Math Values of Starting Hands
| Cards E.V. AA 2.32 KK 1.67 1.22 JJ 0.86 AKs 0.77 AQs 0.59 TT 0.58 AK 0.51 AJs 0.43 KQs 0.39 99 0.38 ATs 0.33 AQ 0.31 KJs 0.29 88 0.25 QJs 0.23 KTs 0.2 AJ 0.19 A9s 0.18 QTs 0.17 KQ 0.16 77 0.16 JTs 0.15 A8s 0.1 K9s 0.09 AT 0.08 Cards E.V. A5s 0.08 A7s 0.08 66 0.07 KJ 0.07 A4s 0.06 Q9s 0.06 T9s 0.05 J9s 0.04 QJ 0.03 A6s 0.03 55 0.02 A3s 0.02 K8s 0.01 KT 0.01 98s 0 T8s 0 K7s 0 A2s 0 87s -0.02 QT -0.02 Q8s -0.02 44 -0.03 A9 -0.03 J8s -0.03 76s -0.03 JT -0.03 |
Cards E.V. A5s 0.08 A7s 0.08 66 0.07 KJ 0.07 A4s 0.06 Q9s 0.06 T9s 0.05 J9s 0.04 QJ 0.03 A6s 0.03 55 0.02 A3s 0.02 K8s 0.01 KT 0.01 98s 0 T8s 0 K7s 0 A2s 0 87s -0.02 QT -0.02 Q8s -0.02 44 -0.03 A9 -0.03 J8s -0.03 76s -0.03 JT -0.03 |
Cards E.V. 97s -0.04 K6s -0.04 K5s -0.05 K4s -0.05 T7s -0.05 Q7s -0.06 K9 -0.07 65s -0.07 86s -0.07 A8 -0.07 J7s -0.07 33 -0.07 J9 -0.08 T9 -0.08 54s -0.08 Q6s -0.08 K3s -0.08 K2s -0.08 Q9 -0.08 75s -0.09 22 -0.09 64s -0.09 T8 -0.09 Q5s -0.09 96s -0.09 J8 -0.1 |
Cards E.V. 98 -0.1 97 -o.i A7 -0.1 T7 -0.1 Q4s -0.1 Q8 -0.11 J5s -0.11 T6 -0.11 Q3s -0.11 75 -0.11 J4s -0.11 74s -0.11 K8 -0.11 86 -0.11 53s -0.11 K7 -0.11 85s -0.11 63s -0.11 J6s -0.11 85 -0.11 T6s -0.11 76 -0.11 A6 -0.12 T2 -0.12 95s -0.12 84 -0.12 62 -0.12 T5s -0.12 95 -0.12 A5 -0.12 Q7 -0.12 |
| Cards E.V. T5 -0.12 87 -0.12 83 -0.12 65 -0.12 Q2s -0.12 94 -0.12 74 -0.12 A4 -0.12 T4 -0.12 82 -0.12 64 -0.12 42 -0.12 J7 -0.12 93 -0.12 73 -0.12 53 -0.12 T3 -0.12 63 -0.12 K6 -0.12 J6 -0.12 96 -0.12 92 -0.12 72 -0.12 52 -0.12 Q4 -0.13 K5 -0.13 J5 -0.13 43s -0.13 Q3 -0.13 43 -0.13 |
Cards E.V. K4 -0.13 J4 -0.13 T4s -0.13 54 -0.13 Q6 -0.13 Q2 -0.13 J3s -0.13 J3 -0.13 T3s -0.13 A3 -0.13 Q5 -0.13 J2 -0.13 84s -0.13 82s -0.14 42s -0.14 93s -0.14 73s -0.14 K3 -0.14 J2s -0.14 92s -0.14 52s -0.14 K2 -0.14 T2s -0.14 62s -0.14 32 -0.14 A2 -0.15 83s -0.15 94s -0.15 72s -0.15 32s -0.16 |
These statistics are not the result of a simulation or mathematical
computation. The expected value averages are based on the actual outcomes of all
122,031,244 hands analyzed. An examination of this table confirms some common
beliefs, but also reveals some surprises.
Confirmations
• Premium pairs play best—AA, KK, QQ, JJ, in that order, are the top four hands
in terms of expected value.
• Any Ace with a face card—AK, AQ, AJ, has a positive expected value, whether
the cards are suited or not.
• Most hands should not be played. Only 40 of the 169 possible starting hands
have produced a positive expected value.
Surprises
• Any hand AX unsuited, in which X is 9 or less, had a negative expected value.
• J-10 and Q-10 unsuited had negative expected values.
Real-world poker plays differently than poker theory. The so-called worst
starting hand—7-2 unsuited—because these are the lowest cards you can hold, with
no possibility of a straight or flush after the flop, has done better in
practice than 37 other starting hands, including many that contain Aces, Kings,
Queens, and Jacks. This is evidence that players routinely overplay hands with
Aces and face cards and lose more money than they should. This is also my
explanation for why 7-2 suited and 3-2 suited end up at the bottom, in places
168 and 169 respectively, of the list.