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eastbay
03-23-2004, 07:03 AM
Most people are familiar with the following way of ranking hands:

http://www.jazbo.com/poker/huholdem.html

which is win percentage against a random hand. Problem is, most people don't play random hands. They play select hands.

If instead of computing these numbers against a random hand, we compute them against typical "push" hands: say any pair, or any ace, how does the list change? What hands have positive expectation against a random hand that is any pair or any ace?

I did a calculation, and came up with these numbers:

Gah! I can't get netscape to paste these damn numbers in. I'll post tomorrow. Anyone want to hazard a guess at what hands have +EV against any pair or any ace?

Also, I want to double-check how I did the calculation. I tried to take into account the probability that your opponent holds hand X given your hole cards Y, since some possibilities are "blocked" by your holdinds.

Details to come.

eastbay

PrayingMantis
03-23-2004, 03:21 PM
From the top of my head:

I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve.

For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better.

Is this even close?

eastbay
03-25-2004, 12:08 PM
Ok, here's the results I'm getting when comparing against the "any pair, any ace" set of hands. These are win fractions.

AAo: 0.868701
KKo: 0.717437
QQo: 0.694589
JJo: 0.671537
TTo: 0.648316
AKs: 0.633812
99o: 0.618106
AKo: 0.615742
AQs: 0.602706
88o: 0.594209
AQo: 0.582691
AJs: 0.570817
77o: 0.568266
AJo: 0.548738
66o: 0.543522
ATs: 0.539245
55o: 0.518897
ATo: 0.515079
A9s: 0.498569
44o: 0.489243
A9o: 0.471471
A8s: 0.468405
33o: 0.45922
A8o: 0.439287
A7s: 0.439104
JTs: 0.435095
QJs: 0.432201
KQs: 0.429669
QTs: 0.428981
22o: 0.428917
KJs: 0.426322
KTs: 0.423085
T9s: 0.421997
J9s: 0.41557
A6s: 0.412231
98s: 0.410088
Q9s: 0.409378
A7o: 0.407937
T8s: 0.407644
A5s: 0.406675
JTo: 0.403909
K9s: 0.40339
87s: 0.401158
J8s: 0.401144
QJo: 0.400481
KQo: 0.397427
QTo: 0.39714
97s: 0.395388
Q8s: 0.394819
KJo: 0.393954
T7s: 0.392131
A4s: 0.391515
76s: 0.390746
KTo: 0.390595
T9o: 0.390155
K8s: 0.38856
86s: 0.386708
K7s: 0.385625
J7s: 0.385609
J9o: 0.383063
A3s: 0.381557
96s: 0.380882
K6s: 0.380852
Q7s: 0.379169
A6o: 0.379119
65s: 0.377947
98o: 0.377458
T6s: 0.377398
Q6s: 0.377175
Q9o: 0.376213
T8o: 0.374833
A5o: 0.373404
K5s: 0.372262
75s: 0.372141
A2s: 0.371275
J6s: 0.37076
K9o: 0.369575
Q5s: 0.368592
87o: 0.368155
85s: 0.36804
J8o: 0.367665
54s: 0.365187
J5s: 0.364974
K4s: 0.364348
95s: 0.362213
97o: 0.361791
Q8o: 0.360678
Q4s: 0.360674
64s: 0.359884
T5s: 0.35859
T7o: 0.358288
76o: 0.357173
A4o: 0.357137
J4s: 0.357052
K3s: 0.356324
74s: 0.353963
K8o: 0.35376
T4s: 0.353475
86o: 0.352724
Q3s: 0.352646
J7o: 0.351098
K7o: 0.350695
84s: 0.349813
J3s: 0.34902
K2s: 0.348201
53s: 0.346731
A3o: 0.346479
96o: 0.346298
K6o: 0.345598
T3s: 0.345439
Q2s: 0.344518
Q7o: 0.343993
94s: 0.34389
65o: 0.343729
T6o: 0.34255
Q6o: 0.3419
63s: 0.341299
J2s: 0.340887
93s: 0.33867
43s: 0.33766
75o: 0.337437
T2s: 0.337301
K5o: 0.336543
73s: 0.335466
A2o: 0.335453
J6o: 0.335241
85o: 0.33291
Q5o: 0.332851
83s: 0.331219
92s: 0.330518
54o: 0.330241
J5o: 0.329216
K4o: 0.328023
52s: 0.327759
95o: 0.326483
82s: 0.325903
64o: 0.324395
Q4o: 0.324329
T5o: 0.322591
62s: 0.322283
J4o: 0.320689
K3o: 0.319379
42s: 0.318872
74o: 0.31797
T4o: 0.317097
72s: 0.316582
Q3o: 0.315681
84o: 0.313391
J3o: 0.312037
K2o: 0.310618
53o: 0.310492
32s: 0.309713
T3o: 0.308441
Q2o: 0.306915
94o: 0.306866
63o: 0.304498
J2o: 0.303267
93o: 0.301252
43o: 0.3009
T2o: 0.299667
73o: 0.298163
83o: 0.293484
92o: 0.292463
52o: 0.290183
82o: 0.287756
62o: 0.284141
42o: 0.280797
72o: 0.277943
32o: 0.271115

Some notes:

* good pairs and aces increase in rank vs. other pairs and aces, due to the "domination" effect.

* There aren't many hands which have a win pct &gt; 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo

* If you want an edge of 70% or better, you have to wait for KK or AA.

* The best hand other than an ace or pair is JTs! Maybe that old idea about JT being the "best hand" wasn't _so_ crazy.

* Note the abysmal rank of A2o, which some guy at the aviation club came over the top all-in with last night on WPT... to lose.

* Fossilman's semi-famous T9s play isn't far from as good as you can do if you don't have an ace or pair in front of you. Higher suited connectors are better, but not by much.

* T8s ranks better than A5s! Beware dominated aces!

Here's a side-by-side on the top 15 hands in each case:

vs. As, pairs vs. random hand
-------------|---------------|
AAo: 0.868701 AAo: 0.852037
KKo: 0.717437 KKo: 0.823957
QQo: 0.694589 QQo: 0.799252
JJo: 0.671537 JJo: 0.774695
TTo: 0.648316 TTo: 0.750118
AKs: 0.633812 99o: 0.720573
99o: 0.618106 88o: 0.69163
AKo: 0.615742 AKs: 0.670446
AQs: 0.602706 77o: 0.66236
88o: 0.594209 AQs: 0.662089
AQo: 0.582691 AJs: 0.653927
AJs: 0.570817 AKo: 0.65318
77o: 0.568266 ATs: 0.646024
AJo: 0.548738 AQo: 0.644298
66o: 0.543522 AJo: 0.635612

Note how much AKo jumps up. Also note that AJs goes down in rank, but AJo goes up!

eastbay

eastbay
03-25-2004, 12:12 PM
[ QUOTE ]
From the top of my head:

I would guess that the win% of the top hands in jazbo's list will improve dramatically, while the bottom hands will lose much value. Pairs lower than 77 will lose some value, Aces with 7 kicker and below will lose value dramatically, while medium and med-high connectors will somewhat improve.

For example: in their list, 55 is little better than QJs. I would say that in your list, QJs will stand better.

Is this even close?

[/ QUOTE ]

Draw your own conclusions from the results I just posted. I'd say you hit some ideas correctly and missed a little with others.

eastbay

hockey1
03-25-2004, 12:21 PM
Interesting. I think the biggest surprise to me was how high JTs ranked, at least relative to KQs, QJs, KJs.

Keep in mind that as the table gets down to 2 or 3 players people will push with hands other than pairs and aces, which will change these odds around a fair bit.

AleoMagus
03-25-2004, 06:38 PM
Very interesting

I think these rankings paint a far more accurate picture of what hands are good calling hands.

How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands

I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards

Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc...

[ QUOTE ]
* There aren't many hands which have a win pct &gt; 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo

[/ QUOTE ]

This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble

Good Post

eastbay
03-25-2004, 11:02 PM
[ QUOTE ]
Very interesting

I think these rankings paint a far more accurate picture of what hands are good calling hands.

How hard would it be for you to rank vs a random chance of a slightly more refined list of possible opposition hands

I'd actually like to take some hands like A2o-A6o off the list and add some hands like KQ, KJ, and suited broadway cards

[/ QUOTE ]

Dirt simple. Give me any list, I'll give you the rankings.

[ QUOTE ]

Also, does this list take into account the greater likelihood that your opponent is holding AK than a pair, etc...

[/ QUOTE ]

Yes it does. This was slightly tricky to get right and there's still one point which seems "wrong" to me but it's the only way I can the probabilities to sum to unity (which is of course a necessary condition for it to be correct)

Here's the case I'm confused by: when you hold an offsuit non-pair hand and your opponent holds a suited hand that matches both of your cards in rank, how many different hands can he be holding?

[ QUOTE ]

[ QUOTE ]
* There aren't many hands which have a win pct &gt; 50% against a random pair or ace! The only "winners" are: AAo, KKo, QQo, JJo, TTo, AKs, 99o, AKo, AQs, 88o, AQo, AJs, 77o, AJo, 66o, ATs, 55o, ATo

[/ QUOTE ]

This is a very powerful point. I think that this point almost comes close to a suggested calling requirement against shortstacks pushing on the bubble

Good Post

[/ QUOTE ]

Thanks. Glad you got something out of it.

eastbay

eastbay
03-25-2004, 11:31 PM
Here's the results for:

column 1: random hand
column 2: any ace, any pair
column 3: aces except A6o-A20, all pairs, KQs, KJs, KTs, QJs

AAo: 0.852037 AAo: 0.868701 AAo: 0.852403
KKo: 0.823957 KKo: 0.717437 KKo: 0.725878
QQo: 0.799252 QQo: 0.694589 QQo: 0.690498
JJo: 0.774695 JJo: 0.671537 JJo: 0.657249
TTo: 0.750118 TTo: 0.648316 TTo: 0.624291
99o: 0.720573 AKs: 0.633812 AKs: 0.609668
88o: 0.69163 99o: 0.618106 AKo: 0.590376
AKs: 0.670446 AKo: 0.615742 99o: 0.587292
77o: 0.66236 AQs: 0.602706 AQs: 0.57245
AQs: 0.662089 88o: 0.594209 88o: 0.557937
AJs: 0.653927 AQo: 0.582691 AQo: 0.550575
AKo: 0.65318 AJs: 0.570817 AJs: 0.536638
ATs: 0.646024 77o: 0.568266 77o: 0.526918
AQo: 0.644298 AJo: 0.548738 AJo: 0.512433
AJo: 0.635612 66o: 0.543522 66o: 0.503295
KQs: 0.634004 ATs: 0.539245 ATs: 0.500597
66o: 0.632847 55o: 0.518897 55o: 0.480924
A9s: 0.627812 ATo: 0.515079 ATo: 0.473856
ATo: 0.627196 A9s: 0.498569 A9s: 0.456724
KJs: 0.625673 44o: 0.489243 44o: 0.45548
A8s: 0.619438 A9o: 0.471471 KQs: 0.435427
KTs: 0.617886 A8s: 0.468405 33o: 0.430012
KQo: 0.614538 33o: 0.45922 A8s: 0.427111
A7s: 0.60984 A8o: 0.439287 A9o: 0.426667
A9o: 0.607708 A7s: 0.439104 KJs: 0.424205
KJo: 0.605667 JTs: 0.435095 QJs: 0.417834
55o: 0.603249 QJs: 0.432201 JTs: 0.413598
QJs: 0.602592 KQs: 0.429669 KTs: 0.412861
K9s: 0.599885 QTs: 0.428981 QTs: 0.409806
A5s: 0.599229 22o: 0.428917 22o: 0.40465
A6s: 0.599058 KJs: 0.426322 KQo: 0.404582
A8o: 0.598706 KTs: 0.423085 A7s: 0.400662
KTo: 0.597369 T9s: 0.421997 T9s: 0.40004
QTs: 0.594676 J9s: 0.41557 A8o: 0.395024
A4s: 0.590336 A6s: 0.412231 J9s: 0.394774
A7o: 0.588392 98s: 0.410088 KJo: 0.39268
K8s: 0.583123 Q9s: 0.409378 Q9s: 0.390815
A3s: 0.582203 A7o: 0.407937 K9s: 0.389992
QJo: 0.581327 T8s: 0.407644 A5s: 0.388996
K9o: 0.578099 A5s: 0.406675 98s: 0.387872
A5o: 0.576945 JTo: 0.403909 QJo: 0.386162
A6o: 0.576804 K9s: 0.40339 T8s: 0.385036
Q9s: 0.576643 87s: 0.401158 A6s: 0.384929
K7s: 0.575377 J8s: 0.401144 JTo: 0.382016
JTs: 0.575279 QJo: 0.400481 KTo: 0.380491
A2s: 0.573789 KQo: 0.397427 J8s: 0.379669
QTo: 0.572887 QTo: 0.39714 A4s: 0.379591
44o: 0.570228 97s: 0.395388 QTo: 0.377687
A4o: 0.567276 Q8s: 0.394819 87s: 0.37745
K6s: 0.566407 KJo: 0.393954 Q8s: 0.375597
K8o: 0.560181 T7s: 0.392131 K8s: 0.374595
Q8s: 0.560177 A4s: 0.391515 97s: 0.372826
A3o: 0.558426 76s: 0.390746 K6s: 0.372184
K5s: 0.557929 KTo: 0.390595 76s: 0.372178
J9s: 0.556625 T9o: 0.390155 A3s: 0.371324
Q9o: 0.553584 K8s: 0.38856 K7s: 0.370786
JTo: 0.552457 86s: 0.386708 T7s: 0.368944
K7o: 0.551853 K7s: 0.385625 86s: 0.368841
A2o: 0.549265 J7s: 0.385609 T9o: 0.36802
K4s: 0.548846 J9o: 0.383063 A7o: 0.366712
Q7s: 0.543023 A3s: 0.381557 65s: 0.366508
K6o: 0.542212 96s: 0.380882 K5s: 0.365975
K3s: 0.54055 K6s: 0.380852 96s: 0.364085
T9s: 0.540275 Q7s: 0.379169 Q6s: 0.363528
J8s: 0.540156 A6o: 0.379119 J7s: 0.363448
33o: 0.536931 65s: 0.377947 A2s: 0.362706
Q6s: 0.536126 98o: 0.377458 J9o: 0.362007
Q8o: 0.535978 T6s: 0.377398 T6s: 0.360074
K5o: 0.533119 Q6s: 0.377175 Q7s: 0.359384
J9o: 0.532492 Q9o: 0.376213 K4s: 0.358869
K2s: 0.532117 T8o: 0.374833 Q9o: 0.357511
Q5s: 0.527694 A5o: 0.373404 Q5s: 0.357398
T8s: 0.523344 K5s: 0.372262 54s: 0.356239
K4o: 0.523254 75s: 0.372141 75s: 0.356145
J7s: 0.523248 A2s: 0.371275 K9o: 0.356027
Q4s: 0.518553 J6s: 0.37076 98o: 0.355184
Q7o: 0.517636 K9o: 0.369575 J6s: 0.354933
T9o: 0.515296 Q5s: 0.368592 A5o: 0.354299
J8o: 0.514881 87o: 0.368155 85s: 0.352519
K3o: 0.514236 85s: 0.36804 T8o: 0.352024
Q6o: 0.51022 J8o: 0.367665 K3s: 0.351458
Q3s: 0.510192 54s: 0.365187 J5s: 0.351416
98s: 0.508008 J5s: 0.364974 Q4s: 0.350273
T7s: 0.50639 K4s: 0.364348 A6o: 0.349771
J6s: 0.506059 95s: 0.362213 64s: 0.34944
K2o: 0.505067 97o: 0.361791 95s: 0.347766
22o: 0.50334 Q8o: 0.360678 J8o: 0.3459
Q2s: 0.50169 Q4s: 0.360674 J4s: 0.344284
Q5o: 0.50118 64s: 0.359884 87o: 0.344273
J5s: 0.499868 T5s: 0.35859 A4o: 0.344211
T8o: 0.497192 T7o: 0.358288 K2s: 0.343822
J7o: 0.496799 76o: 0.357173 T5s: 0.343757
Q4o: 0.491256 A4o: 0.357137 Q3s: 0.342832
97s: 0.491177 J4s: 0.357052 Q8o: 0.34129
J4s: 0.490705 K3s: 0.356324 K8o: 0.339623
T6s: 0.489407 74s: 0.353963 T4s: 0.339354
J3s: 0.482316 K8o: 0.35376 97o: 0.33917
Q3o: 0.482174 T4s: 0.353475 53s: 0.338841
98o: 0.48095 86o: 0.352724 74s: 0.338648
87s: 0.479363 Q3s: 0.352646 76o: 0.338626
T7o: 0.479061 J7o: 0.351098 K6o: 0.336951
J6o: 0.478422 K7o: 0.350695 J3s: 0.336835
96s: 0.474283 84s: 0.349813 K7o: 0.335606
J2s: 0.473782 J3s: 0.34902 A3o: 0.335351
Q2o: 0.472934 K2s: 0.348201 Q2s: 0.335165
T5s: 0.472163 53s: 0.346731 84s: 0.335088
J5o: 0.471789 A3o: 0.346479 86o: 0.334934
T4s: 0.465305 96o: 0.346298 T7o: 0.334884
97o: 0.462958 K6o: 0.345598 65o: 0.332685
86s: 0.462433 T3s: 0.345439 T3s: 0.331932
J4o: 0.461843 Q2s: 0.344518 63s: 0.331813
T6o: 0.4609 Q7o: 0.343993 43s: 0.330534
95s: 0.457219 94s: 0.34389 K5o: 0.330441
T3s: 0.456925 65o: 0.343729 94s: 0.330436
76s: 0.453718 T6o: 0.34255 96o: 0.329697
J3o: 0.452735 Q6o: 0.3419 J2s: 0.329159
87o: 0.450488 63s: 0.341299 J7o: 0.328611
T2s: 0.448395 J2s: 0.340887 Q6o: 0.328314
85s: 0.44545 93s: 0.33867 A2o: 0.326099
96o: 0.444893 43s: 0.33766 93s: 0.325807
J2o: 0.443464 75o: 0.337437 T6o: 0.325271
T5o: 0.442489 T2s: 0.337301 T2s: 0.324283
94s: 0.43862 K5o: 0.336543 Q7o: 0.32402
75s: 0.436755 73s: 0.335466 K4o: 0.322831
T4o: 0.435021 A2o: 0.335453 54o: 0.321911
93s: 0.432643 J6o: 0.335241 Q5o: 0.321886
86o: 0.432389 85o: 0.33291 75o: 0.321674
65s: 0.431334 Q5o: 0.332851 52s: 0.320948
84s: 0.427016 83s: 0.331219 73s: 0.320877
95o: 0.426671 92s: 0.330518 J6o: 0.319385
T3o: 0.425925 54o: 0.330241 92s: 0.318174
92s: 0.424152 J5o: 0.329216 85o: 0.317667
76o: 0.423207 K4o: 0.328023 83s: 0.317427
74s: 0.418493 52s: 0.327759 J5o: 0.315777
T2o: 0.416663 95o: 0.326483 K3o: 0.314888
54s: 0.414534 82s: 0.325903 64o: 0.314505
85o: 0.414255 64o: 0.324395 Q4o: 0.314258
64s: 0.413333 Q4o: 0.324329 62s: 0.313897
83s: 0.408735 T5o: 0.322591 42s: 0.312957
94o: 0.40669 62s: 0.322283 82s: 0.312573
75o: 0.405099 J4o: 0.320689 95o: 0.31243
82s: 0.402716 K3o: 0.319379 J4o: 0.308142
73s: 0.400359 42s: 0.318872 T5o: 0.307999
93o: 0.400175 74o: 0.31797 K2o: 0.306695
65o: 0.399423 T4o: 0.317097 Q3o: 0.306286
53s: 0.39693 72s: 0.316582 32s: 0.304503
63s: 0.395336 Q3o: 0.315681 53o: 0.303372
84o: 0.394448 84o: 0.313391 T4o: 0.303309
92o: 0.390959 J3o: 0.312037 74o: 0.303023
43s: 0.386419 K2o: 0.310618 72s: 0.302883
74o: 0.385478 53o: 0.310492 J3o: 0.300162
72s: 0.381559 32s: 0.309713 84o: 0.299082
54o: 0.381532 T3o: 0.308441 Q2o: 0.298062
64o: 0.380084 Q2o: 0.306915 63o: 0.295713
52s: 0.378493 94o: 0.306866 T3o: 0.295358
62s: 0.37669 63o: 0.304498 43o: 0.294601
83o: 0.374818 J2o: 0.303267 94o: 0.29395
42s: 0.36829 93o: 0.301252 J2o: 0.291929
82o: 0.368256 43o: 0.3009 93o: 0.289012
73o: 0.366002 T2o: 0.299667 T2o: 0.287156
53o: 0.362627 73o: 0.298163 52o: 0.284284
63o: 0.360756 83o: 0.293484 73o: 0.284069
32s: 0.359844 92o: 0.292463 92o: 0.280829
43o: 0.351438 52o: 0.290183 83o: 0.280242
72o: 0.345816 82o: 0.287756 62o: 0.2766
52o: 0.342826 62o: 0.284141 42o: 0.275857
62o: 0.340731 42o: 0.280797 82o: 0.275057
42o: 0.331977 72o: 0.277943 32o: 0.266933
32o: 0.323012 32o: 0.271115 72o: 0.264864

eastbay

AleoMagus
03-25-2004, 11:59 PM
great info. printed off and tucked into my poker binder already

Thanks

eastbay
03-26-2004, 12:33 AM
http://rwa.homelinux.net/poker/hand-rankings.html

Notice our friend at the bottom of the rankings for the "refined set" of push hands, set C. /images/graemlins/wink.gif

eastbay

AleoMagus
03-26-2004, 01:08 AM
can you do results for more than one opponent?

I have always been interested what hand rankings would be with 2-9 opponents for each of the sklansky hand groups

Regards,

AleoMagus
03-26-2004, 01:14 AM
lol. sorry

looking back on that post, I realize that even if it is possible with your current program, that's a lot of work

Still, as long as I'm wishing, I have also wanted rankings that only calculate who's ahead on the flop and the turn.

This would be very useful in my opinion in determining relative hand strengths when you might intend on a 'stop and go' move.

I don't want you to run all these sims for me, but I would be very interested in a program that I could use to do this.

Regards,

eastbay
03-26-2004, 02:37 AM
[ QUOTE ]
can you do results for more than one opponent?

I have always been interested what hand rankings would be with 2-9 opponents for each of the sklansky hand groups

Regards,

[/ QUOTE ]

Hmm. Not even sure how to formulate that problem. In any case, my current code can't do that.

I am definitely interested in expanding my push/fold strategy results to 3-handed, but I haven't started work on it yet. I'm pretty sure I will use one of these hand rankings as the basis, though, since the vast majority of the time you're going to end up "racing" somebody heads-up.

eastbay

Nottom
03-26-2004, 04:31 AM
[ QUOTE ]
Here's the case I'm confused by: when you hold an offsuit non-pair hand and your opponent holds a suited hand that matches both of your cards in rank, how many different hands can he be holding?

[/ QUOTE ]

You mean if you hold AKo how many ways can someone hold AKs?

Great work btw, some interesting info there.

Nottom
03-26-2004, 04:34 AM
I was noticing the same thing. I find it interesting that the bottom of the list changes so much in the different runs.

eastbay
03-26-2004, 11:36 AM
[ QUOTE ]

You mean if you hold AKo how many ways can someone hold AKs?

Great work btw, some interesting info there.

[/ QUOTE ]

For the "you hold offsuit cards" case I get a total of 1224 possible opponent's hands unless I make that number 3 instead of 2.

So here's the cases I'm considering, using AKo as an example:

You hold AKo.
How many AKs can your opponent hold? 2.
How many AKo can your opponent hold?
How many AA?
How many KK?
How many Axs?
How many Kxs?
How many Axo?
How many Kxo?

Is there some other case which is not the usual 6, 4, 12 for pair, suited, offsuit that I'm forgetting?

eastbay

DarkKnight
03-26-2004, 11:43 AM
Assume Ac Kd

How many AKo can your opponent hold?
7

How many AA?
3

How many KK?
KcKh KcKs KhKs
3

How many Axs?
Ah w/ 2-Qh
As w/ 2-Qs
11 x 3 = 33

How many Kxs?
33

How many Axo?
Ad w/ 2-Q c, h, s = 3 x 11 = 22 x 3 for Ad, Ah, As = 99
99

How many Kxo?
99

eastbay
03-26-2004, 12:19 PM
[ QUOTE ]
Assume Ac Kd

How many AKo can your opponent hold?
7

How many AA?
3

How many KK?
KcKh KcKs KhKs
3

How many Axs?
Ah w/ 2-Qh
As w/ 2-Qs
11 x 3 = 33

How many Kxs?
33

How many Axo?
Ad w/ 2-Q c, h, s = 3 x 11 = 22 x 3 for Ad, Ah, As = 99
99

How many Kxo?
99

[/ QUOTE ]

Thank you - you helped me spot the bug. Here's the corrected results. I didn't check carefully but at first glance none of the rankings changed (although some of the percentages changed slightly).

http://rwa.homelinux.net/poker/hand-rankings.html

I'm also now exactly duplicating Jazbo's results for all hands in the case of random hands, so that's a good sign.

eastbay

AA suited
06-03-2004, 12:24 PM
the link no longer works /images/graemlins/frown.gif

anyone make a copy of the website?

Bozeman
06-03-2004, 03:31 PM
FWIW, Allenciox did essentially the same thing several months ago (using karlson's data, I think), and these are his results:

Craig

06-03-2004, 03:51 PM
No but I printed out the results /images/graemlins/cool.gif

AA suited
06-04-2004, 02:37 PM
hm..

Against aces (except A6o-A2o), all pairs, KQs, KJs, KTs, QJs: k6s is ranked higher than k7s

WHY??

or is there errors in this chart?

eastbay
06-05-2004, 02:45 AM
Link should be back up now.

eastbay

AA suited
06-05-2004, 10:29 PM
Why is K6s ranked higher than K7s?

ps- thx for getting the link back up /images/graemlins/smile.gif

eastbay
06-07-2004, 03:14 AM
In the 3rd column?

Presumably because 6 is more likely to be a "live" card than 7, due to the choice of A6-A2 not being included in the list of "all-in" hands.

eastbay

durron597
06-07-2004, 04:01 AM
Hey eastbay...

I dont know how much processor power this took to calculate, but would it be possible to run this simulation against two - three random hands? I realize that adding an extra hand to the comparison is on the order of exponential increase in runtime, but hopefully one more hand wouldn't be too bad. I'm curious how these percentages change relatively speaking in multiway pots; for example, say you are BB, CO-1 is a thief but not insanely LAG, bets 3xBB, Button is a very LAG (borderline maniac) and goes allin. All others fold. What hands are you better than 33%? 40%? (Assuming CO-1 calls, definitely something to consider)

By the way, I just wanted to say great job with the list as it is so far. You rock.

hummusx
07-28-2004, 02:45 PM
Because you have more outs with K6s than K7s when you cut out A6. If you have K7 and your opponent has A7 and a 7 hits, you still lose. On the other hand if you have K6 and a 6 hits, the calculation assumes it will help you but not your opponent (except if he has 66). So that's 3 outs you pick up against one specific hand.

filsho
07-29-2004, 12:48 AM
The link still isn't coming up for me...anyone else?

stupidsucker
07-29-2004, 04:08 AM
Can you do one more for me?

Here are the hands I think an average SnG player will push with.

ANy Pair
Ax
K5s-KQs
K8o-KQo
Q8-QJ
J9-JT

Some of those hands are a little low, but lets face it, but I see them alll the time.

If its too much trouble don't worry bout it.

ilya
08-06-2004, 03:17 PM
Does this take into account that if you're holding KQ (for example) the chances that your opponent is pushing with AK, AQ, KK, or QQ are lower than if you're holding, say, 54o?

eastbay
08-06-2004, 10:10 PM
[ QUOTE ]
Does this take into account that if you're holding KQ (for example) the chances that your opponent is pushing with AK, AQ, KK, or QQ are lower than if you're holding, say, 54o?

[/ QUOTE ]

Yes.

eastbay

ilya
10-03-2004, 12:07 AM
Do y'all think it might be a good idea to add this thread to the FAQ sticky. I found it really useful &amp; keep coming back to it.

Scuba Chuck
12-10-2004, 03:32 PM

I've been back here many times myself...

Unless you have another thread that addresses the top 10 hands, top 1/3 of hands, etc. But this thread does that and much more...

leftyelvis
02-27-2005, 03:42 PM
[ QUOTE ]
Here's the results for:

column 1: random hand
column 2: any ace, any pair
column 3: aces except A6o-A20, all pairs, KQs, KJs, KTs, QJs

AAo: 0.852037 AAo: 0.868701 AAo: 0.852403
KKo: 0.823957 KKo: 0.717437 KKo: 0.725878
QQo: 0.799252 QQo: 0.694589 QQo: 0.690498
JJo: 0.774695 JJo: 0.671537 JJo: 0.657249
TTo: 0.750118 TTo: 0.648316 TTo: 0.624291
99o: 0.720573 AKs: 0.633812 AKs: 0.609668
88o: 0.69163 99o: 0.618106 AKo: 0.590376
AKs: 0.670446 AKo: 0.615742 99o: 0.587292
77o: 0.66236 AQs: 0.602706 AQs: 0.57245
AQs: 0.662089 88o: 0.594209 88o: 0.557937
AJs: 0.653927 AQo: 0.582691 AQo: 0.550575
AKo: 0.65318 AJs: 0.570817 AJs: 0.536638
ATs: 0.646024 77o: 0.568266 77o: 0.526918
AQo: 0.644298 AJo: 0.548738 AJo: 0.512433
AJo: 0.635612 66o: 0.543522 66o: 0.503295
KQs: 0.634004 ATs: 0.539245 ATs: 0.500597
66o: 0.632847 55o: 0.518897 55o: 0.480924
A9s: 0.627812 ATo: 0.515079 ATo: 0.473856
ATo: 0.627196 A9s: 0.498569 A9s: 0.456724
KJs: 0.625673 44o: 0.489243 44o: 0.45548
A8s: 0.619438 A9o: 0.471471 KQs: 0.435427
KTs: 0.617886 A8s: 0.468405 33o: 0.430012
KQo: 0.614538 33o: 0.45922 A8s: 0.427111
A7s: 0.60984 A8o: 0.439287 A9o: 0.426667
A9o: 0.607708 A7s: 0.439104 KJs: 0.424205
KJo: 0.605667 JTs: 0.435095 QJs: 0.417834
55o: 0.603249 QJs: 0.432201 JTs: 0.413598
QJs: 0.602592 KQs: 0.429669 KTs: 0.412861
K9s: 0.599885 QTs: 0.428981 QTs: 0.409806
A5s: 0.599229 22o: 0.428917 22o: 0.40465
A6s: 0.599058 KJs: 0.426322 KQo: 0.404582
A8o: 0.598706 KTs: 0.423085 A7s: 0.400662
KTo: 0.597369 T9s: 0.421997 T9s: 0.40004
QTs: 0.594676 J9s: 0.41557 A8o: 0.395024
A4s: 0.590336 A6s: 0.412231 J9s: 0.394774
A7o: 0.588392 98s: 0.410088 KJo: 0.39268
K8s: 0.583123 Q9s: 0.409378 Q9s: 0.390815
A3s: 0.582203 A7o: 0.407937 K9s: 0.389992
QJo: 0.581327 T8s: 0.407644 A5s: 0.388996
K9o: 0.578099 A5s: 0.406675 98s: 0.387872
A5o: 0.576945 JTo: 0.403909 QJo: 0.386162
A6o: 0.576804 K9s: 0.40339 T8s: 0.385036
Q9s: 0.576643 87s: 0.401158 A6s: 0.384929
K7s: 0.575377 J8s: 0.401144 JTo: 0.382016
JTs: 0.575279 QJo: 0.400481 KTo: 0.380491
A2s: 0.573789 KQo: 0.397427 J8s: 0.379669
QTo: 0.572887 QTo: 0.39714 A4s: 0.379591
44o: 0.570228 97s: 0.395388 QTo: 0.377687
A4o: 0.567276 Q8s: 0.394819 87s: 0.37745
K6s: 0.566407 KJo: 0.393954 Q8s: 0.375597
K8o: 0.560181 T7s: 0.392131 K8s: 0.374595
Q8s: 0.560177 A4s: 0.391515 97s: 0.372826
A3o: 0.558426 76s: 0.390746 K6s: 0.372184
K5s: 0.557929 KTo: 0.390595 76s: 0.372178
J9s: 0.556625 T9o: 0.390155 A3s: 0.371324
Q9o: 0.553584 K8s: 0.38856 K7s: 0.370786
JTo: 0.552457 86s: 0.386708 T7s: 0.368944
K7o: 0.551853 K7s: 0.385625 86s: 0.368841
A2o: 0.549265 J7s: 0.385609 T9o: 0.36802
K4s: 0.548846 J9o: 0.383063 A7o: 0.366712
Q7s: 0.543023 A3s: 0.381557 65s: 0.366508
K6o: 0.542212 96s: 0.380882 K5s: 0.365975
K3s: 0.54055 K6s: 0.380852 96s: 0.364085
T9s: 0.540275 Q7s: 0.379169 Q6s: 0.363528
J8s: 0.540156 A6o: 0.379119 J7s: 0.363448
33o: 0.536931 65s: 0.377947 A2s: 0.362706
Q6s: 0.536126 98o: 0.377458 J9o: 0.362007
Q8o: 0.535978 T6s: 0.377398 T6s: 0.360074
K5o: 0.533119 Q6s: 0.377175 Q7s: 0.359384
J9o: 0.532492 Q9o: 0.376213 K4s: 0.358869
K2s: 0.532117 T8o: 0.374833 Q9o: 0.357511
Q5s: 0.527694 A5o: 0.373404 Q5s: 0.357398
T8s: 0.523344 K5s: 0.372262 54s: 0.356239
K4o: 0.523254 75s: 0.372141 75s: 0.356145
J7s: 0.523248 A2s: 0.371275 K9o: 0.356027
Q4s: 0.518553 J6s: 0.37076 98o: 0.355184
Q7o: 0.517636 K9o: 0.369575 J6s: 0.354933
T9o: 0.515296 Q5s: 0.368592 A5o: 0.354299
J8o: 0.514881 87o: 0.368155 85s: 0.352519
K3o: 0.514236 85s: 0.36804 T8o: 0.352024
Q6o: 0.51022 J8o: 0.367665 K3s: 0.351458
Q3s: 0.510192 54s: 0.365187 J5s: 0.351416
98s: 0.508008 J5s: 0.364974 Q4s: 0.350273
T7s: 0.50639 K4s: 0.364348 A6o: 0.349771
J6s: 0.506059 95s: 0.362213 64s: 0.34944
K2o: 0.505067 97o: 0.361791 95s: 0.347766
22o: 0.50334 Q8o: 0.360678 J8o: 0.3459
Q2s: 0.50169 Q4s: 0.360674 J4s: 0.344284
Q5o: 0.50118 64s: 0.359884 87o: 0.344273
J5s: 0.499868 T5s: 0.35859 A4o: 0.344211
T8o: 0.497192 T7o: 0.358288 K2s: 0.343822
J7o: 0.496799 76o: 0.357173 T5s: 0.343757
Q4o: 0.491256 A4o: 0.357137 Q3s: 0.342832
97s: 0.491177 J4s: 0.357052 Q8o: 0.34129
J4s: 0.490705 K3s: 0.356324 K8o: 0.339623
T6s: 0.489407 74s: 0.353963 T4s: 0.339354
J3s: 0.482316 K8o: 0.35376 97o: 0.33917
Q3o: 0.482174 T4s: 0.353475 53s: 0.338841
98o: 0.48095 86o: 0.352724 74s: 0.338648
87s: 0.479363 Q3s: 0.352646 76o: 0.338626
T7o: 0.479061 J7o: 0.351098 K6o: 0.336951
J6o: 0.478422 K7o: 0.350695 J3s: 0.336835
96s: 0.474283 84s: 0.349813 K7o: 0.335606
J2s: 0.473782 J3s: 0.34902 A3o: 0.335351
Q2o: 0.472934 K2s: 0.348201 Q2s: 0.335165
T5s: 0.472163 53s: 0.346731 84s: 0.335088
J5o: 0.471789 A3o: 0.346479 86o: 0.334934
T4s: 0.465305 96o: 0.346298 T7o: 0.334884
97o: 0.462958 K6o: 0.345598 65o: 0.332685
86s: 0.462433 T3s: 0.345439 T3s: 0.331932
J4o: 0.461843 Q2s: 0.344518 63s: 0.331813
T6o: 0.4609 Q7o: 0.343993 43s: 0.330534
95s: 0.457219 94s: 0.34389 K5o: 0.330441
T3s: 0.456925 65o: 0.343729 94s: 0.330436
76s: 0.453718 T6o: 0.34255 96o: 0.329697
J3o: 0.452735 Q6o: 0.3419 J2s: 0.329159
87o: 0.450488 63s: 0.341299 J7o: 0.328611
T2s: 0.448395 J2s: 0.340887 Q6o: 0.328314
85s: 0.44545 93s: 0.33867 A2o: 0.326099
96o: 0.444893 43s: 0.33766 93s: 0.325807
J2o: 0.443464 75o: 0.337437 T6o: 0.325271
T5o: 0.442489 T2s: 0.337301 T2s: 0.324283
94s: 0.43862 K5o: 0.336543 Q7o: 0.32402
75s: 0.436755 73s: 0.335466 K4o: 0.322831
T4o: 0.435021 A2o: 0.335453 54o: 0.321911
93s: 0.432643 J6o: 0.335241 Q5o: 0.321886
86o: 0.432389 85o: 0.33291 75o: 0.321674
65s: 0.431334 Q5o: 0.332851 52s: 0.320948
84s: 0.427016 83s: 0.331219 73s: 0.320877
95o: 0.426671 92s: 0.330518 J6o: 0.319385
T3o: 0.425925 54o: 0.330241 92s: 0.318174
92s: 0.424152 J5o: 0.329216 85o: 0.317667
76o: 0.423207 K4o: 0.328023 83s: 0.317427
74s: 0.418493 52s: 0.327759 J5o: 0.315777
T2o: 0.416663 95o: 0.326483 K3o: 0.314888
54s: 0.414534 82s: 0.325903 64o: 0.314505
85o: 0.414255 64o: 0.324395 Q4o: 0.314258
64s: 0.413333 Q4o: 0.324329 62s: 0.313897
83s: 0.408735 T5o: 0.322591 42s: 0.312957
94o: 0.40669 62s: 0.322283 82s: 0.312573
75o: 0.405099 J4o: 0.320689 95o: 0.31243
82s: 0.402716 K3o: 0.319379 J4o: 0.308142
73s: 0.400359 42s: 0.318872 T5o: 0.307999
93o: 0.400175 74o: 0.31797 K2o: 0.306695
65o: 0.399423 T4o: 0.317097 Q3o: 0.306286
53s: 0.39693 72s: 0.316582 32s: 0.304503
63s: 0.395336 Q3o: 0.315681 53o: 0.303372
84o: 0.394448 84o: 0.313391 T4o: 0.303309
92o: 0.390959 J3o: 0.312037 74o: 0.303023
43s: 0.386419 K2o: 0.310618 72s: 0.302883
74o: 0.385478 53o: 0.310492 J3o: 0.300162
72s: 0.381559 32s: 0.309713 84o: 0.299082
54o: 0.381532 T3o: 0.308441 Q2o: 0.298062
64o: 0.380084 Q2o: 0.306915 63o: 0.295713
52s: 0.378493 94o: 0.306866 T3o: 0.295358
62s: 0.37669 63o: 0.304498 43o: 0.294601
83o: 0.374818 J2o: 0.303267 94o: 0.29395
42s: 0.36829 93o: 0.301252 J2o: 0.291929
82o: 0.368256 43o: 0.3009 93o: 0.289012
73o: 0.366002 T2o: 0.299667 T2o: 0.287156
53o: 0.362627 73o: 0.298163 52o: 0.284284
63o: 0.360756 83o: 0.293484 73o: 0.284069
32s: 0.359844 92o: 0.292463 92o: 0.280829
43o: 0.351438 52o: 0.290183 83o: 0.280242
72o: 0.345816 82o: 0.287756 62o: 0.2766
52o: 0.342826 62o: 0.284141 42o: 0.275857
62o: 0.340731 42o: 0.280797 82o: 0.275057
42o: 0.331977 72o: 0.277943 32o: 0.266933
32o: 0.323012 32o: 0.271115 72o: 0.264864

eastbay

[/ QUOTE ]

Irieguy
02-27-2005, 04:09 PM
Thank you, Eastbay. This went right onto my desktop. This information is quite valuable.

Since most opponents do not understand hand rankings beyond the top few (I once had an opponent in a live game tell me that KQ was the second best hand), you can use the "vs. random hands" list to select your top X% push hands in short-handed strategy. Since opponents don't really know which hands are better to call with, you can just assign them a random hand.

But your standard monkey will select the hands they push usually using a combination of any ace/pair plus broadway cards. So instead of selecting a top X% calling range from the random list, I can refine my calling range a bit and gain a little extra advantage short-handed.

I just try to play a non-exploitable short-handed game, and this helps.

Thank you,

Iriebot

eastbay
02-27-2005, 04:13 PM
[ QUOTE ]
Thank you, Eastbay. This went right onto my desktop. This information is quite valuable.

[/ QUOTE ]

You'll notice this thread is a year old with ~3000 reads. Ah, the old days before I'd helped make all this stuff well-known. Maybe I'm an idiot after all, lol.

eastbay

lastchance
02-27-2005, 08:03 PM
The one thing I note most is how crappy any ace, any pair is as a range to call/push with.

1C5
02-27-2005, 09:43 PM
[ QUOTE ]
The one thing I note most is how crappy any ace, any pair is as a range to call/push with.

[/ QUOTE ]

That is good to know...

ZebraAss
03-11-2005, 05:40 PM
*bump*

jgunnip
05-15-2005, 09:14 PM
A must read for all newbies.
And yes, I realize this thread is over a year old.
BUMP