** I just realised that the Dragon's stats are do not have the same distribution as player's The dragons stats : 1d10 + 10 player stats: 3d6 In my calculations test rolls of both parties were 3d6, so it was in error: I should've use a normal distribution with mean -5 and standard deviation SQRT(17) (the difference between a 3d6 distribution (u=10.5,s=sqrt(8.75)) and a 1d10+10(u=15.5,s=sqrt(8.25)) - negative values in this distribution represent circumstances where the Dragon has a higher test roll. without doing any calculations it can been seen that the range of values which would permit the player to win (0 to 7) represent a small percentage of the range of values that permit the dragon to win (-17 to 0) when their stats are equal (the dragon's stats are generally higher) doing the calculations reveals the probability of a player rescuing the rule as several orders of magnitude worse. (0.00000677% for rufus/rufus) Even under the previously proposed scheme the best legal combo only had a 0.69% chance of success :/ The proposal I just submitted gives rAtF/rufus ~30% chance; two perfect players ~100%. The values will vary depending on the dragon tho.... K 2 ------------------------------ From: K 2 Subject: Re: Acka: Proposal 4110 Date: Tue, 02 Mar 1999 11:14:32 -0500 (EST) #harfy 4110 #end 'tis Harfy K 2 ackabot@ackanomic.org wrote: > Proposal 4110 > Paradigm Type: Painless Precedence > rice > Due: Tue Mar 9 04:56:37 1999 ------------------------------ From: K 2 Subject: Re: Acka: Proposal 4107 Date: Tue, 02 Mar 1999 11:22:03 -0500 (EST) #harfy 4107 4110 #end What the heck, this is harfy as well K 2 ackabot@ackanomic.org wrote: > Proposal 4107 > strawberry cake > two-star > Due: Mon Mar 8 10:38:02 1999 > > {{two-star is removed from vacation}} ------------------------------ From: JT Subject: Re: Acka: Proposal 4106 Date: Tue, 02 Mar 1999 12:33:29 -0500 (EST) On Tue, 2 Mar 1999, K 2 wrote: >Probabilities of winning individual tests were calculated using the >central limit theorem - ie by approximating the distribution of the >difference in test rolls to a normal distribution of mean 0 and standard >deviation SQRT(8.75*2). (the difference of two 3d6 distributions of >u=10.5 and s=8.75) Here's where I think you are wrong.. the current rule already says to use the same distribution as the range of the stat, so the test roll for the dragon would (I think) be 1d9+11 and the player would be 3d6. This means that the dragon has a linear test roll and a players chances improves greatly at higher player stats since the test is at how well you 'beat' your current score. Your range for the dragon below is wrong since the dragon cannot ever get lower than an 11 on his roll so cannot ever beat his score by more than 9. The player on the other hand can beat his score by 15 in the extreme case (he has a 18 and rolls a 3), by 10 in the 'average' case (he has an 18 and rolls a 10), and in the normal case will probably be somewhere around 0-4 beating the score (stat of 10-14 and a roll of 10). I agree that the extra 40% survival rate needs to go, but I think changing the actual test distribution is wrong. Since I see you did not do so, I will be voting for your prop. --JT -- [-------------------------------------------------------------------------] [ Practice random kindness and senseless acts of beauty. ] [ It's hard to seize the day when you must first grapple with the morning ] [-------------------------------------------------------------------------] ------------------------------ From: JT Subject: Acka: Potato (/dev/joe) Date: Tue, 02 Mar 1999 13:05:53 -0500 (EST) /dev/joe has the Potato since yesterday at 12:00 Blest Lax Monk Pal therefore has the Tuba. --JT -- [-------------------------------------------------------------------------] [ Practice random kindness and senseless acts of beauty. ] [ It's hard to seize the day when you must first grapple with the morning ] [-------------------------------------------------------------------------] ------------------------------ From: JT Subject: Acka: Phoebe (Still on Vacation) Date: Tue, 02 Mar 1999 13:08:48 -0500 (EST) Using my trained Carrier Mosquitos, I have recieved a message from Phoebe. She says that she is enjoying her Leave of Absence and is considering returning soon, but hopes she'll be more appreciated this time around. She says she will be gone for at least another week. --JT -- [-------------------------------------------------------------------------] [ Practice random kindness and senseless acts of beauty. ] [ It's hard to seize the day when you must first grapple with the morning ] [-------------------------------------------------------------------------] ------------------------------ From: K 2 Subject: Re: Acka: Proposal 4106 Date: Tue, 02 Mar 1999 20:23:44 -0500 (EST) JT wrote: > On Tue, 2 Mar 1999, K 2 wrote: > >Probabilities of winning individual tests were calculated using the > >central limit theorem - ie by approximating the distribution of the > >difference in test rolls to a normal distribution of mean 0 and standard > >deviation SQRT(8.75*2). (the difference of two 3d6 distributions of > >u=10.5 and s=8.75) > > Here's where I think you are wrong.. the current rule already says to use > the same distribution as the range of the stat, so the test roll for the > dragon would (I think) be 1d9+11 and the player would be 3d6. I address this under **Brain Wave** it makes things worse. ------------------------------ From: "Gavin M. Doig" Subject: acka: What is it? Date: Tue, 02 Mar 1999 21:32:44 -0500 (EST) I convert all my points into as much Mannna as I get for converting all my points into Manna. BLMP. ------------------------------ Subject: Re: Acka: What is it? From: Joseph DeVincentis Date: Tue, 02 Mar 1999 22:21:11 -0500 (EST) #mannna 20 gavindoig #end BLiMP wrote: > I convert all my points into as much Mannna as I get for converting all my > points into Manna. > > BLMP. The best I can figure is that this converted 40 points into 20 mannna. K2's site is down so I'm going from the ackanomic.org mirror + recent props. If this is wrong we can fix it later when K2 gives us the real total. /dev/joe ------------------------------ End of ackanomic Digest V4 #59 ******************************