The Beginners Guide Series: Expected Value (EV)
Poker Expected Value (EV): A Guide for Beginners
Article Written by: RiverKingDan
During your time at the poker tables, after you have been playing long enough, you will eventually hear someone mention EV. But what is this “EV” and why should it matter to you? Simply stated, EV, or Expected Value, is a term used in poker to refer to the potential outcomes of a hand. If you were to play a certain hand infinitely, what should you expect as the result? To help clarify this concept, and keep it easy to understand, let us consider flipping a coin. Of course, if you don’t want to read about it, you can always watch me explain it here.
When you flip a coin there is a 50% chance it will land on heads and a 50% chance it will land on tails – assuming that it doesn’t, through some weird circumstances, land on its side causing you to scream with elated excitement while your friend posts it onto the web. The video, as expected, goes viral and you become an international sensation as millions of people around the world try to emulate your miraculous coin flip…but I digress.
You and a friend (not the same one who recorded that crazy coin flip from earlier and let the fame go to his head) decide to start betting on a coin flip. Each time the coin shows heads, you win $1 and each time it is tails your friend wins $1. We know that a coin will land on each side half the time, so you and your friend can both expect to win 50% of the time. As you both are going to win as often as you lose, the Expected Value (EV) of the bet is $0. The expectation is to simply break even if you kept flipping the coin infinitely.
EV becomes important in understanding if something is a good or bad bet. In the coin flip example above, if your friend had offered $1 each time you win but you would lose $2 every time you lost, we can use EV to show why this is a bad bet. On average, every 2 flips will have 1 head (you win $1) and 1 tail (you lose $2) with the net result being you lose $1 every 2 flips. From this we can find our EV is -$0.50, or a loss of $0.50 per flip. A negative EV is always a bad deal and not a bet anyone should ever accept.
The reason why this concept is important is in poker, as long as you only make plays that are positive EV, you will be able to make money in the long run. You will find the opposite results if you consistently make negative EV plays. This is the same as flipping a coin; however, unlike the coin flip which is completely random, you can avoid a lot of the plays that would lead to negative EV results.
Aces vs Kings – a classic hand
There you are, sitting at your favorite table and BOOM, you wake up with Aces or Kings. Obviously this makes you very happy. Naturally you want to play a big pot and win as much as possible, but how should you play them? What should you do in this case? Betting your hand, raising when against a bet, or even going all in against re-raises is the generally accepted strategy as either hand is strong enough to go all in preflop.
Now let’s say we do get it all in preflop with AA and get a call from someone holding KK. How much money can we expect to make? What is our EV?
In keeping things simple, we are first going to use the percentages from the CardPlayer Odds Calculator as seen above. Looking at the numbers, we see that our Aces should win 81% of the time and the Kings will win the other 19% of the time when we get it all in preflop – Poker is a game of incomplete information and these percentages change as more cards are exposed. We know that we will win 81% of the time, but what does that mean for our bankroll?
You and your opponent both have $50 in your respective stacks and go all in preflop with the hands above. This creates a total pot of $100. We know that our Aces will win 81% of the time and lose 19% of the time. This means our EV for this hand is $81 – we win the $100 pot 81% of the time. Remember that your expected value is simply your odds to win multiplied by the current pot.
If you and your opponent bet $100 each for 100 hands, with you holding AA and your opponent having KK, your EV would be $16,200 for a profit of $6,200.
Your Bet: $100 x 100 hands = $10,000 total wagered
Your Opponent: $100 x 100 hands = $10,000 total wagered
Pot Total: $20,000
Your Win Percentage: 81%
EV: $20,000 x 81% = $16,200
That would be a nice bonus to have after a 100 hands if you can find a sucker opponent to play you with these conditions. However, all of this beautiful and logical math can be instantly undermined by that timeless and foul villain, Variance.. at least in the short term.
Variance can make a short term difference to your expected value
Most people that play poker are familiar with the term variance and probably understand what it does both for and against you. For those who don’t know, variance is when the result is different from what is expected.
If you flip a coin 10 times the expectation is it will land on heads 5 times and tails 5 times. That is the expected result. However, if the coin landed on heads 7 times and tails 3 times, you have a variance, in this case the variance is +/-2 (the result is 2 off the expectation). The difference between what you expect to happen and the result is caused due to variance. In smaller samples, 10 coin flips or a single hand of poker, the results can be vastly different than the expectation. Over a larger sample, the variance will reduce and become closer to what is expected – if you flipped the coin 1,000 times, the results will normally be very close to 50/50.
So how does this apply to poker? Simply put, to go back to the AA v KK example above, this means that although you have 81% chance to win with AA vs KK, it should not be a surprise if you lose 7 times out of 10. Is this frustrating? Yes. Rage inducing? Absolutely. Reason to call someone a cheat or claim a site is rigged? Definitely not. Just like in the heads or tails example, while it is unusual for this to occur, it is an absolute possibility. Remember, the more you play the scenario, the closer you will get to the overall expected results, in this case winning 81% of the time. So don’t be discouraged when you make a good play and still lose. In the long run, YOU will be the one who is going to earn the most chips. If you are interested in learning more about EV, get ready for an intermediate guide, which will go more in depth about EV and offer more complex examples, which will be coming soon and be linked here.
So why is EV important?
A play has positive EV if the reward is high enough that it warrants the risk (Like in the AA vs KK example). You either need to win a large % of the time or get enough $ for the amount of risk you are taking. I hope I have explained basic EV that you have an understanding of EV of what it is and why it is important. If not, jump into the GGPoker Subreddit and ask. Someone will absolutely be there to help.
Hopefully you now know what EV is and why it is important to know the expected value of your plays. If a play is positive EV, you will make money over enough hands. And making money is a good thing, trust me on that. If you have questions regarding EV jump over to the GGPoker subreddit where someone will help.