#1
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Chances of a given hold\'em hand against a random range
Is there a chart for this somewhere? I'm doing a maths problem, and I'm stuck. I started to make one myself with Pokerstove, but it takes a while.
If it's not clear what I meant, I mean a chart where I can look up any two-card starting hand, say the 68 of spades, and find out the win % and split % against 2 random cards from the rest of the deck. For example, pokerstove gives me 84.93% win and .27% tie for AA. Or let P be the chance that the hand I have been dealt will win the pot. What is the distribution of P? |
#2
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Re: Chances of a given hold\'em hand against a random range
Here's the equity list together with loads of characters I won't bother to get rid of.
This is Pwin + Ptie/2... <ul type="square"> \!\(\* TagBox[GridBox[{ {"\<\"AAo\"\>", "0.8520371330210103`"}, {"\<\"AKs\"\>", "0.6704463230923519`"}, {"\<\"AKo\"\>", "0.6532007178870205`"}, {"\<\"AQs\"\>", "0.662088623973122`"}, {"\<\"AQo\"\>", "0.6443183937298184`"}, {"\<\"AJs\"\>", "0.6539267903219935`"}, {"\<\"AJo\"\>", "0.6356325791186038`"}, {"\<\"ATs\"\>", "0.6460238678769803`"}, {"\<\"ATo\"\>", "0.627216546375229`"}, {"\<\"A9s\"\>", "0.6278121391662093`"}, {"\<\"A9o\"\>", "0.6077280638799408`"}, {"\<\"A8s\"\>", "0.6194381064033835`"}, {"\<\"A8o\"\>", "0.5987260508862529`"}, {"\<\"A7s\"\>", "0.6098395855132337`"}, {"\<\"A7o\"\>", "0.5884119542190771`"}, {"\<\"A6s\"\>", "0.5990582804197846`"}, {"\<\"A6o\"\>", "0.5768245229580633`"}, {"\<\"A5s\"\>", "0.5992292561629815`"}, {"\<\"A5o\"\>", "0.5769653436038729`"}, {"\<\"A4s\"\>", "0.5903363597842914`"}, {"\<\"A4o\"\>", "0.567296776263837`"}, {"\<\"A3s\"\>", "0.5822032059537015`"}, {"\<\"A3o\"\>", "0.5584460233649147`"}, {"\<\"A2s\"\>", "0.5737889786307256`"}, {"\<\"A2o\"\>", "0.5492855867573389`"}, {"\<\"KKo\"\>", "0.8239567978678592`"}, {"\<\"KQs\"\>", "0.6340040329478017`"}, {"\<\"KQo\"\>", "0.6145580004771233`"}, {"\<\"KJs\"\>", "0.625673401309056`"}, {"\<\"KJo\"\>", "0.6056868516195197`"}, {"\<\"KTs\"\>", "0.6178855816848084`"}, {"\<\"KTo\"\>", "0.5973891513828083`"}, {"\<\"K9s\"\>", "0.5998847551102408`"}, {"\<\"K9o\"\>", "0.5781192465633129`"}, {"\<\"K8s\"\>", "0.5831234993366619`"}, {"\<\"K8o\"\>", "0.5602017255757179`"}, {"\<\"K7s\"\>", "0.5753773750550877`"}, {"\<\"K7o\"\>", "0.5518735017203699`"}, {"\<\"K6s\"\>", "0.5664073552359862`"}, {"\<\"K6o\"\>", "0.5422327894379235`"}, {"\<\"K5s\"\>", "0.5579291763659744`"}, {"\<\"K5o\"\>", "0.5331397283354797`"}, {"\<\"K4s\"\>", "0.5488463656844454`"}, {"\<\"K4o\"\>", "0.5232747210537283`"}, {"\<\"K3s\"\>", "0.540549764575468`"}, {"\<\"K3o\"\>", "0.5142568964484852`"}, {"\<\"K2s\"\>", "0.5321172832937732`"}, {"\<\"K2o\"\>", "0.5050872377516029`"}, {"\<\"QQo\"\>", "0.7992516406108315`"}, {"\<\"QJs\"\>", "0.6025920514114319`"}, {"\<\"QJo\"\>", "0.5813468967745764`"}, {"\<\"QTs\"\>", "0.5946755930808395`"}, {"\<\"QTo\"\>", "0.5729078259706315`"}, {"\<\"Q9s\"\>", "0.5766432171781052`"}, {"\<\"Q9o\"\>", "0.5536043492467769`"}, {"\<\"Q8s\"\>", "0.5601773297551013`"}, {"\<\"Q8o\"\>", "0.5359979207392319`"}, {"\<\"Q7s\"\>", "0.5430226320197575`"}, {"\<\"Q7o\"\>", "0.5176566594316364`"}, {"\<\"Q6s\"\>", "0.5361256643632422`"}, {"\<\"Q6o\"\>", "0.5102405230446397`"}, {"\<\"Q5s\"\>", "0.5276941089137136`"}, {"\<\"Q5o\"\>", "0.5012008279189789`"}, {"\<\"Q4s\"\>", "0.5185530203868051`"}, {"\<\"Q4o\"\>", "0.49127684102822866`"}, {"\<\"Q3s\"\>", "0.5101924648703426`"}, {"\<\"Q3o\"\>", "0.48219436025188`"}, {"\<\"Q2s\"\>", "0.501690352619056`"}, {"\<\"Q2o\"\>", "0.4729543688217863`"}, {"\<\"JJo\"\>", "0.7746947290114993`"}, {"\<\"JTs\"\>", "0.5752785710757828`"}, {"\<\"JTo\"\>", "0.5524770308285901`"}, {"\<\"J9s\"\>", "0.5566247055405568`"}, {"\<\"J9o\"\>", "0.5325119688359743`"}, {"\<\"J8s\"\>", "0.540156441799101`"}, {"\<\"J8o\"\>", "0.5149016300939122`"}, {"\<\"J7s\"\>", "0.5232478118514527`"}, {"\<\"J7o\"\>", "0.49681933600956996`"}, {"\<\"J6s\"\>", "0.5060590714294295`"}, {"\<\"J6o\"\>", "0.4784427305107559`"}, {"\<\"J5s\"\>", "0.49986849512321957`"}, {"\<\"J5o\"\>", "0.4718088822583669`"}, {"\<\"J4s\"\>", "0.4907045339650733`"}, {"\<\"J4o\"\>", "0.4618638453194751`"}, {"\<\"J3s\"\>", "0.4823162401927102`"}, {"\<\"J3o\"\>", "0.45275544887032265`"}, {"\<\"J2s\"\>", "0.47378152406086177`"}, {"\<\"J2o\"\>", "0.4434846761427639`"}, {"\<\"TTo\"\>", "0.7501177995095664`"}, {"\<\"T9s\"\>", "0.5402752865646021`"}, {"\<\"T9o\"\>", "0.5153167239900754`"}, {"\<\"T8s\"\>", "0.5233437072303201`"}, {"\<\"T8o\"\>", "0.4972127367331872`"}, {"\<\"T7s\"\>", "0.506390375369165`"}, {"\<\"T7o\"\>", "0.47908135518945616`"}, {"\<\"T6s\"\>", "0.48940675682994306`"}, {"\<\"T6o\"\>", "0.4609200328436817`"}, {"\<\"T5s\"\>", "0.47216258971561614`"}, {"\<\"T5o\"\>", "0.44250949550060814`"}, {"\<\"T4s\"\>", "0.46530493607753415`"}, {"\<\"T4o\"\>", "0.43504108010765224`"}, {"\<\"T3s\"\>", "0.4569251202008569`"}, {"\<\"T3o\"\>", "0.42594550848399776`"}, {"\<\"T2s\"\>", "0.44839482727747554`"}, {"\<\"T2o\"\>", "0.41668350589471903`"}, {"\<\"99o\"\>", "0.7205725194515339`"}, {"\<\"98s\"\>", "0.5080075538751367`"}, {"\<\"98o\"\>", "0.48097032765114606`"}, {"\<\"97s\"\>", "0.491177310971483`"}, {"\<\"97o\"\>", "0.462978064070637`"}, {"\<\"96s\"\>", "0.4742829077079771`"}, {"\<\"96o\"\>", "0.44491345257021897`"}, {"\<\"95s\"\>", "0.4572187455841812`"}, {"\<\"95o\"\>", "0.42669142814808203`"}, {"\<\"94s\"\>", "0.43861970819219404`"}, {"\<\"94o\"\>", "0.4067105352358754`"}, {"\<\"93s\"\>", "0.43264257791530825`"}, {"\<\"93o\"\>", "0.4001951434429629`"}, {"\<\"92s\"\>", "0.42415171867249973`"}, {"\<\"92o\"\>", "0.39097936285774926`"}, {"\<\"88o\"\>", "0.6916303546900218`"}, {"\<\"87s\"\>", "0.47936340242653835`"}, {"\<\"87o\"\>", "0.45050812262785295`"}, {"\<\"86s\"\>", "0.46243269266891585`"}, {"\<\"86o\"\>", "0.4324090186350658`"}, {"\<\"85s\"\>", "0.44544992702039743`"}, {"\<\"85o\"\>", "0.4142752598193988`"}, {"\<\"84s\"\>", "0.4270162729543924`"}, {"\<\"84o\"\>", "0.3944679146712648`"}, {"\<\"83s\"\>", "0.40873504104077646`"}, {"\<\"83o\"\>", "0.37483812596885796`"}, {"\<\"82s\"\>", "0.4027163443798173`"}, {"\<\"82o\"\>", "0.3682767410078431`"}, {"\<\"77o\"\>", "0.6623602279473172`"}, {"\<\"76s\"\>", "0.453717666431919`"}, {"\<\"76o\"\>", "0.4232274688110883`"}, {"\<\"75s\"\>", "0.4367553663463535`"}, {"\<\"75o\"\>", "0.4051196885981147`"}, {"\<\"74s\"\>", "0.4184931187595719`"}, {"\<\"74o\"\>", "0.38549827839077216`"}, {"\<\"73s\"\>", "0.4003593587520507`"}, {"\<\"73o\"\>", "0.3660225699480027`"}, {"\<\"72s\"\>", "0.38155893474761576`"}, {"\<\"72o\"\>", "0.34583647315344146`"}, {"\<\"66o\"\>", "0.632847482165574`"}, {"\<\"65s\"\>", "0.4313338621827787`"}, {"\<\"65o\"\>", "0.3994430230393954`"}, {"\<\"64s\"\>", "0.41333319031085647`"}, {"\<\"64o\"\>", "0.3801048824345705`"}, {"\<\"63s\"\>", "0.3953355993814564`"}, {"\<\"63o\"\>", "0.3607763095567048`"}, {"\<\"62s\"\>", "0.37668964108223385`"}, {"\<\"62o\"\>", "0.34075138336107014`"}, {"\<\"55o\"\>", "0.6032492051287481`"}, {"\<\"54s\"\>", "0.4145342036823139`"}, {"\<\"54o\"\>", "0.3815528708329685`"}, {"\<\"53s\"\>", "0.3969296239786526`"}, {"\<\"53o\"\>", "0.36264771123037287`"}, {"\<\"52s\"\>", "0.37849327989822873`"}, {"\<\"52o\"\>", "0.34284645502581923`"}, {"\<\"44o\"\>", "0.5702282119082042`"}, {"\<\"43s\"\>", "0.38641948378039276`"}, {"\<\"43o\"\>", "0.35145893390855065`"}, {"\<\"42s\"\>", "0.36829014721970954`"}, {"\<\"42o\"\>", "0.33199750125430705`"}, {"\<\"33o\"\>", "0.5369307638677933`"}, {"\<\"32s\"\>", "0.3598443059700824`"}, {"\<\"32o\"\>", "0.32303228126952854`"}, {"\<\"22o\"\>", "0.5033401907843561`"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], Function[ BoxForm`e$, TableForm[ BoxForm`e$]]]\)[/list] Regards. |
#3
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Re: Chances of a given hold\'em hand against a random range
Why not set up a Pokerstove player 2 with a random hand and give player 1 6s8s
There are only 169 hand types (you don't need to bother with 6d8d, 6h8h, 6c8c) so enumerating them all wouldnt take you forever. EDIT oops never mind I see someone did it for you. |
#4
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Re: Chances of a given hold\'em hand against a random range
Thanks well. FilledRoll that was more or less what I was doing before I decided that 2+2 might already have all the answers.
I think I'll use this and make some kind of approximation for the tie%. |
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