Heads Up Hold'em Percentages

Has anyone calculated the chance that any particular 2-card hand will beat any randomly-dealt 2-card hand for all the possible random boards? I'd like to know for judging the relative value of 2-card hands.

There are 47,008 possible distinct head-to-head matchups. I have calculated the exact W/L/T values for all these (and boy are my arms tired).

From this, it isn't hard to calculate the expectation of any two card hand. The exact ranking of all 169 hands is given below. It is interesting to compare these values with Justin Cases' table in _Percentage Hold'Em_, which used simulation to estimate the hand values. I think the main difference is that I counted ties as worth 1/2, while I think Justin's table counted ties as 1.

Note: These numbers do not give necessarily indicate how hands match up against each other, but how each hand will do independently against a random, unknown hand. For example, Q7s (0.5430) ranks just above K6off (0.5422) in the table. That means, if you all-in preflop against an unknown hand, you would pick Q7s instead of K6off. However, if you have a proposition bet where you can take either Qd7d or Kh6c against each other, then you should take Kh6c, since it is favored against Qd7d.

AA	0.8520371	A4s	0.5903364	K5	0.5331397	96s	0.4742829	85	0.4142753
KK	0.8239568	A7	0.5884120	J9	0.5325120	J2s	0.4737815	64s	0.4133332
QQ	0.7992516	K8s	0.5831235	K2s	0.5321173	Q2	0.4729544	83s	0.4087350
JJ	0.7746947	A3s	0.5822032	Q5s	0.5276941	T5s	0.4721626	94	0.4067105
TT	0.7501178	QJ	0.5813469	T8s	0.5233437	J5	0.4718089	75	0.4051197
99	0.7205725	K9	0.5781192	K4	0.5232747	T4s	0.4653049	82s	0.4027163
88	0.6916304	A5	0.5769653	J7s	0.5232478	97	0.4629781	73s	0.4003594
AKs	0.6704463	A6	0.5768245	Q4s	0.5185530	86s	0.4624327	93	0.4001951
77	0.6623602	Q9s	0.5766432	Q7	0.5176567	J4	0.4618638	65	0.3994430
AQs	0.6620886	K7s	0.5753774	T9	0.5153167	T6	0.4609200	53s	0.3969296
AJs	0.6539268	JTs	0.5752786	J8	0.5149016	95s	0.4572187	63s	0.3953356
AK	0.6532007	A2s	0.5737890	K3	0.5142569	T3s	0.4569251	84	0.3944679
ATs	0.6460239	QT	0.5729078	Q6	0.5102405	76s	0.4537177	92	0.3909794
AQ	0.6443184	44	0.5702282	Q3s	0.5101925	J3	0.4527554	43s	0.3864195
AJ	0.6356326	A4	0.5672968	98s	0.5080076	87	0.4505081	74	0.3854983
KQs	0.6340040	K6s	0.5664074	T7s	0.5063904	T2s	0.4483948	72s	0.3815589
66	0.6328475	K8	0.5602017	J6s	0.5060591	85s	0.4454499	54	0.3815529
A9s	0.6278121	Q8s	0.5601773	K2	0.5050872	96	0.4449135	64	0.3801049
AT	0.6272165	A3	0.5584460	22	0.5033402	J2	0.4434847	52s	0.3784933
KJs	0.6256734	K5s	0.5579292	Q2s	0.5016904	T5	0.4425095	62s	0.3766896
A8s	0.6194381	J9s	0.5566247	Q5	0.5012008	94s	0.4386197	83	0.3748381
KTs	0.6178856	Q9	0.5536043	J5s	0.4998685	75s	0.4367554	42s	0.3682901
KQ	0.6145580	JT	0.5524770	T8	0.4972127	T4	0.4350411	82	0.3682767
A7s	0.6098396	K7	0.5518735	J7	0.4968193	93s	0.4326426	73	0.3660226
A9	0.6077281	A2	0.5492856	Q4	0.4912768	86	0.4324090	53	0.3626477
KJ	0.6056869	K4s	0.5488464	97s	0.4911773	65s	0.4313339	63	0.3607763
55	0.6032492	Q7s	0.5430226	J4s	0.4907045	84s	0.4270163	32s	0.3598443
QJs	0.6025921	K6	0.5422328	T6s	0.4894068	95	0.4266914	43	0.3514589
K9s	0.5998848	K3s	0.5405498	J3s	0.4823162	T3	0.4259455	72	0.3458365
A5s	0.5992293	T9s	0.5402753	Q3	0.4821944	92s	0.4241517	52	0.3428465
A6s	0.5990583	J8s	0.5401564	98	0.4809703	76	0.4232275	62	0.3407514
A8	0.5987261	33	0.5369308	87s	0.4793634	74s	0.4184931	42	0.3319975
KT	0.5973892	Q6s	0.5361257	T7	0.4790814	T2	0.4166835	32	0.3230323
QTs	0.5946756	Q8	0.5359979	J6	0.4784427	54s	0.4145342

--jazbo