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#1
04-26-2005, 04:43 PM
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Pure Theory Questions #2 and #3
Same as before except this time player moves in $1000 into a $500 pot. What about into a $2500 pot? The second question by the way can easily be answered without a computer.
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#2
04-26-2005, 04:55 PM
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Re: Pure Theory Questions #2 and #3
On the second question, you're getting 3.5:1 pot odds, so the only time that learning your opponent's cards would make you fold rather than call is when your opponent has a overpair to your cards. That's most likely to happen if your cards are 32. Therefore in question #3, being able to see your opponent's cards before you act is worth the most if your cards are 32o.
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#3
04-26-2005, 05:41 PM
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Re: Pure Theory Questions #2 and #3
Where the opponent moves in $1000 into a $500 pot, you're getting 60:40 pot odds.
I would guess that being shown the opponent's cards would be most valuable with something like 92o, because it is 39% against a random hand (http://www.jazbo.com/poker/huholdem.html) but there is a sizeable class of hands against which the 92o is considerably better than 40%, namely eight-high and below. The alternative would be to look at other hands near the 40% mark such as 65o or 73s, but I suspect they won't gain as much as 92o would, because there aren't that many hands the opponent could have against which 65o (or 73s) is much better than 40%.
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#4
04-26-2005, 06:03 PM
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Re: Pure Theory Questions #2 and #3
I agree with your reasoning, but isn't the overpair to your cards more likely with 22? 32 is probably still the one here, because you're more of a dog against overpairs than you are with 22, but with 22 it should be slightly more probable to be up against an overpair.
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#5
04-26-2005, 06:19 PM
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Re: Pure Theory Questions #2 and #3
On question #2, it's whatever hand is the most likely to be a >3.5:1 shot, weighted by how much worse than 3.5:1 the hand is.
The worst situation you can be in is when the opponent has a pair of your highest card's rank, but that is equally likely for all non-pair hands. You want the hand to be as bad as possible when it is >3.5:1, and you want to maximize the number of situations. It seems like it's 72o,62o,52o,42o,or 32o. I'm not sure if the decreased odds for 72o vs 32o against say, an overpair, compensate for the increased overpairs to 32o vs 72o.
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#6
04-27-2005, 05:35 PM
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Re: Pure Theory Questions #2 and #3
[ QUOTE ]
On the second question, you're getting 3.5:1 pot odds, so the only time that learning your opponent's cards would make you fold rather than call is when your opponent has a overpair to your cards. That's most likely to happen if your cards are 32. Therefore in question #3, being able to see your opponent's cards before you act is worth the most if your cards are 32o. [/ QUOTE ] I think that in a dominated situation where you would lose if you make a flush (such as when you have A[img]/images/graemlins/spade.gif[/img]J[img]/images/graemlins/heart.gif[/img] vs. J[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img]), you need more than 3.5:1 pot odds, depending on the actual cards. Of course, this is a rare occurence, and 32o doesn't have any such hands because its straight possibilities give it additional wins against a dominating flush-proof hand.
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#7
04-27-2005, 06:22 PM
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Re: Pure Theory Questions #2 and #3
[ QUOTE ]
I think that in a dominated situation where you would lose if you make a flush (such as when you have A[img]/images/graemlins/spade.gif[/img]J[img]/images/graemlins/heart.gif[/img] vs. J[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img]), you need more than 3.5:1 pot odds, depending on the actual cards. [/ QUOTE ] That's true, but it's close. The J[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img] is a 3.5912:1 underdog to A[img]/images/graemlins/spade.gif[/img]J[img]/images/graemlins/heart.gif[/img], so in finding out your opponent has those cards you would save only $19.86 of EV by folding. By contrast, if you have 3[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img] and your opponent shows you 7[img]/images/graemlins/diamond.gif[/img]7[img]/images/graemlins/club.gif[/img], you would be a 5.7861:1 underdog so you would save $336.88 by folding. That's a huge amount more, and the probability of your opponent showing you a hand that will make you fold is much higher when you have 32o than J2o. If you have 22 and your opponent shows you 77, you save about $184 by folding.
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#8
06-06-2005, 09:56 AM
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Tables for the amounts again...
About the same calculations as in the answer to #1, except that with an initial pot of $p, one would call only with hands that have a better EQ than 1000/(2000+p).
Here are the lists. #2 - $500 in the pot AAo 0. AKs 2.066516392950348 AKo 2.63586146060959 KKo 2.6872714858373 32o 4.433130413043194 QQo 5.324309902247251 AQs 5.5800623377779175 AQo 7.63109523656874 42o 7.909735082326618 JJo 7.91637132525193 32s 8.49705998229189 AJs 8.846188336573505 KQs 9.91950337447247 TTo 10.461911112102598 ATs 11.730481865607544 AJo 12.35876792619922 99o 13.0379861977583 KJs 13.291503430346438 KQo 13.420730316625963 A9s 15.349145755350492 88o 15.550312589924829 KTs 16.25498123449745 ATo 16.67293939412957 42s 16.740201434763314 QJs 16.886246334094608 A5s 16.96523073530136 52o 17.06545552372825 A8s 17.2035254897512 77o 18.05101840584757 A4s 18.513880617422785 A7s 18.58947979578818 KJo 18.979513889484906 QTs 19.687783840024053 A6s 19.83469176081769 A3s 20.128878626549408 66o 20.52744973188942 K9s 20.985264680256137 A2s 21.763982020358753 A9o 21.823548617439087 JTs 22.219936842227355 43o 22.779906309789375 55o 23.003755913263376 QJo 23.79759513902792 KTo 24.064042199448636 Q9s 24.83541307084414 A8o 25.039176359300313 K8s 25.50089176898007 44o 25.933207359135622 K7s 26.2545894720958 K6s 26.88540536193176 A5o 27.258602372914368 J9s 27.52538851579203 A7o 27.7646577300506 K5s 28.18386709798392 33o 28.862483602472537 T9s 28.91244016177916 QTo 29.31788516572783 A4o 29.343055929798197 Q8s 29.93419261714257 A6o 30.288501841462107 52s 30.86330667299012 K4s 30.87450414107292 62o 31.16843678435129 A3o 31.51516343369093 22o 31.77922750127732 K9o 32.685918374021526 J8s 32.81683149530312 JTo 33.27200160051723 53o 33.44350068679396 A2o 33.79729097789482 K3s 33.8800738177153 T8s 34.05374040962806 98s 34.72993351743196 Q6s 35.126908253559975 Q7s 35.71925538779976 43s 35.92407823443904 Q5s 36.31035012188386 K2s 37.04196551213232 Q9o 38.92045680997717 J7s 38.979017363119226 87s 39.31935317226737 Q4s 39.51422141614813 97s 40.17974242510053 T7s 40.332619627336555 K8o 40.658738287174344 62s 41.403569669394926 76s 42.8030989538193 Q3s 43.104501899433444 J9o 43.27370881214904 K7o 43.383732785576285 65s 44.54461989011649 63o 45.183631682987425 86s 45.19006447643926 J5s 45.19865619417948 54s 45.65583159370321 J6s 45.697046619225375 T9o 45.7320325391388 K6o 46.051291245060156 Q2s 47.163619239078855 96s 47.392774618887955 T6s 47.39280834835546 J4s 48.72675944344002 Q8o 48.74104047612343 K5o 49.684791333066414 75s 50.24773829022561 72o 52.534484506947166 J3s 52.75391817226466 53s 53.11136197253546 J8o 53.30574072198925 K4o 53.93683657832372 54o 54.73991469853437 85s 54.930532433588525 T8o 55.6169299567448 T5s 56.270119567743905 95s 57.02687294607762 64s 57.24455494361004 J2s 57.43928731613798 T4s 58.00610910975007 98o 58.18543033365518 K3o 58.29165360394654 Q7o 59.68767657316596 Q6o 61.35289096576537 T3s 62.25518401653281 72s 62.453776208153805 K2o 62.73927851072011 64o 63.76456266777725 63s 65.4133171994445 J7o 65.47145202234725 Q5o 65.65307412035003 74s 66.09406843358505 73o 67.00111066488094 T2s 67.25393435764138 T7o 67.58665731871741 97o 69.09717800444005 87o 69.56786759780036 84s 70.0985256814021 Q4o 71.75069892700708 94s 72.09516987351637 93s 73.71460789625175 Q3o 78.0816267653019 J6o 78.94847419807849 92s 79.26452681680965 76o 80.56850588327754 J5o 81.19899460919669 T6o 81.80931728506684 86o 81.96784172980199 96o 82.92085579501307 82o 84.34581864730879 74o 84.57748252217657 Q2o 84.6300087186508 73s 84.8203780713362 J4o 88.8764461717742 65o 89.27436890855343 83s 89.50477096761945 82s 91.14471793679219 83o 93.23877676403453 75o 95.41671207630297 J3o 96.93965950829642 85o 98.85283030039886 T5o 99.34027068624678 95o 100.83272405758211 T4o 104.82848696903099 J2o 105.36502959325747 84o 111.40787845988045 T3o 114.38084723559533 92o 122.34720396301937 T2o 124.44621041447729 94o 126.82174999060837 93o 133.35468349030538 And #3 - $2500 in the pot AAo 0 KKo 0.9187213275663453 ATs 0.9792681053568231 A5s 0.9825022011157216 AJs 1.0231938835568144 A4s 1.0265824435912236 AQs 1.0671196617595342 A3s 1.0706626860658162 AKs 1.1110454399577065 A2s 1.1147429285397266 A8s 1.1302472801410204 A7s 1.13032451228014 A6s 1.1521039750512045 A9s 1.1741730583414665 ATo 1.5524517771114006 A5o 1.5560902689207978 AJo 1.600465495255321 A4o 1.6043914622462125 AQo 1.6484792133996962 A3o 1.652782759726506 AKo 1.6964929315413428 A2o 1.701295268760532 A8o 1.7156969170659977 A7o 1.715788093894389 A6o 1.739465107378237 QQo 1.7470231301699641 A9o 1.7637063445322383 KTs 1.7914187372039123 KJs 1.924467184064497 65s 2.036994408392502 KQs 2.0575156309269005 54s 2.071938732603712 K9s 2.118554763593238 JTs 2.1218853995201243 QTs 2.16397047844589 T9s 2.170918152812874 76s 2.1915809675983837 87s 2.2684848685080397 98s 2.315136297559775 QJs 2.3861415939668404 K6s 2.3904923377131126 K7s 2.3930828323250353 K5s 2.4444422037586264 JJo 2.494366344637001 K8s 2.5261312791867567 Q9s 2.5578543796639224 J9s 2.5730079686420595 K4s 2.577954043446425 K3s 2.7114658831328597 T8s 2.7133612885068032 K2s 2.844977722819749 97s 3.046270417173673 Q8s 3.0511617858833233 J8s 3.0956378430601035 TTo 3.157970614028727 86s 3.216992057102516 KTo 3.26049949455728 75s 3.3786357028724296 KJo 3.404937536363377 Q6s 3.507069529518276 T7s 3.5093156975169677 KQo 3.5493755781669734 Q5s 3.555429719614267 K9o 3.6093806583271544 Q7s 3.732062836067371 Q4s 3.7783731565129983 J7s 3.862269783869806 99o 3.876538421271107 K6o 3.9004760932211866 K7o 3.9032081800842207 K5o 3.9586973255363773 Q3s 4.001316593410138 K8o 4.047312621962419 96s 4.101232453287821 K4o 4.1041308037815725 64s 4.167201570730072 Q2s 4.224260030311143 K3o 4.271365198167587 K2o 4.4726214217917 88o 4.480358580232405 QTo 4.500590182249653 J5s 4.54460928261642 T6s 4.546449981893602 53s 4.55022148460796 85s 4.573098287334801 QJo 4.741452547716108 J6s 4.813673177621695 J4s 4.856984316726084 Q9o 4.918959889060261 77o 5.0632617019537065 J3s 5.169359350839159 JTo 5.299865573174429 Q8o 5.4445696367849905 95s 5.445255072005239 J2s 5.481734384949959 66o 5.602470741891011 74s 5.652011940087391 J9o 5.777810220043193 T5s 5.810485850213809 T4s 5.811180939451788 Q6o 5.92959496892604 Q5o 5.981914378736747 55o 6.141454521425658 Q7o 6.172760353825424 T9o 6.19306489730684 T3s 6.212987570774658 Q4o 6.22448014190104 J8o 6.332409908712407 43s 6.347744778679271 Q3o 6.471594019828217 T2s 6.614794202097528 84s 6.73936963987569 T8o 6.76674092393705 Q2o 6.7706164755040845 63s 6.803179475473712 J7o 7.148310589899211 98o 7.194228313642952 94s 7.436518400985392 93s 7.437367954497745 44o 7.496099777055406 52s 7.548801056880166 T7o 7.611663726123425 J5o 7.873247903147103 92s 7.928606183033821 87o 7.931764119321997 97o 7.96675242294441 J6o 8.16382631178817 73s 8.180884960156618 J4o 8.212945951233223 J3o 8.553545040924291 76o 8.633598296775062 T6o 8.71495377227393 33o 8.850429668124207 J2o 8.936728000425319 86o 8.991806313813186 96o 9.08657872786614 83s 9.09323463638259 82s 9.094238654169772 65o 9.239713966488239 42s 9.382806881899342 62s 9.694654163069572 75o 10.007899131395106 T5o 10.063215577207075 T4o 10.066747874827911 54o 10.111714141548191 22o 10.182201339033554 85o 10.432053739837784 T3o 10.504749561923404 95o 10.516452376089774 72s 10.897351624192765 T2o 10.968175639610536 32s 11.307933757137107 64o 11.70658352484054 74o 12.437681173722353 94o 12.648180582468399 93o 12.653984792134224 84o 12.748427896934459 53o 12.968258449624386 92o 13.191328461416447 63o 14.525770004410333 73o 15.143189455582615 83o 15.269019915594527 82o 15.278227702653794 43o 15.749131352986979 52o 16.178260998286305 62o 17.62173072071323 72o 18.06804237126744 42o 18.9968553648024 32o 21.91736719075834 I used a computer to come up with these results. Regards, Daan.
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#9
06-06-2005, 05:03 PM
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Re: Tables for the amounts again...
Cool, thanks for posting this.
[ QUOTE ] 95o 100.83272405758211 T4o 104.82848696903099 J2o 105.36502959325747 84o 111.40787845988045 T3o 114.38084723559533 92o 122.34720396301937 T2o 124.44621041447729 94o 126.82174999060837 93o 133.35468349030538 [/ QUOTE ] My guess of 92o turned out to be very close.
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Linear Mode
