[SETUP]Mafia Rebels

[Allomancer]

2 : 2 : 2

Town: lynch a mafia
Loyalists: Lynch a rebel
Rebels: lynch anyone

An (mostly) uninformed majority is hunting an informed minority. But does every faction have a path to victory?

lynch a rebel -> 2 : 2 : 1, mafia endgames the town, townies lose, mafia fight it out
lynch a loyalist -> 2 : 1 : 2, same thing but rebels win.

I don't think town getting endgamed here is necessarily the right way to go. Especially with 2:1:2. In 2:1:2, if mafia were to gang up on town, the loyalist would have no chance of winning in 0:1:2. Therefore, the loyalist has no incentive to team up with the rebels, and would instead work with the town to hunt rebels. Therefore, town would have a path to victory by lynching a rebel, which would leave 2:1:1. 2:2:1 is a bit different, because the rebel might have incentive to work with the loyalists if the rebel believes they could survive LyLo. However, the rebel could just as well team up with town to hunt loyalists, so town would still have a shot at winning. At 1:2:1 or 1:1:2, however, town has no chance of winning and gets endgamed.

[Awoo]

Point noted. That correction I made in my last post indeed invalidates my conclusion on 2..2..2.

I am scratching my head a bit on 2..2..1. Sure rebel and loyalists could genocide town... but town could do the same thing with the loyalists??? Super weird

[Bicephalous Bob]

when the last goon is close to being lynched, they have no incentive not to out the rebels, and vice versa.

[Sukima]

Do Lynched Mafia Rebels appear as Rebels or Goons? IE Do the Loyalists know how many of each are alive in their minigame?

[Awoo]

when the last goon is close to being lynched, they have no incentive not to out the rebels, and vice versa.

Counterpoint: when the last goon is close to being lynched, they have no incentive to out the rebels since they lost anyways lmao. Technically I would count that as gamethrowing/playing against wincon since you're not lynched until the hammer has come down. See: reaction tests, see : wiki article on the l-1 trust tell. So it's a bannable offense. And in twilight just don't be a salty bitch and the game is fine.

Do Lynched Mafia Rebels appear as Rebels or Goons? IE Do the Loyalists know how many of each are alive in their minigame?

Open setup, everyone flips as expected.

[Bicephalous Bob]

idk, if I'm the last goon and one rebel remains, I'll tell them in the PT that they'd better make sure I'm not lynched or I'll tell the town their identity

if I do get lynched next day, I'll out the rebel in twilight to make sure the next time I'm in the same situation the rebel will try harder

[northsidegal]

reminds me of like a game theory problem

in that it is beneficial to have the threat of outing the rebel if you're lynched but once you're lynched there's not actually a reason in that game for you to follow through with the threat

[callforjudgement]

Is there a reason for you to

not

follow through, though?

Technically speaking, following through rather than not following through would be playing to help your wincon in future games, but that's allowed in cases where you can't do anything about the current game.

[Awoo]

I'll out the rebel in twilight to make sure the next time I'm in the same situation the rebel will try harder

new rule: no talking in twilight if you got lynched, fuck that man

in a live game you wouldn't have that happen

[Awoo]

OK now that the blackmail BS has been taken care of lets get back to the fun stuff.

Mafia == 0: Townies win.

Rebels == 0, Town <= Loyalists, , Loyalists win.

Town == 0, Loyalists == Rebels : Rebels win.

Town == 1 : Townie gets endgamed. Game continues.

That looks a lot cleaner. Will come back later with a script that considers
- the new endgaming rules,
- 2-1-1 always has a mafia lynch
- X-X-X, X > 1, 3X is even always has a mafia lynch, since loyalists are working with the town to hunt the rebels and won't vote to kill a townie, but at odd numbers (3-3-3), majority wagon could be TTRRR on a townie,

feel free to add more special cases?

[Awoo]

Damn son, do I ever have some fruity flavors for you. Fixed my script, it goes a bit faster now. These numbers might not be the closest to 33/33/33 for each # of loyalists, especially at higher counts, but they're close enough.

White = balanced (~33/33/33)
Green = town-sided
Blue = loyalist-sided
Red = rebel-sided

Town ~= 1.439 * mafia, to achieve a number close to 0.33 winrate (experimentally determined)

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)

(2, 1, 1) : (0.3333333333333333, 0.3333333333333333, 0.3333333333333333)

(5, 2, 2) : (0.30952380952380953, 0.2976190476190476, 0.39285714285714285)

(7, 3, 2) : (0.33156565656565656, 0.36969696969696975, 0.29873737373737375)

(10, 4, 3) : (0.3377798671916319, 0.3418272903567021, 0.32039284245166594)

(12, 5, 4) : (0.31819070408190264, 0.3340082321727611, 0.3478010637453361)

(15, 6, 5) : (0.3247424884085269, 0.323481789220785, 0.35177572237068794)

(17, 7, 5) : (0.3331216062929153, 0.3511074451498975, 0.3157709485571869)

(20, 8, 6) : (0.3363249638084577, 0.3402160453312447, 0.32345899086029745)

(23, 9, 7) : (0.33862372587644596, 0.33220304939482476, 0.3291732247287293)

(25, 10, 8) : (0.32903776374343585, 0.3294754251834078, 0.34148681107315626)

(28, 11, 9) : (0.3315704390504144, 0.32420855520623804, 0.34422100574334763)

(30, 12, 9) : (0.33611376712146285, 0.33971656483603085, 0.3241696680425062)

(33, 13, 10) : (0.3377542180945532, 0.3341863414826711, 0.3280594404227756)

(35, 14, 11) : (0.3309732199772894, 0.33209266857785436, 0.336934111444856)

(38, 15, 12) : (0.33272449561083917, 0.3279823933765202, 0.3392931110126404)

(40, 16, 12) : (0.3360542371405945, 0.33947147966574026, 0.32447428319366506)

(43, 17, 13) : (0.33732181974093317, 0.33524792916149204, 0.3274302510975746)

(46, 18, 14) : (0.33840951757468973, 0.3315809572081033, 0.3300095252172067)

(48, 19, 15) : (0.33340577685442885, 0.3302013663276503, 0.3363928568179205)

(51, 20, 16) : (0.33457653189669884, 0.3272376938041801, 0.3381857742991207)

(53, 21, 16) : (0.3370636474569935, 0.33590889259673967, 0.32702745994626653)

(56, 22, 17) : (0.3379743814878407, 0.3328619492506305, 0.3291636692615285)

(58, 23, 18) : (0.33385525737002003, 0.3316620856131608, 0.3344826570168189)

(61, 24, 19) : (0.3348199377039419, 0.3291072017753312, 0.3360728605207266)

(64, 25, 20) : (0.3356900537358969, 0.32679133448241793, 0.3375186117816848)

(66, 26, 20) : (0.33767452709135753, 0.3337545370621238, 0.32857093584651825)

(69, 27, 21) : (0.33838287848123205, 0.3313778037126729, 0.3302393178060947)

(71, 28, 22) : (0.33499417458629516, 0.33045433695232196, 0.33455148846138255)

(74, 29, 23) : (0.33574441508132796, 0.3283939068190933, 0.33586167809957834)

(76, 30, 23) : (0.3374553581856525, 0.33441209287689777, 0.32813254893744936)

(79, 31, 24) : (0.3380839756655746, 0.33231122940934854, 0.3296047949250766)

(82, 32, 25) : (0.33866263996228313, 0.33036545535725337, 0.3309719046804633)

(84, 33, 26) : (0.3357845068588453, 0.32961769424889065, 0.3345977988922637)

(87, 34, 27) : (0.33639598275490623, 0.3278920891611723, 0.3357119280839212)

(89, 35, 27) : (0.3378528577826973, 0.33303481730006906, 0.32911232491723336)

(92, 36, 28) : (0.338377518965343, 0.3312768099970507, 0.330345671037606)

(94, 37, 29) : (0.33581526264730427, 0.33058278979475836, 0.3336019475579369)

(97, 38, 30) : (0.336365038182627, 0.3290038892454323, 0.33463107257194025)

(99, 39, 30) : (0.33766881468860976, 0.3336121717950113, 0.32871901351637844)

(102, 40, 31) : (0.33814841905828835, 0.3320094419572197, 0.3298421389844915)

(105, 41, 32) : (0.3385982688820158, 0.3304990807697329, 0.3309026503482507)

(107, 42, 33) : (0.3363389959814329, 0.32990912812713036, 0.33375187589143623)

(110, 43, 34) : (0.33680951538438064, 0.32853435556064575, 0.3346561290549732)

(112, 44, 34) : (0.337960307335746, 0.33261122728166864, 0.32942846538258497)

(115, 45, 35) : (0.33837679787270925, 0.3312163767681721, 0.33040682535911814)

(117, 46, 36) : (0.3363168071978033, 0.33066047598285325, 0.3330227168193429)

(120, 47, 37) : (0.3367499994282723, 0.3293807384864287, 0.33386926208529843)

(122, 48, 37) : (0.33780308769782225, 0.3331143444354414, 0.32908256786673573)

(125, 49, 38) : (0.33819068536826374, 0.33181891039779665, 0.3299904042339391)

(128, 50, 39) : (0.33855856265051126, 0.33058470647337695, 0.3308567308761111)

[Awoo]

Attempt at hitting 25/35/40

These are some... unintuitive results to say the least. Does it really make sense for random lynching to continue even if town has minority? Might need to rethink this one a bit before we try this again

Town ~= 1.05 * mafia

Spoiler: results

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)

(2, 1, 1) : (0.3333333333333333, 0.3333333333333333, 0.3333333333333333)

(4, 2, 2) : (0.2523809523809524, 0.30714285714285716, 0.44047619047619047)

(5, 3, 2) : (0.2396825396825397, 0.3968253968253968, 0.3634920634920634)

(7, 4, 3) : (0.2401931401931402, 0.3655011655011655, 0.3943056943056942)

(9, 5, 4) : (0.2411967117849471, 0.3498929175399763, 0.40891037067507646)

(11, 6, 5) : (0.24155222142838245, 0.3399804284368636, 0.4184673501347538)

(13, 7, 6) : (0.24185686660447736, 0.3333102288298142, 0.4248329045657083)

(14, 8, 6) : (0.23967407375133853, 0.36386275349347985, 0.3964631727551814)

(16, 9, 7) : (0.2404019241238113, 0.355222576580243, 0.4043754992959456)

(18, 10, 8) : (0.24091147435264335, 0.3485959489286229, 0.41049257671873357)

(21, 11, 9) : (0.2534571562666714, 0.3417481217211427, 0.4047947220121856)

(23, 12, 10) : (0.252624349078903, 0.33770991322163446, 0.40966573769946213)

(24, 13, 10) : (0.25092629146991363, 0.35578792483432153, 0.3932857836957644)

(26, 14, 11) : (0.2504773168114658, 0.35103489645569924, 0.3984877867328347)

(28, 15, 12) : (0.2500707339435054, 0.3470068580003045, 0.40292240805618984)

(30, 16, 13) : (0.2497025585815153, 0.343549807819801, 0.4067476335986835)

(31, 17, 13) : (0.24845145237161212, 0.3573109987051955, 0.39423754892319207)

(33, 18, 14) : (0.24826670490449693, 0.3534857325106874, 0.3982475625848154)

(35, 19, 15) : (0.248087248462828, 0.35012565659263584, 0.4017870949445359)

(37, 20, 16) : (0.2479148736895418, 0.3471508407794714, 0.4049342855309865)

(39, 21, 17) : (0.24775044484899084, 0.34449866371229665, 0.4077508914387121)

(40, 22, 17) : (0.24685776419572916, 0.35506264273706417, 0.39807959306720625)

(43, 23, 18) : (0.2526754785444076, 0.3512778140693404, 0.39604670738625164)

(45, 24, 19) : (0.25232693533653117, 0.34874882631912596, 0.3989242383443425)

(47, 25, 20) : (0.252001390967684, 0.34645002248643225, 0.40154858654588343)

(49, 26, 21) : (0.2516969032604193, 0.34435136767636854, 0.40395172906321164)

(50, 27, 21) : (0.25090309495711804, 0.35288054564490967, 0.39621635939797184)

(52, 28, 22) : (0.2506783648595799, 0.3506321224781672, 0.3986895126622524)

(54, 29, 23) : (0.2504646390114513, 0.34856141607795266, 0.4009739449105957)

(56, 30, 24) : (0.25026137922499003, 0.3466481725951477, 0.4030904481798617)

(57, 31, 24) : (0.2495809124467998, 0.354077300044081, 0.3963417875091186)

(59, 32, 25) : (0.24943291003064302, 0.35205670205087014, 0.39851038791848625)

(61, 33, 26) : (0.24928988365133203, 0.350177227143831, 0.4005328892048364)

(64, 34, 27) : (0.25309766612755424, 0.3478187366348233, 0.39908359723762193)

(66, 35, 28) : (0.2528404701956569, 0.3462110534268438, 0.40094847637749886)

(67, 36, 28) : (0.25222333538538244, 0.3525731870990083, 0.3952034775156087)

(69, 37, 29) : (0.2520140895571506, 0.3508840243567167, 0.3971018860861322)

(71, 38, 30) : (0.25181344610272466, 0.3492967170789176, 0.3988898368183572)

(73, 39, 31) : (0.25162097994797605, 0.3478023290795086, 0.40057669097251486)

(75, 40, 32) : (0.2514362791250121, 0.346392939197799, 0.4021707816771884)

(76, 41, 32) : (0.2509177059778999, 0.35197381129247873, 0.3971084827296209)

(78, 42, 33) : (0.25076665787175445, 0.35050146191538656, 0.39873188021285855)

(80, 43, 34) : (0.250620655838995, 0.3491076472573072, 0.40027169690369724)

(82, 44, 35) : (0.25047952639978927, 0.3477862515738982, 0.4017342220263119)

(85, 45, 36) : (0.25330947104177837, 0.3460781444950473, 0.4006123844631738)

(86, 46, 36) : (0.2528287698940495, 0.35103464442888094, 0.396136585677069)

(88, 47, 37) : (0.2526479786751398, 0.3497479540237878, 0.3976040673010718)

(90, 48, 38) : (0.25247337970740447, 0.34852248883931575, 0.39900413145327907)

(92, 49, 39) : (0.25230469965068164, 0.34735398370857695, 0.4003413166407407)

(94, 50, 40) : (0.2521416764208823, 0.3462385604092497, 0.4016197631698674)

[Sukima]

How is 2-1-1 a 33% town winrate? It says nightless but the mafia does get kills during the day? Or is this just the pure nightless version? IE 2-1-1 either loyalist or rebel gets lynched, and then 33% town 66% the surviving mafia.

[Awoo]

Here a consideration: 2:1:1 will never become 1:1:1. The loyalist has no incentive to lynch a townie in 2:1:1, because that would cause him to be endgamed by the rebel. Therefore, 2:1:1 will always result in a mafia lynch, and go to 3p LyLo with either a loyalist or a rebel. The only exception is if a plurality lynch were to happen, but by nature of the fact that a townie cannot be lynched, town should never let that happen. If nearing deadline with only 2 votes on a wagon, you can assume that wagon is on town and the person not voting is the loyalist.

[Sukima]

I mean, it's nightless, correct? Since if it's a version with kills, 2-1-1 is 0/50/50 because whoever doesn't get lynched gets to shoot town.

[Awoo]

nightless

gonna come back to rethink the whole "town doesn't lose until there's only one of them" thing. gonna run some numbers on a new script to give mafia the numbers to see what descision they should collectively make. Seems like if they can steal from town's slice of the EV and both make a profit, they absolutely should.

[Awoo]

Today we look at the situation where Mafia is strictly greater then Town. Should the townies be endgamed? The answer might surprise you.

Now, in order for the mafia to endgame the townies, a majority of people in the game must agree to pick off the townies one by one. According to the math, when townies are endgamed, Town EV always drops to zero, and Rebel EV always increases. But Loyalist EV sometimes goes up and sometimes goes down. Most of the time, Loyalist EV goes down. But when Loyalists >> Rebels, sometimes they can get an increase in EV. Usually it is a fraction of a percent, and the greatest I have seen it was around 4% at (36, 36, 1). The EV that loyalists get from endgaming townies is maximized at (X, X, 1).

Here is the minimum number of loyalists required for it to be worth it for the Loyalists co-operate with X rebels to endgame the townies, assuming the mafia has majority over the town.

(Rebels : Minumum # of Loyalists in order for it to be worth it for Loyalists to genocide town)

1 : 8
2 : 12
3 : 17
4 : 22
5 : 27
6 : 32
7 : 37
8 : 42
9 : 47

So basically if there are... 25 loyalists, and mafia outnumber town, the loyalists will agree to endgame the townies if and only if there are 4 or less rebels. Otherwise it becomes a -EV play for them, and they won't agree to it.

Neat. Seems to be a linear +5 kind of relationship with the first result being an edge case. And if you aren't paying attention you might ask the question "What about in the case where rebels already have majority of the vote?" well in that case they already won the game lmao

That being said, here are your new numbers given this new strategy mafia can take to steal some of town's EV. The 25/35/40 numbers are still really weird (town ~= 1.07 * mafia???) but that's simply because the mafia literally cannot agree to genocide the townies unless a LOT of the rebels die, and a lot of the townies die... and so yeah basically it would be a loyalist stomp anyways, lol. super weird game. i think 33/33/33 is closer to balanced/humanly playable.

Spoiler: 33/33/33

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)

(2, 1, 1) : (0.3333333333333333, 0.3333333333333333, 0.3333333333333333)

(5, 2, 2) : (0.3042328042328042, 0.2857142857142857, 0.41005291005291006)

(7, 3, 2) : (0.3285353535353535, 0.3628787878787878, 0.3085858585858585)

(10, 4, 3) : (0.3348710113415996, 0.33528236469412936, 0.329846623964271)

(12, 5, 4) : (0.31479420378137757, 0.3265377946050214, 0.3586680016136008)

(14, 6, 4) : (0.32555535840298255, 0.36057013124922666, 0.3138745103477907)

(17, 7, 5) : (0.33030351670768304, 0.3449303840055832, 0.3247660992867336)

(20, 8, 6) : (0.33350315842185313, 0.3340871314831376, 0.3324097100950092)

(23, 9, 7) : (0.3358051716088628, 0.3261261865558693, 0.33806864183526775)

(24, 10, 7) : (0.32862376672950083, 0.3489799357181533, 0.32239629755234567)

(27, 11, 8) : (0.3312353802666046, 0.3404964950456947, 0.3282681246877006)

(30, 12, 9) : (0.3332787844203904, 0.33374115433666274, 0.3329800612429468)

(33, 13, 10) : (0.3349201192240998, 0.32823455434958465, 0.3368453264263153)

(34, 14, 10) : (0.3299053747493422, 0.34427010708232775, 0.32582451816832975)

(37, 15, 11) : (0.33169400680499267, 0.3384812614728363, 0.3298247317221708)

(40, 16, 12) : (0.3331906993534664, 0.3335753954865756, 0.33323390515995777)

(43, 17, 13) : (0.33446104157236034, 0.32936476964116684, 0.33617418878647254)

(46, 18, 14) : (0.33555243778505534, 0.32571135138379664, 0.3387362108311478)

(47, 19, 14) : (0.33196207154909024, 0.3373295880319356, 0.3307083404189738)

(50, 20, 15) : (0.3331426621315704, 0.3334781723979372, 0.333379165470492)

(53, 21, 16) : (0.33417821549130733, 0.3300693110844264, 0.33575247342426595)

(56, 22, 17) : (0.335093717499441, 0.32703086361752104, 0.3378754188830376)

(57, 23, 17) : (0.3321374068809846, 0.3365843519910876, 0.3312782411279276)

(60, 24, 18) : (0.333112115801098, 0.33341429454547167, 0.33347358965343)

(63, 25, 19) : (0.333985993074693, 0.3305505565897953, 0.33546345033551117)

(66, 26, 20) : (0.3347737935263548, 0.327950784041163, 0.33727542243248176)

(67, 27, 20) : (0.33226082772562726, 0.33606267780605326, 0.3316764944683191)

(70, 28, 21) : (0.33309081997717116, 0.33336913396495804, 0.3335400460578705)

(73, 29, 22) : (0.3338466565139424, 0.3309001472606768, 0.33525319622538047)

(76, 30, 23) : (0.3345377696790975, 0.3286287600727968, 0.33683347024810545)

(77, 31, 23) : (0.3323523375071032, 0.33567709188244294, 0.3319705706104536)

(80, 32, 24) : (0.33307505022890366, 0.3333355226415396, 0.33358942712955636)

(83, 33, 25) : (0.33374093560368945, 0.33116561142173795, 0.33509345297457227)

(86, 34, 26) : (0.33435638651326655, 0.3291491502123991, 0.33649446327433397)

(87, 35, 26) : (0.3324228588732073, 0.3353804890772372, 0.332196652049555)

(90, 36, 27) : (0.33306286509863375, 0.33330953622056736, 0.33362759868079833)

(93, 37, 28) : (0.3336579341327956, 0.33137405643523943, 0.3349680094319646)

(96, 38, 29) : (0.3342125978210913, 0.3295611783823598, 0.3362262237965485)

(97, 39, 29) : (0.3324788513154641, 0.33514525460449424, 0.3323758940800412)

(100, 40, 30) : (0.333053147239128, 0.3332888463955342, 0.33365800636533743)

(103, 41, 31) : (0.3335910176630361, 0.33154207263292756, 0.3348669097040358)

(106, 42, 32) : (0.3340957915170941, 0.3298955005342189, 0.3360087079486866)

(107, 43, 32) : (0.3325243755072459, 0.3349541287026636, 0.33252149579009005)

(110, 44, 33) : (0.33304520511219393, 0.3332719847174547, 0.33368281017035106)

(113, 45, 34) : (0.3335359115679034, 0.3316803829257211, 0.33478370550637504)

(116, 46, 35) : (0.3339990118585772, 0.330172205348747, 0.3358287827926753)

(117, 47, 35) : (0.3325621105033691, 0.3347957690572998, 0.3326421204393306)

(120, 48, 36) : (0.3330385862919387, 0.3332579793635849, 0.3337034343444757)

(123, 49, 37) : (0.3334897356724681, 0.3317962260440886, 0.3347140382834426)

(126, 50, 38) : (0.33391750780692775, 0.3304050062736094, 0.3356774859194622)

Spoiler: 25/35/40

(Town, Loyalists, Rebels) : (Town EV, Loyalist EV, Rebel EV)

(2, 1, 1) : (0.3333333333333333, 0.3333333333333333, 0.3333333333333333)

(4, 2, 2) : (0.24285714285714283, 0.2857142857142857, 0.4714285714285714)

(5, 3, 2) : (0.2333333333333333, 0.3825396825396825, 0.3841269841269841)

(7, 4, 3) : (0.23459873459873457, 0.3529137529137529, 0.4124875124875125)

(9, 5, 4) : (0.23540838246720597, 0.3375611316787787, 0.4270304858540152)

(10, 6, 4) : (0.231620082703674, 0.3814493555979624, 0.3869305616983635)

(12, 7, 5) : (0.23337509620993266, 0.36461083729390364, 0.40201406649616367)

(14, 8, 6) : (0.23442020695486837, 0.3529415573118179, 0.4126382357333135)

(17, 9, 7) : (0.2508292454589185, 0.3429756245353707, 0.4061951300057105)

(19, 10, 8) : (0.24956800225795528, 0.3367077211222518, 0.4137242766197927)

(20, 11, 8) : (0.2471819235029959, 0.35878198175350684, 0.394036094743497)

(22, 12, 9) : (0.24656469712749457, 0.35176180110537103, 0.4016735017671342)

(24, 13, 10) : (0.2460119193228099, 0.34601582193758135, 0.4079722587396084)

(26, 14, 11) : (0.2455185232943984, 0.341226381171311, 0.4132550955342903)

(27, 15, 11) : (0.24389054223111806, 0.3572472644715492, 0.3988621932973324)

(29, 16, 12) : (0.24366405359661286, 0.35208962811576583, 0.40424631828762103)

(32, 17, 13) : (0.2517024243632382, 0.34669049188054135, 0.4016070837562202)

(34, 18, 14) : (0.25097908718887374, 0.3429437073782299, 0.4060772054328961)

(35, 19, 14) : (0.24952049149103836, 0.35540876158174195, 0.39507074692721933)

(37, 20, 15) : (0.24902191040514032, 0.3514363945560149, 0.3995416950388444)

(39, 21, 16) : (0.24856077012366679, 0.34790880231852783, 0.40353042755780505)

(41, 22, 17) : (0.2481337850102528, 0.34475535689287423, 0.4071108580968725)

(42, 23, 17) : (0.2469869646199726, 0.3550278952885728, 0.3979851400914541)

(44, 24, 18) : (0.24669215383188803, 0.35172706110002955, 0.4015807850680818)

(47, 25, 19) : (0.2520152501786475, 0.34803394036086477, 0.39995080946048733)

(49, 26, 20) : (0.2515099035224973, 0.3453723001119967, 0.4031177963655056)

(50, 27, 20) : (0.2504593591614441, 0.35405790255816694, 0.3954827382803885)

(52, 28, 21) : (0.2500675086320634, 0.35128905825541945, 0.3986434331125167)

(54, 29, 22) : (0.24969757025443567, 0.34874436236726036, 0.40155806737830346)

(56, 30, 23) : (0.24934804849640438, 0.3463976999479926, 0.4042542515556026)

(57, 31, 23) : (0.2484666523952958, 0.35395858387966334, 0.3975747637250402)

(59, 32, 24) : (0.2481946121492105, 0.35153283428534904, 0.40027255356544)

(62, 33, 25) : (0.2521738861150388, 0.34872754402113604, 0.39909856986382464)

(64, 34, 26) : (0.2517860864757535, 0.346665163513411, 0.401548750010835)

(65, 35, 26) : (0.25096513986595487, 0.35333017631296326, 0.3957046838210816)

(67, 36, 27) : (0.25064561298748156, 0.3512053475567349, 0.39814903945578306)

(69, 37, 28) : (0.25034024558775014, 0.3492152226122317, 0.40044453180001766)

(71, 38, 29) : (0.25004825955386906, 0.3473474075101228, 0.4026043329360075)

(72, 39, 29) : (0.24933332797113625, 0.35332946786149055, 0.3973372041673726)

(74, 40, 30) : (0.24909201262550004, 0.3514123765404453, 0.39949561083405405)

(77, 41, 31) : (0.25226931087329796, 0.3491510315278783, 0.3985796575988233)

(79, 42, 32) : (0.25195487530202576, 0.3474680548429086, 0.40057706985506536)

(81, 43, 33) : (0.25165335412137535, 0.34587586693244526, 0.40247077894617883)

(82, 44, 33) : (0.25101225245777686, 0.3511514227283464, 0.3978363248138762)

(84, 45, 34) : (0.2507532086077187, 0.34951741434125777, 0.39972937705102296)

(86, 46, 35) : (0.25050356535485546, 0.34796638246840395, 0.4015300521767401)

(87, 47, 35) : (0.2499024641128437, 0.35291515233385523, 0.3971823835533005)

(89, 48, 36) : (0.24968847720302675, 0.35133048793694, 0.3989810348600328)

(92, 49, 37) : (0.2523328864614152, 0.34943648952176787, 0.3982306240168164)

(94, 50, 38) : (0.25206854915159604, 0.3480151537842038, 0.39991629706419973)