Chances of a given hold'em hand against a random range

RoundTower · #1 09-26-2005, 08:35 AM

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?

well · #2 09-26-2005, 08:43 AM

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 09-26-2005, 08:46 AM

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.

RoundTower · #4 09-26-2005, 09:51 AM

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%.