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.

Your 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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