#1
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odds that my hand is dominated
Does anybody know where I can find odds that a specific hand is dominated (a couple of examples: you have A6 and one of the other players has Ax with x > 6, or another player has a pocket pair 6s or higher, or you have a pocket pair, but somebody else has a higher pocket pair). I would like to know the odds of having a dominated hand depending on the number of players at the table.
I hope somebody can help me out with this. |
#2
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Re: odds that my hand is dominated
This is the most complicated question I have ever seen. If you want to mess around, you can use the odds calculator at cardplayer:
http://www.cardplayer.com/poker_odds...ldem/index.php Or you can look at the odds that certain hands have against other random hands at wizardofodds: http://wizardofodds.com/holdem But trying to understand how one would even begin to answer this question gives me a headache. |
#3
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Re: odds that my hand is dominated
[ QUOTE ]
This is the most complicated question I have ever seen. [/ QUOTE ] Hmmm, yes, I'm starting to think this is indeed really complicated. Exact calculations are probably out of the question so I suppose I need to try to run some simulations. |
#4
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Re: odds that my hand is dominated
I dont think its that complicated. Here is an example if you are first in with AQo
Hands that dominate you AK AA KK KK - 6 combinations, AK- 12 combinations, AA - 3 QQ - 3 This is because you have an A and a Q in your hand. So thats 24 combinations of hands that dominate you, out of C(50,2) = 1225. Now it depends on how many people have to act behind you.. say you are first position at a 9 handed table. it would be 8 * 24/1225 ~15.6% of the time you will be dominated. But if you are opening from the button its 2 * 24 /1225 ~ 3.9% |
#5
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Re: odds that my hand is dominated
you're right, it's not so bad to work out specific hand domination.
btw, your calculation is off. you can't simply add up the probability that you're dominated. you can find out the probability that one person is dominating you by finding the probability that you're not dominated by anyone and subtracting from one, though: 1 - (1201/1225)^8 = 14.64% and similarly for the heads-up situation. to find if more than one person is dominating you is a bit more complex, but not too bad. |
#6
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Re: odds that my hand is dominated
My mistake, I think I wanted to start to do inclusion-exclusion and forgot to finish.
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#7
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Re: odds that my hand is dominated
I did these using simulations over about 10 million hands, so while the numbers aren't exact, they come close. In order from least likely to be dominated with (n-1) players remaining to most likely. Note that AKs == AK for the sake of this problem.
Ten handed AA 0.007381046526954 AK 0.043748142767524 KK 0.0496223432285263 QQ 0.0893896630799083 JJ 0.13575304688195 AQ 0.165675966553523 TT 0.174328910829991 99 0.207368188837415 88 0.241813152493977 KQ 0.243355000909707 77 0.272686832740214 AJ 0.275510877818494 66 0.308907165981276 55 0.339728570797047 44 0.370277078085642 AT 0.376603258153713 33 0.39472290857748 22 0.420782749704168 JK 0.429580617879707 9A 0.467675355645095 JQ 0.488308412300646 8A 0.541147421450351 KT 0.575094314536903 7A 0.611903737296832 6A 0.666299215189457 QT 0.670263371620838 9K 0.686925408736272 JT 0.708201997411991 5A 0.72269869444767 4A 0.768282744282744 8K 0.776496512417781 9Q 0.797516270421039 3A 0.80620992125461 7K 0.839595899667095 2A 0.842448762133094 9J 0.848693921552368 9T 0.86776172504946 8Q 0.876755844542612 6K 0.88712146422629 5K 0.923199448257742 8J 0.925437501040678 7Q 0.926489374056439 8T 0.945891382330858 4K 0.94955376397598 89 0.955820767053449 6Q 0.960353447273573 7J 0.965510376748121 3K 0.967285294166514 2K 0.980013291244393 5Q 0.980534395293884 7T 0.981662856856823 6J 0.985173172709371 79 0.987292261482349 4Q 0.989473335212108 78 0.989810074318745 6T 0.993834463681658 5J 0.994119699008322 3Q 0.994812985764712 69 0.99759687593872 4J 0.997906328821774 2Q 0.9980714879468 5T 0.998194587073906 68 0.998575427785784 67 0.998705028804808 3J 0.99943594677992 59 0.999587690074875 4T 0.999634745650153 58 0.999765084905027 2J 0.999867694241392 3T 0.999917099132857 57 0.999933736436677 56 0.999934409025318 49 0.999983259675907 39 0.999983369642946 2T 0.999983441241245 26 1 27 1 35 1 48 1 29 1 45 1 25 1 28 1 24 1 46 1 23 1 36 1 47 1 38 1 34 1 37 1 Six handed: AA 0.00441423148229893 AK 0.0247596514320942 KK 0.0277692476420268 QQ 0.054613267027795 JJ 0.0754466066758278 AQ 0.0957609635988554 TT 0.0983964365256125 99 0.124257995924515 KQ 0.140139957548421 88 0.14326888967719 AJ 0.164411984397045 77 0.165971276735913 66 0.185799806320979 55 0.204731776866869 44 0.223738846187826 AT 0.228409752850129 33 0.24339464514137 JK 0.264845841181719 22 0.265926023894547 9A 0.288900311733103 JQ 0.303397375432326 8A 0.343728343728344 KT 0.366640727188436 7A 0.395183315401804 6A 0.44776218220339 QT 0.449064932047857 9K 0.463424337361381 JT 0.476754407788891 5A 0.489800945999212 4A 0.534453476676505 8K 0.542934180272278 9Q 0.56656434082801 3A 0.578161835508185 7K 0.618877857000067 2A 0.619348404255319 9J 0.629041906217806 9T 0.654034331204909 8Q 0.671171245406154 6K 0.681397738951696 8J 0.735921593215305 5K 0.738407684523118 7Q 0.753304769496479 8T 0.780958214687769 4K 0.787651872055542 89 0.79606428228596 6Q 0.811424764759764 3K 0.825665899647392 7J 0.82595762359784 2K 0.860740838866719 5Q 0.861447972772032 7T 0.867776657131992 6J 0.885858953569183 79 0.890896168721695 78 0.902228012158867 4Q 0.904447335935675 6T 0.92576931335789 5J 0.926008706820343 3Q 0.931507305221819 69 0.948943137838642 2Q 0.954437169940194 4J 0.956347690314436 68 0.959671692566842 5T 0.961068438625635 67 0.962138451898024 3J 0.97535689443874 59 0.97809242156393 4T 0.982042574339435 58 0.984816337355788 2J 0.987547813415906 57 0.988268917616563 56 0.990975690975691 49 0.99137444846233 3T 0.992055049531281 48 0.996298438403702 2T 0.996743532523349 39 0.997294443711231 47 0.998226244943969 46 0.998951310861423 45 0.999030781056783 38 0.999191218948585 29 0.999437402786511 37 0.99991716642921 28 0.999917419525327 36 0.999950294916827 26 1 27 1 35 1 25 1 24 1 23 1 34 1 AA 0.000707307369258654 AK 0.00498997032542564 KK 0.00566647483288326 QQ 0.010393369293514 JJ 0.0143203348755232 AQ 0.0193707835147953 TT 0.0198469945355191 99 0.0246499094402969 88 0.0285564350373901 KQ 0.0291890996438333 AJ 0.034042131678003 77 0.0352393617021277 66 0.0412516527104451 55 0.0454808677446657 AT 0.0486322691747251 44 0.0522143489813995 33 0.0533350863353493 JK 0.0573093976783965 22 0.0602463010543103 9A 0.0620425924704952 JQ 0.0690054417042955 8A 0.0792491138145085 KT 0.0842138333581361 7A 0.0935867456092343 6A 0.107308584686775 QT 0.107865761192062 9K 0.114008349347293 JT 0.117181763567185 5A 0.123561216704813 4A 0.137988984841678 8K 0.141036265994829 9Q 0.148619781748332 3A 0.154045651776363 2A 0.16515604249668 7K 0.169326489858565 9J 0.169567010309278 9T 0.182056341297607 8Q 0.188505286365686 6K 0.192626407978961 5K 0.2244346889754 8J 0.224750973019328 7Q 0.231396096933305 8T 0.248140512905088 4K 0.250653475829666 89 0.261829915340219 6Q 0.271896307520011 3K 0.27771124417831 7J 0.280701462489393 2K 0.309192887806964 7T 0.312436603089612 5Q 0.312444851410971 6J 0.332933832709114 79 0.336942126870613 78 0.345710606260732 4Q 0.355731225296443 6T 0.384775305192429 5J 0.387994457457689 3Q 0.393843607778237 69 0.419989728467057 2Q 0.43278976792024 4J 0.439213674647957 68 0.443251102922952 5T 0.44752999586264 67 0.452604287082604 3J 0.491959698405285 59 0.497790525104637 4T 0.514938312770924 58 0.532217114979341 2J 0.545579175131725 57 0.556951075474523 56 0.565466762258866 49 0.579796772265392 3T 0.583123007438895 48 0.621714172277457 2T 0.648449894235854 39 0.658928571428571 47 0.659691593433925 46 0.683275145469659 45 0.694204195248037 38 0.722247903321667 29 0.735777538690722 37 0.772008019485361 36 0.804147657960261 28 0.814530027840382 35 0.828543773572311 34 0.837770507050207 27 0.874080791426216 26 0.926497202344386 25 0.959934383854452 24 0.982678258569965 23 0.991574434140991 |
#8
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Re: odds that my hand is dominated
FYI, the reason why you may see some funky numbers (like AA can be dominated), is that a tie counts as domination here, so they are off by some tiny %)
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