Expected Value and Why You Might Never Bet Again

I was talking to someone the other day about a baseball simulation game and he mentioned that he didn’t think an activity in the game had a positive EV. The game in question doesn’t have anything to do with gambling and I didn’t know anything about the background of the person I was talking to.

As soon as he mentioned EV I asked him if he was a poker player or gambler.

The only people I know who even know what EV means are gamblers; with most of them being poker players.

EV is short for expected value and is often stated with a positive or negative sign. This means that when you see +EV in relation to an activity it means positive expected value or expectation, and –EV means negative expected value or expectation.

It turns out he used to be a full time online poker player. We talked for quite a while about gambling and poker and I found out he has a strong understanding of expected value.

He understands it so much that he won’t play any casino games other than poker.

The sad fact is most poker players play with a negative expected value overall, which means most of them should probably stop playing as well.

After you learn a little more about EV below, you’ll see why it may be a good idea for you to just stop betting. But I’ll also show you how to find gambling activities that have possible positive EV, so all hope is not lost for your gambling career.

Defining EV

Expected value, or EV, is a mathematical way of expressing the long term value of a situation. To get a true picture of the profitability of a situation you often need to simulate the exact same set of circumstances hundreds or thousands of times.

Don’t worry; this isn’t a complicated as it sounds. I’ll show you how to do it shortly.

But first, what exactly can we use EV for?

Most conversations about EV start with the example of a coin flip. We’ll use this example, but quickly move into areas where it’s more useful to gamblers.

A coin flip using a fair coin has the exact same chance to come up heads as it does tails. In the short term it can land on tails more than heads or heads more than tales. But as you flip the coin thousands of times the percentages get closer and closer to the true odds. Each side has a 50% chance to win.

If you bet $1 on each flip and win $1 when it comes up heads and lose the $1 on tails you’re payouts match your odds.

When the payouts match the odds the expected value is zero or even.

In other words, if you made the bet a million times the odds are you’re going to be even or about even.

Now let’s look at an actual gambling game.

If you play roulette on a single zero wheel the house edge is 2.7%. This edge is created because the payouts are based on 36 numbers and the wheel has 37 numbers.

When you know the house edge you can easily determine the long term EV. If the game has a house edge your long term EV will always be negative.

This means if you play a game with a –EV long enough you’re going to lose. Most casino players know this at some level, but either choose to ignore it for the chance at a short term win or are in denial about the true odds.

In a roulette game with a house edge of 2.7% you simply multiply the percentage, in this case 2.7%, times $1 to get the expected value of every dollar wagered.

First you convert the percentage to a decimal by moving the decimal two places to the left, and then you multiply it by one.

.027 X 1 = .027

This means for every dollar you bet you can expect to lose 2.7 cents.

Notice that multiplying by one really isn’t required to find out how much you lose per $1 wagered, but I showed you how it works so you know how to do it for other amounts and in other situations.

So if you make $25 bets on roulette your expected loss per bet is .027 X $25, or 67.5 cents.

If you make 100 bets at $50 each your expected loss is $135. 100 X 50 X .027 = $135.

Here’s a list of the house edge of many popular casino games. On the games that involve strategy these edges are based on you using the best possible strategy when you play.

• Blackjack – .5% to 3%
• Baccarat banker bet – 1.06%
• Baccarat player bet – 1.24%
• Roulette single zero wheel – 2.7%
• Roulette double zero wheel – 5.26%
• Craps don’t pass bet – 1.36%
• Craps pass bet – 1.41%
• Caribbean Stud Poker – 5.22%
• Let It Ride – 3.51%
• Three Card Poker – 3.37%
• Jacks or Better video poker – .46%
• Deuces Wild video poker NSUD – .27%
• Pai Gow Poker if you bank every other hand – 1.46%
• Slot machines – 1% to 20%
• Keno – 25% to 30%

So why are casinos filled with people playing all of the games listed above if they all have a negative EV in the long run?

This is a good question and why I mentioned in the title that you might not ever place a bet again.

But before you give up let’s look at a different example and then in the next section I’ll show you some games and situations that can have a positive EV.

Now that you see how simple it is to determine the expected value of a bet using the house edge percentages, let’s look at how you can use EV calculations in poker.

Here’s an example:

You’re playing in a no limit Texas holdem game against a single opponent after the turn card has been dealt. The pot has $120 in it, your opponent bets $20, and you have an open end straight draw. The only way you can win is if you complete your straight.

You can determine the EV of this situation by determining how often you’ll hit your straight and comparing this to the amount of money in the pot and how much you must put in to see the river.

Poker players may recognize this as a pot odds discussion. This is exactly what it is, but what you’re doing when you look at pot odds and your odds of hitting your hand is determining EV.

In this example you’ve seen six cards so the unseen cards number 46. Eight of the 46 unseen cards complete your open end straight and 38 of them don’t. This is a ratio of 38 to 8, or 4.75 to 1.

The pot has a total of $140 in it after your opponent’s bet and you have to put $20 in. This is a ratio of 7 to 1.

When you compare 4.75 to 1 to 7 to 1 you can see in the long run it’s profitable to make the call.

The way to convert this to EV is to determine the average return when you make this play.

Because the deck has 46 unseen cards we run the numbers 46 times with each of the possible cards coming on the river once.

You’re total investment to see the river 46 times is $920. The 38 times you lose you get nothing back. The eight times you win you get $1,280.

Subtract $920 from $1,280 and your long term expected value by playing this exact situation 46 times is $360. Divide that by the 46 hands and your average EV is a positive $7.83.

This means on average you win $7.83 every time you play this situation.

You can use this type of calculation in almost every gambling situation if you have enough information.

Gambling Activities with Possible Positive EV

You can find a few gambling activities that offer +EV situations. Here’s a quick overview of the games and activities you should consider.

Poker – You play against the other players instead of the house. So if you can beat the players and the rake you can play with a +EV.

Sports betting – A few sports bettors are good enough to beat the book makers over time. You have to be able to find value bets where the line is inefficient, but it’s possible to be a winner.

Horse and dog racing – You compete against the other bettors, much like poker, so you can win in the long run if you’re better than they are.

Blackjack – If you learn how to count cars you can get a sloth edge over the house. This is a +EV situation.

All of these require work to master your skills and give you a chance to win.

Conclusion

Now that you know more about EV you can quickly see which gambling activities offer positive and negative returns. You also know which activities to concentrate on if you want to have the chance to be a +EV player over time.

It’s up to you to if you want to continue playing –EV games, but if you do try to reduce the negative expected value as much as possible to extend your bankroll.