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View Full Version : Chances of a given hold'em hand against a random range

RoundTower
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
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[{
{"\&lt;\"AAo\"\&gt;", "0.8520371330210103`"},
{"\&lt;\"AKs\"\&gt;", "0.6704463230923519`"},
{"\&lt;\"AKo\"\&gt;", "0.6532007178870205`"},
{"\&lt;\"AQs\"\&gt;", "0.662088623973122`"},
{"\&lt;\"AQo\"\&gt;", "0.6443183937298184`"},
{"\&lt;\"AJs\"\&gt;", "0.6539267903219935`"},
{"\&lt;\"AJo\"\&gt;", "0.6356325791186038`"},
{"\&lt;\"ATs\"\&gt;", "0.6460238678769803`"},
{"\&lt;\"ATo\"\&gt;", "0.627216546375229`"},
{"\&lt;\"A9s\"\&gt;", "0.6278121391662093`"},
{"\&lt;\"A9o\"\&gt;", "0.6077280638799408`"},
{"\&lt;\"A8s\"\&gt;", "0.6194381064033835`"},
{"\&lt;\"A8o\"\&gt;", "0.5987260508862529`"},
{"\&lt;\"A7s\"\&gt;", "0.6098395855132337`"},
{"\&lt;\"A7o\"\&gt;", "0.5884119542190771`"},
{"\&lt;\"A6s\"\&gt;", "0.5990582804197846`"},
{"\&lt;\"A6o\"\&gt;", "0.5768245229580633`"},
{"\&lt;\"A5s\"\&gt;", "0.5992292561629815`"},
{"\&lt;\"A5o\"\&gt;", "0.5769653436038729`"},
{"\&lt;\"A4s\"\&gt;", "0.5903363597842914`"},
{"\&lt;\"A4o\"\&gt;", "0.567296776263837`"},
{"\&lt;\"A3s\"\&gt;", "0.5822032059537015`"},
{"\&lt;\"A3o\"\&gt;", "0.5584460233649147`"},
{"\&lt;\"A2s\"\&gt;", "0.5737889786307256`"},
{"\&lt;\"A2o\"\&gt;", "0.5492855867573389`"},
{"\&lt;\"KKo\"\&gt;", "0.8239567978678592`"},
{"\&lt;\"KQs\"\&gt;", "0.6340040329478017`"},
{"\&lt;\"KQo\"\&gt;", "0.6145580004771233`"},
{"\&lt;\"KJs\"\&gt;", "0.625673401309056`"},
{"\&lt;\"KJo\"\&gt;", "0.6056868516195197`"},
{"\&lt;\"KTs\"\&gt;", "0.6178855816848084`"},
{"\&lt;\"KTo\"\&gt;", "0.5973891513828083`"},
{"\&lt;\"K9s\"\&gt;", "0.5998847551102408`"},
{"\&lt;\"K9o\"\&gt;", "0.5781192465633129`"},
{"\&lt;\"K8s\"\&gt;", "0.5831234993366619`"},
{"\&lt;\"K8o\"\&gt;", "0.5602017255757179`"},
{"\&lt;\"K7s\"\&gt;", "0.5753773750550877`"},
{"\&lt;\"K7o\"\&gt;", "0.5518735017203699`"},
{"\&lt;\"K6s\"\&gt;", "0.5664073552359862`"},
{"\&lt;\"K6o\"\&gt;", "0.5422327894379235`"},
{"\&lt;\"K5s\"\&gt;", "0.5579291763659744`"},
{"\&lt;\"K5o\"\&gt;", "0.5331397283354797`"},
{"\&lt;\"K4s\"\&gt;", "0.5488463656844454`"},
{"\&lt;\"K4o\"\&gt;", "0.5232747210537283`"},
{"\&lt;\"K3s\"\&gt;", "0.540549764575468`"},
{"\&lt;\"K3o\"\&gt;", "0.5142568964484852`"},
{"\&lt;\"K2s\"\&gt;", "0.5321172832937732`"},
{"\&lt;\"K2o\"\&gt;", "0.5050872377516029`"},
{"\&lt;\"QQo\"\&gt;", "0.7992516406108315`"},
{"\&lt;\"QJs\"\&gt;", "0.6025920514114319`"},
{"\&lt;\"QJo\"\&gt;", "0.5813468967745764`"},
{"\&lt;\"QTs\"\&gt;", "0.5946755930808395`"},
{"\&lt;\"QTo\"\&gt;", "0.5729078259706315`"},
{"\&lt;\"Q9s\"\&gt;", "0.5766432171781052`"},
{"\&lt;\"Q9o\"\&gt;", "0.5536043492467769`"},
{"\&lt;\"Q8s\"\&gt;", "0.5601773297551013`"},
{"\&lt;\"Q8o\"\&gt;", "0.5359979207392319`"},
{"\&lt;\"Q7s\"\&gt;", "0.5430226320197575`"},
{"\&lt;\"Q7o\"\&gt;", "0.5176566594316364`"},
{"\&lt;\"Q6s\"\&gt;", "0.5361256643632422`"},
{"\&lt;\"Q6o\"\&gt;", "0.5102405230446397`"},
{"\&lt;\"Q5s\"\&gt;", "0.5276941089137136`"},
{"\&lt;\"Q5o\"\&gt;", "0.5012008279189789`"},
{"\&lt;\"Q4s\"\&gt;", "0.5185530203868051`"},
{"\&lt;\"Q4o\"\&gt;", "0.49127684102822866`"},
{"\&lt;\"Q3s\"\&gt;", "0.5101924648703426`"},
{"\&lt;\"Q3o\"\&gt;", "0.48219436025188`"},
{"\&lt;\"Q2s\"\&gt;", "0.501690352619056`"},
{"\&lt;\"Q2o\"\&gt;", "0.4729543688217863`"},
{"\&lt;\"JJo\"\&gt;", "0.7746947290114993`"},
{"\&lt;\"JTs\"\&gt;", "0.5752785710757828`"},
{"\&lt;\"JTo\"\&gt;", "0.5524770308285901`"},
{"\&lt;\"J9s\"\&gt;", "0.5566247055405568`"},
{"\&lt;\"J9o\"\&gt;", "0.5325119688359743`"},
{"\&lt;\"J8s\"\&gt;", "0.540156441799101`"},
{"\&lt;\"J8o\"\&gt;", "0.5149016300939122`"},
{"\&lt;\"J7s\"\&gt;", "0.5232478118514527`"},
{"\&lt;\"J7o\"\&gt;", "0.49681933600956996`"},
{"\&lt;\"J6s\"\&gt;", "0.5060590714294295`"},
{"\&lt;\"J6o\"\&gt;", "0.4784427305107559`"},
{"\&lt;\"J5s\"\&gt;", "0.49986849512321957`"},
{"\&lt;\"J5o\"\&gt;", "0.4718088822583669`"},
{"\&lt;\"J4s\"\&gt;", "0.4907045339650733`"},
{"\&lt;\"J4o\"\&gt;", "0.4618638453194751`"},
{"\&lt;\"J3s\"\&gt;", "0.4823162401927102`"},
{"\&lt;\"J3o\"\&gt;", "0.45275544887032265`"},
{"\&lt;\"J2s\"\&gt;", "0.47378152406086177`"},
{"\&lt;\"J2o\"\&gt;", "0.4434846761427639`"},
{"\&lt;\"TTo\"\&gt;", "0.7501177995095664`"},
{"\&lt;\"T9s\"\&gt;", "0.5402752865646021`"},
{"\&lt;\"T9o\"\&gt;", "0.5153167239900754`"},
{"\&lt;\"T8s\"\&gt;", "0.5233437072303201`"},
{"\&lt;\"T8o\"\&gt;", "0.4972127367331872`"},
{"\&lt;\"T7s\"\&gt;", "0.506390375369165`"},
{"\&lt;\"T7o\"\&gt;", "0.47908135518945616`"},
{"\&lt;\"T6s\"\&gt;", "0.48940675682994306`"},
{"\&lt;\"T6o\"\&gt;", "0.4609200328436817`"},
{"\&lt;\"T5s\"\&gt;", "0.47216258971561614`"},
{"\&lt;\"T5o\"\&gt;", "0.44250949550060814`"},
{"\&lt;\"T4s\"\&gt;", "0.46530493607753415`"},
{"\&lt;\"T4o\"\&gt;", "0.43504108010765224`"},
{"\&lt;\"T3s\"\&gt;", "0.4569251202008569`"},
{"\&lt;\"T3o\"\&gt;", "0.42594550848399776`"},
{"\&lt;\"T2s\"\&gt;", "0.44839482727747554`"},
{"\&lt;\"T2o\"\&gt;", "0.41668350589471903`"},
{"\&lt;\"99o\"\&gt;", "0.7205725194515339`"},
{"\&lt;\"98s\"\&gt;", "0.5080075538751367`"},
{"\&lt;\"98o\"\&gt;", "0.48097032765114606`"},
{"\&lt;\"97s\"\&gt;", "0.491177310971483`"},
{"\&lt;\"97o\"\&gt;", "0.462978064070637`"},
{"\&lt;\"96s\"\&gt;", "0.4742829077079771`"},
{"\&lt;\"96o\"\&gt;", "0.44491345257021897`"},
{"\&lt;\"95s\"\&gt;", "0.4572187455841812`"},
{"\&lt;\"95o\"\&gt;", "0.42669142814808203`"},
{"\&lt;\"94s\"\&gt;", "0.43861970819219404`"},
{"\&lt;\"94o\"\&gt;", "0.4067105352358754`"},
{"\&lt;\"93s\"\&gt;", "0.43264257791530825`"},
{"\&lt;\"93o\"\&gt;", "0.4001951434429629`"},
{"\&lt;\"92s\"\&gt;", "0.42415171867249973`"},
{"\&lt;\"92o\"\&gt;", "0.39097936285774926`"},
{"\&lt;\"88o\"\&gt;", "0.6916303546900218`"},
{"\&lt;\"87s\"\&gt;", "0.47936340242653835`"},
{"\&lt;\"87o\"\&gt;", "0.45050812262785295`"},
{"\&lt;\"86s\"\&gt;", "0.46243269266891585`"},
{"\&lt;\"86o\"\&gt;", "0.4324090186350658`"},
{"\&lt;\"85s\"\&gt;", "0.44544992702039743`"},
{"\&lt;\"85o\"\&gt;", "0.4142752598193988`"},
{"\&lt;\"84s\"\&gt;", "0.4270162729543924`"},
{"\&lt;\"84o\"\&gt;", "0.3944679146712648`"},
{"\&lt;\"83s\"\&gt;", "0.40873504104077646`"},
{"\&lt;\"83o\"\&gt;", "0.37483812596885796`"},
{"\&lt;\"82s\"\&gt;", "0.4027163443798173`"},
{"\&lt;\"82o\"\&gt;", "0.3682767410078431`"},
{"\&lt;\"77o\"\&gt;", "0.6623602279473172`"},
{"\&lt;\"76s\"\&gt;", "0.453717666431919`"},
{"\&lt;\"76o\"\&gt;", "0.4232274688110883`"},
{"\&lt;\"75s\"\&gt;", "0.4367553663463535`"},
{"\&lt;\"75o\"\&gt;", "0.4051196885981147`"},
{"\&lt;\"74s\"\&gt;", "0.4184931187595719`"},
{"\&lt;\"74o\"\&gt;", "0.38549827839077216`"},
{"\&lt;\"73s\"\&gt;", "0.4003593587520507`"},
{"\&lt;\"73o\"\&gt;", "0.3660225699480027`"},
{"\&lt;\"72s\"\&gt;", "0.38155893474761576`"},
{"\&lt;\"72o\"\&gt;", "0.34583647315344146`"},
{"\&lt;\"66o\"\&gt;", "0.632847482165574`"},
{"\&lt;\"65s\"\&gt;", "0.4313338621827787`"},
{"\&lt;\"65o\"\&gt;", "0.3994430230393954`"},
{"\&lt;\"64s\"\&gt;", "0.41333319031085647`"},
{"\&lt;\"64o\"\&gt;", "0.3801048824345705`"},
{"\&lt;\"63s\"\&gt;", "0.3953355993814564`"},
{"\&lt;\"63o\"\&gt;", "0.3607763095567048`"},
{"\&lt;\"62s\"\&gt;", "0.37668964108223385`"},
{"\&lt;\"62o\"\&gt;", "0.34075138336107014`"},
{"\&lt;\"55o\"\&gt;", "0.6032492051287481`"},
{"\&lt;\"54s\"\&gt;", "0.4145342036823139`"},
{"\&lt;\"54o\"\&gt;", "0.3815528708329685`"},
{"\&lt;\"53s\"\&gt;", "0.3969296239786526`"},
{"\&lt;\"53o\"\&gt;", "0.36264771123037287`"},
{"\&lt;\"52s\"\&gt;", "0.37849327989822873`"},
{"\&lt;\"52o\"\&gt;", "0.34284645502581923`"},
{"\&lt;\"44o\"\&gt;", "0.5702282119082042`"},
{"\&lt;\"43s\"\&gt;", "0.38641948378039276`"},
{"\&lt;\"43o\"\&gt;", "0.35145893390855065`"},
{"\&lt;\"42s\"\&gt;", "0.36829014721970954`"},
{"\&lt;\"42o\"\&gt;", "0.33199750125430705`"},
{"\&lt;\"33o\"\&gt;", "0.5369307638677933`"},
{"\&lt;\"32s\"\&gt;", "0.3598443059700824`"},
{"\&lt;\"32o\"\&gt;", "0.32303228126952854`"},
{"\&lt;\"22o\"\&gt;", "0.5033401907843561`"}
},
RowSpacings-&gt;1,
ColumnSpacings-&gt;3,
RowAlignments-&gt;Baseline,
ColumnAlignments-&gt;{Left}],
Function[ BoxForm`e\$,
TableForm[ BoxForm`e\$]]]\) [/list]

Regards.

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
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%.