Expected Value

Fri, 06 Jun 2008 00:40

Expected Value

The average result of poker situations in the long run.


Gamblers should know that mathematics has an effect in their winning streaks. Their gambling destinies are not merely determined by luck. Most professional players and gambling pros have already found game strategies based on mathematical theories. For instance, Blackjack has card counting, while roulette and poker have the expected value. Also known as mean or mathematical expectation, the expected value helps players know whether they should dump their second best hand or not. It also tells them when to check-raise, bluff, call, or fold in games. Poker players don't usually compute at tables, but they should learn to use the expected value in analyzing their games. Intermediate level players should learn about these mathematical computations to help them play as competitive as poker pros do.

In poker, the expected value means the average result of poker situations in the long run. To compute for the value, players should multiply each possible result by its probability of happening. Then, they add all these numbers to come up with the expected value.

To help you understand the theory, let's try doing the computations in getting the expected value of a typical dice. Through the expected value, we can find out any side's probability of turning up. A dice having six sides would then have 1/6 probability for each side to come up. Now, let's multiply each probability to its corresponding number. For 1, we would get a 1/6. The 2 would have a 2/6; 3 with 3/6; 4 with 4/6; 5 with 5/6; and 6 with a 6/6. Adding all these numbers together would get us a 3.5. This is a dice's expected value, but it can change according to your numbers' designated probabilities. Adjusting the values would help players predict the chances of their preferred numbers or cards coming up.

Applying this mathematical theory in poker games will help players decide which move is the best to make. In a game where all other players have limped, getting the expected value will ensure players a move that gives them the highest probability of winning the pot. Now, let's try computing for the expected value in a given poker situation. In a Hold'em game, you're heads-up at the river and you have an ace of hearts and a jack of clubs. The flop has an ace of clubs, a ten of clubs, a five of diamonds, an eight of clubs, and a three of clubs. The game's pot is worth $100 and the bet is $10. So, what do you do?

Let's cover all your bases through computing for expected values. If you go for a bet, there are six possibilities of you winning. Why is this so? That's because your opponents can call you with six probable clubs from a total of eight available ones. So that gives you two possibilities of losing. When you multiply the bet to the probabilities, you will get an expected value of $5. Although that isn't bad, computing for the expected value when you check can give you more options. After all, you would not want to lose your poker room promotions to a mere losing streak.