#1
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self-balanced hand rankings
Recently there have been some threads about ranking hands vs. random hands, or ranking hands vs. selected hands for their win pcts. If you're jumping into this thread fresh, you might want to search for and read those first to get the background on this. The basic context is "at the end, when blinds are huge, HU, what hands are best for going all-in?"
I put some of those results up here: http://rwa.homelinux.net/poker/hand-rankings.html The question then came up - what happens if you keep repeating the process, re-ranking hands as they do against the top hands of the list that was just generated? What I did was start with the hand rankings associated with how hands do against a randomly chosen hand: http://www.jazbo.com/poker/huholdem.html I then took the top half of those hands, and re-ranked according to how each hand fares against this new list of select hands. I then took the top half of that list and ranked all the hands against that. And so on. The process does converge quite quickly to a list that does not change upon re-ranking. I think it took 3 iterations. The list on the left below is the ranking and win pct against a random hand. The list on the right is the new "self-balanced" list which is the result of the re-ranking iteration I described, using the top half of each subsequent ranking (the top 84 hands, to be precise). vs. random | self-balanced (50%) AAo: 0.852037 AAo: 0.852774 KKo: 0.823957 KKo: 0.786445 QQo: 0.799252 QQo: 0.732733 JJo: 0.774695 JJo: 0.699019 TTo: 0.750118 TTo: 0.669922 99o: 0.720573 AKs: 0.669236 88o: 0.69163 AKo: 0.652736 AKs: 0.670446 AQs: 0.641415 77o: 0.66236 99o: 0.633504 AQs: 0.662089 AJs: 0.622761 AJs: 0.653927 AQo: 0.622686 AKo: 0.65318 ATs: 0.607714 ATs: 0.646024 AJo: 0.602546 AQo: 0.644298 88o: 0.6019 AJo: 0.635612 ATo: 0.586468 KQs: 0.634004 A9s: 0.579613 66o: 0.632847 77o: 0.575587 A9s: 0.627812 KQs: 0.567876 ATo: 0.627196 A8s: 0.560263 KJs: 0.625673 A9o: 0.556357 A8s: 0.619438 66o: 0.553482 KTs: 0.617886 KJs: 0.550502 KQo: 0.614538 KQo: 0.544779 A7s: 0.60984 A7s: 0.543824 A9o: 0.607708 KTs: 0.535916 KJo: 0.605667 A8o: 0.535642 55o: 0.603249 55o: 0.533648 QJs: 0.602592 A6s: 0.527961 K9s: 0.599885 A5s: 0.526257 A5s: 0.599229 KJo: 0.525986 A6s: 0.599058 A7o: 0.518098 A8o: 0.598706 A4s: 0.517687 KTo: 0.597369 44o: 0.511433 QTs: 0.594676 A3s: 0.511124 A4s: 0.590336 KTo: 0.510402 A7o: 0.588392 K9s: 0.507929 K8s: 0.583123 A2s: 0.504211 A3s: 0.582203 A6o: 0.500889 QJo: 0.581327 A5o: 0.499103 K9o: 0.578099 QJs: 0.49305 A5o: 0.576945 A4o: 0.489862 A6o: 0.576804 33o: 0.489583 Q9s: 0.576643 A3o: 0.482721 K7s: 0.575377 K8s: 0.480828 JTs: 0.575279 K9o: 0.480425 A2s: 0.573789 QTs: 0.480021 QTo: 0.572887 A2o: 0.475245 44o: 0.570228 22o: 0.470103 A4o: 0.567276 K7s: 0.466971 K6s: 0.566407 QJo: 0.465063 K8o: 0.560181 JTs: 0.45915 Q8s: 0.560177 K6s: 0.454267 A3o: 0.558426 Q9s: 0.45305 K5s: 0.557929 K8o: 0.451482 J9s: 0.556625 QTo: 0.451136 Q9o: 0.553584 K5s: 0.443539 JTo: 0.552457 K7o: 0.436688 K7o: 0.551853 K4s: 0.435184 A2o: 0.549265 J9s: 0.432513 K4s: 0.548846 JTo: 0.429237 Q7s: 0.543023 Q8s: 0.428724 K6o: 0.542212 K3s: 0.428569 K3s: 0.54055 T9s: 0.426697 T9s: 0.540275 K2s: 0.423425 J8s: 0.540156 K6o: 0.422876 33o: 0.536931 Q9o: 0.422256 Q6s: 0.536126 J8s: 0.412752 Q8o: 0.535978 K5o: 0.411397 K5o: 0.533119 Q7s: 0.410816 J9o: 0.532492 T8s: 0.409699 K2s: 0.532117 98s: 0.409047 Q5s: 0.527694 Q6s: 0.406624 T8s: 0.523344 K4o: 0.402398 K4o: 0.523254 87s: 0.401403 J7s: 0.523248 J9o: 0.400719 Q4s: 0.518553 Q5s: 0.400122 Q7o: 0.517636 J7s: 0.398888 T9o: 0.515296 97s: 0.396527 J8o: 0.514881 Q8o: 0.396259 K3o: 0.514236 T7s: 0.39591 Q6o: 0.51022 76s: 0.395908 Q3s: 0.510192 K3o: 0.395209 98s: 0.508008 T9o: 0.394834 T7s: 0.50639 Q4s: 0.393548 J6s: 0.506059 86s: 0.389837 K2o: 0.505067 K2o: 0.389606 22o: 0.50334 65s: 0.388659 Q2s: 0.50169 Q3s: 0.387367 Q5o: 0.50118 J6s: 0.384417 J5s: 0.499868 Q2s: 0.383829 T8o: 0.497192 96s: 0.38376 J7o: 0.496799 T6s: 0.382255 Q4o: 0.491256 J5s: 0.381525 97s: 0.491177 54s: 0.381423 J4s: 0.490705 75s: 0.381279 T6s: 0.489407 J8o: 0.379583 J3s: 0.482316 Q7o: 0.377172 Q3o: 0.482174 T8o: 0.376602 98o: 0.48095 98o: 0.375978 87s: 0.479363 J4s: 0.375293 T7o: 0.479061 85s: 0.374928 J6o: 0.478422 64s: 0.372926 96s: 0.474283 Q6o: 0.372488 J2s: 0.473782 J3s: 0.369675 Q2o: 0.472934 95s: 0.368701 T5s: 0.472163 87o: 0.367893 J5o: 0.471789 T5s: 0.367251 T4s: 0.465305 53s: 0.366116 97o: 0.462958 J2s: 0.366104 86s: 0.462433 Q5o: 0.36554 J4o: 0.461843 74s: 0.365054 T6o: 0.4609 J7o: 0.364793 95s: 0.457219 T4s: 0.36355 T3s: 0.456925 97o: 0.362635 76s: 0.453718 76o: 0.362227 J3o: 0.452735 T7o: 0.361889 87o: 0.450488 43s: 0.35944 T2s: 0.448395 84s: 0.358449 85s: 0.44545 Q4o: 0.358441 96o: 0.444893 T3s: 0.357946 J2o: 0.443464 63s: 0.357131 T5o: 0.442489 86o: 0.355704 94s: 0.43862 65o: 0.354818 75s: 0.436755 T2s: 0.354352 T4o: 0.435021 94s: 0.352282 93s: 0.432643 52s: 0.352081 86o: 0.432389 Q3o: 0.351749 65s: 0.431334 93s: 0.349265 84s: 0.427016 J6o: 0.349202 95o: 0.426671 73s: 0.34914 T3o: 0.425925 96o: 0.349042 92s: 0.424152 Q2o: 0.347823 76o: 0.423207 T6o: 0.347252 74s: 0.418493 54o: 0.347227 T2o: 0.416663 75o: 0.346689 54s: 0.414534 J5o: 0.346141 85o: 0.414255 92s: 0.345695 64s: 0.413333 42s: 0.345694 83s: 0.408735 62s: 0.343039 94o: 0.40669 83s: 0.342429 75o: 0.405099 82s: 0.341623 82s: 0.402716 85o: 0.339807 73s: 0.400359 J4o: 0.339419 93o: 0.400175 32s: 0.339395 65o: 0.399423 64o: 0.337991 53s: 0.39693 72s: 0.335287 63s: 0.395336 J3o: 0.333384 84o: 0.394448 95o: 0.33298 92o: 0.390959 T5o: 0.331259 43s: 0.386419 53o: 0.33088 74o: 0.385478 J2o: 0.329425 72s: 0.381559 74o: 0.329317 54o: 0.381532 T4o: 0.327264 64o: 0.380084 43o: 0.323787 52s: 0.378493 84o: 0.322163 62s: 0.37669 T3o: 0.321247 83o: 0.374818 63o: 0.321114 42s: 0.36829 T2o: 0.317262 82o: 0.368256 52o: 0.315778 73o: 0.366002 94o: 0.315401 53o: 0.362627 73o: 0.3123 63o: 0.360756 93o: 0.312173 32s: 0.359844 42o: 0.309001 43o: 0.351438 92o: 0.308215 72o: 0.345816 62o: 0.305946 52o: 0.342826 83o: 0.305037 62o: 0.340731 82o: 0.304059 42o: 0.331977 32o: 0.302362 32o: 0.323012 72o: 0.297382 Discuss. The most obvious thing that I see is the increased rank of AK and AQ, which makes intuitive sense - if you're up against more aces, your big aces are going to do even better due to the "domination" effect. Also, it might be interesting to compare this against the Karlson/Sklansky rankings. Another interesting exercise would be to repeat with a "tighter" criterion for selecting the top hands. Say, the top third. eastbay |
#2
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weird
AKo ranks above AQs and ATo is ahead of A9s
...but... AQo is below AJs and AJo is below ATs The differences are miniscule for the most part, but it still seems odd at first glance. I wonder why it worked out that way... Che BTW- Thanks for sharing all this data eastbay. [img]/images/graemlins/laugh.gif[/img] |
#3
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Re: self-balanced hand rankings
Great job, eastbay. Fascinating stuff.
[ QUOTE ] The most obvious thing that I see is the increased rank of AK and AQ, which makes intuitive sense - if you're up against more aces, your big aces are going to do even better due to the "domination" effect. [/ QUOTE ] I also noticed some interesting patterns with the pairs. The medium pairs (99 down to 66) drop significantly in rank, while TT and above stay even. 44 and below increase significantly; 55 stays even. |
#4
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Re: self-balanced hand rankings
"using the top half of each subsequent ranking (the top 84 hands, to be precise). "
To use the top 50% you need to weight these by frequency; as it is, you are probably selecting significantly less that 50% of hands since pp's and suited hands are more likely to be in the top. Craig |
#5
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Re: self-balanced hand rankings
[ QUOTE ]
"using the top half of each subsequent ranking (the top 84 hands, to be precise). " To use the top 50% you need to weight these by frequency; as it is, you are probably selecting significantly less that 50% of hands since pp's and suited hands are more likely to be in the top. Craig [/ QUOTE ] What I mean by top 50% is 50% of the "hand types" and nothing more. It doesn't mean the top of 50% of hands you would see; it would be more or less depending on what kinds of hands those are. In any case this is a bit of an arbitrary parameter. It might be interesting to vary it. But for the time I spend on this stuff I think there's more interesting things to look at. When it comes to computing the win percentage of each hand against the set, I not only account for the relative frequency of each hand, but also the fact that you're holding two of the cards in the deck already, which changes the frequency of some opposing hands. eastbay |
#6
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Re: weird
[ QUOTE ]
AKo ranks above AQs and ATo is ahead of A9s ...but... AQo is below AJs and AJo is below ATs The differences are miniscule for the most part, but it still seems odd at first glance. I wonder why it worked out that way... Che BTW- Thanks for sharing all this data eastbay. [img]/images/graemlins/laugh.gif[/img] [/ QUOTE ] Yeah I noticed some weird stuff, too. Little aces ranking higher? Does that make any sense? I don't see how. eastaby |
#7
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Re: self-balanced hand rankings
Well, what fraction of hands is this?
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#8
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Re: self-balanced hand rankings
[ QUOTE ]
Well, what fraction of hands is this? [/ QUOTE ] 13*6 pairs = 78 42*4 suited = 168 29*12 offsuit = 348 594/1326 = 45%, counted as a fraction of all possible hands you could be dealt. eastbay |
#9
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Re: self-balanced hand rankings
[ QUOTE ]
The most obvious thing that I see is the increased rank of AK and AQ, which makes intuitive sense - if you're up against more aces, your big aces are going to do even better due to the "domination" effect. [/ QUOTE ] Oddly enough, A2o goes UP in value. I would have assumed teh opposite since it is more likely to be dominated. Can anyone explain this? Thank you for compiling this btw. It seems like it could be very helpful. |
#10
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Re: self-balanced hand rankings
[ QUOTE ]
[ QUOTE ] The most obvious thing that I see is the increased rank of AK and AQ, which makes intuitive sense - if you're up against more aces, your big aces are going to do even better due to the "domination" effect. [/ QUOTE ] Oddly enough, A2o goes UP in value. I would have assumed teh opposite since it is more likely to be dominated. Can anyone explain this? Thank you for compiling this btw. It seems like it could be very helpful. [/ QUOTE ] That one bothers me as well. It bothers me enough to think I need to double-check the answers. eastbay |
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