Understanding Expected Value

f you are learning the game of poker, you'll want to understand the phrase and concept of Expected Value (EV). Expected Value involves being able to take calculated risks by using probabilities, and it's important for calculating poker pot odds. It's how you calculate how much money you can expect to make in the long run by making a certain move right now.

expected valueYour ability to calculate poker probabilities is very important to your success in the game of poker. Some new poker players are intimated by the idea of EV because it does have a mathematical basis and, well, not everyone who desires to play poker also desires to be a mathematician. But, while Expected Value does have roots in math, learning the high art of being able to accurately calculate probability doesn't mean you have to come up with a new theory for the speed of light!

However, there are poker players who ignore EV because they think they "just aren't good at math". This is a bad mistake indeed. For you see, all poker decisions are mathematical; thus, if you shy away from poker strategies because they are mathematical, you can forget about being successful at the game. After all, even if you're just playing symbolically for pennies, you're still playing for money; and money is about numbers and about value. Therefore, poker is a game where each hand and reach round have a value or values; and that involves math.

Not understanding EV will lead you to make blind decisions and take many shots in the dark. You will get lucky sometimes and come out on top, but in the long run you'll never be able to sustain any success. You'll always be a loser at poker.

Now, keep in mind that this is still a game and it's not about plotting the trajectory for getting a spaceship to Mars. The math is kind of in the background in poker; you can't and don't need to know every variable at any time, for there are just too many of them. All you want to do here is play your hands based on probability and expectation. You're not always going to be right, but if you think long term and you're right more than you're wrong, you can become very successful and, if you're serious enough, win yourself a lot of money at poker.

We use probability "calculations" at the back of our minds constantly, in fact probably every day. For instance, think about gas prices. We know that they go up and down based on several factors, but mainly on the price of oil. When we see that oil prices are on a downward trend, we know that we can rationally expect gas prices to begin going down in the very near future. So, what if we decided to hold off on filling the half-full tank for a few days (by first calculating whether or not that's possible--let's assume it is), so we could get those lower gas prices when they came? The majority of the time, we'll be taking a rewarding risk, a good gamble, and we'll be rewarded with more gas for less money. We rightly figured the probability of what was going to happen--we "won". We played our hand the right way. And we were able to do that because of our knowledge.

Same thing here with using Expected Value. You have to have a basic knowledge of the power of the different hands even to play the game, so there's your "oil price news" (oil changes, by the way, change in part because of another highly important factor in poker playing: psychology). Now you look at your situation. You consider your hand; any previously used cards from the deck; and the cards face up on the table. Next, think of each possibility based on what you know, and mentally calculate the statistical odds for that possibility coming about (this will take some practice and experience).

Now, consider your opponents. How have they been doing in this game round by round? What cards do you know they drew this round? Have they tended to raise, call, or fold? And so on.

At this point you'll be able to start figuring out Expected Value. For a real-world situation, let's say you're on the River with two pair. Your opponent bet $100 into a $100 pot. It's your turn and you're either going to fold or call (you decided not to raise). If you call, you've got 2:1 odds for "positive EV", for if you call with $100 you could make $200. What this means for you is, in thinking long-term, if you call, you will need to win more than one out of three times to be +EV (winning one out of three only breaks even). Knowing your opponents as you do, what decision do you make with this hand?

You can use an online Pot Odds Calculator such as Holdem Genius to help you get better at using Expected Value. Remember, in poker you must be able to calculate probability accurately in order to be successful.

Expected Value Poker Hand Ranking Chart
Total EV stats ordered by value

Cards
EV
Count
AA
2.32
521,324
KK
1.67
522,652
QQ
1.22
520,663
JJ
0.86
521,866
AK s
0.78
348,364
AQ s
0.59
348,759
TT
0.58
520,705
AK
0.51
1,048,008
AJ s
0.44
348,126
KQ s
0.39
346,772
99
0.38
522,454
AT s
0.32
348,013
AQ
0.31
1,042,962
KJ s
0.29
346,582
88
0.25
521,972
QJ s
0.23
348,870
KT s
0.20
348,774
A9 s
0.19
348,992
AJ
0.19
1,045,857
QT s
0.17
346,115
KQ
0.16
1,045,069
77
0.16
524,345
JT s
0.15
348,235
A8 s
0.10
349,431
K9 s
0.09
348,286
AT
0.08
1,047,289
A5 s
0.08
348,544
A7s
0.08
349,949
KJ
0.08
1,047,098
66
0.07
520,946
T9 s
0.05
348,264
A4 s
0.05
347,862
Q9 s
0.05
348,760
J9 s
0.04
349,965
QJ
0.03
1,044,338
A6 s
0.03
347,677
55
0.02
521,945
A3 s
0.02
347,895
K8 s
0.01
350,401
KT
0.01
1,045,392
98 s
0.00
348,759
T8 s
-0.00
347,443
K7 s
-0.00
348,341
A2 s
0.00
347,318
87 s
-0.02
348,348
QT
-0.02
1,047,827
Q8 s
-0.02
348,381
44
-0.03
523,398
A9
-0.03
1,047,672
J8 s
-0.03
348,046
76 s
-0.03
347,540
JT
-0.03
1,043,812
97 s
-0.04
350,158
K6 s
-0.04
347,029
K5 s
-0.05
349,320
K4 s
-0.05
348,681
T7 s
-0.05
347,638
   
Cards
EV
Count
Q7 s
-0.06
348,073
K9
-0.07
1,045,630
65 s
-0.07
348,590
T9
-0.07
1,045,306
86 s
-0.07
348,374
A8
-0.07
1,042,209
J7 s
-0.07
345,009
33
-0.07
522,632
54 s
-0.08
348,260
Q6 s
-0.08
349,068
K3 s
-0.08
348,865
Q9
-0.08
1,049,468
75 s
-0.09
349,781
22
-0.09
524,131
J9
-0.09
1,044,150
64 s
-0.09
349,689
Q5 s
-0.09
350,110
K2 s
-0.09
349,276
96 s
-0.09
349,514
Q3 s
-0.10
348,009
J8
-0.10
1,046,506
98
-0.10
1,044,759
T8
-0.10
1,048,779
97
-0.10
1,046,152
A7
-0.10
1,046,587
T7
-0.10
1,044,950
Q4 s
-0.10
348,979
Q8
-0.11
1,048,251
J5 s
-0.11
348,923
T6
-0.11
1,043,014
75
-0.11
1,047,447
J4 s
-0.11
347,508
74 s
-0.11
350,325
K8
-0.11
1,048,167
86
-0.11
1,047,524
53 s
-0.11
346,930
K7
-0.11
1,043,698
63 s
-0.11
346,449
J6 s
-0.11
347,570
85
-0.11
1,048,159
T6 s
-0.11
348,875
76
-0.11
1,046,722
A6
-0.12
1,046,762
T2
-0.12
1,047,032
95 s
-0.12
348,477
84
-0.12
1,046,266
62
-0.12
1,049,495
T5 s
-0.12
348,928
95
-0.12
1,044,601
A5
-0.12
1,046,285
Q7
-0.12
1,046,099
T5
-0.12
1,048,428
87
-0.12
1,044,635
83
-0.12
1,048,550
65
-0.12
1,045,971
Q2 s
-0.12
348,912
94
-0.12
1,047,422
   
Cards
EV
Count
74
-0.12
1,043,278
54
-0.12
1,046,435
A4
-0.12
1,046,931
T4
-0.12
1,047,976
82
-0.12
1,043,638
64
-0.12
1,043,079
42
-0.12
1,043,357
J7
-0.12
1,046,565
93
-0.12
1,045,989
85 s
-0.12
347,928
73
-0.12
1,047,020
53
-0.12
1,047,022
T3
-0.12
1,043,908
63
-0.12
1,044,818
K6
-0.12
1,045,039
J6
-0.12
1,045,991
96
-0.12
1,047,156
92
-0.12
1,049,342
72
-0.12
1,046,167
52
-0.12
1,049,213
Q4
-0.13
1,045,087
K5
-0.13
1,047,359
J5
-0.13
1,047,697
43 s
-0.13
348,802
Q3
-0.13
1,047,649
43
-0.13
1,047,900
K4
-0.13
1,046,562
J4
-0.13
1,048,129
T4 s
-0.13
350,639
Q6
-0.13
1,046,958
Q2
-0.13
1,046,353
J3 s
-0.13
349,254
J3
-0.13
1,046,204
T3 s
-0.13
349,673
A3
-0.13
1,046,970
Q5
-0.13
1,047,946
J2
-0.13
1,045,715
84 s
-0.13
349,390
82 s
-0.14
348,622
42 s
-0.14
350,591
93 s
-0.14
348,835
73 s
-0.14
349,007
K3
-0.14
1,045,968
J2 s
-0.14
348,259
92 s
-0.14
347,868
52 s
-0.14
348,401
K2
-0.14
1,048,521
T2 s
-0.14
349,612
62 s
-0.14
348,033
32
-0.14
1,044,956
A2
-0.15
1,047,979
83 s
-0.15
349,355
94 s
-0.15
348,259
72 s
-0.15
348,368
32 s
-0.15
349,794

The statistics are based on 115,591,080 pair of pocket cards dealt at the real money tables. The unit for EV is average profit in big bets.
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