Expected Value Poker Quiz

The idea of expected value is one that comes up often in poker and trading discussions. Expected value is the sum of the probability of each possible event times that event’s payoff. For example, if you were to flip a fair coin where you got paid $2 for heads and lost $1 for tails your expected value would be:

This means on average you are making 0.50 each time you play this game.

Before we consider expected value we need to calculate the probability of an event occurring. Imagine you’re playing Texas Hold’em. Assume that your opponent flipped over their hand and showed 6d7c. You have KsQs on a board of As 5d 8d 4s.

How often do you make a flush with the last card?

.205 Good, you have 9 possible spades left in the deck with 44 cards total left in the deck
.228 Try again!
.152 Try again!
.18 Try again!

Now that you know the probability of hitting your flush is 20.5% we can start thinking about expected value. The only way for you to win is to hit your flush. Your opponent bets their last $5 into the pot, putting them all in. What is the minimum amount of money there needs to be in the pot (including your opponents bet) for calling to have a positive expected value?

20That is correct!
15Incorrect. Try looking at the probability of each event occurring and the payoff of that event. Winning the hand would win $15, losing would mean losing $5.
24This has positive expectancy but what would you do if there was less $ in the pot?
34This has positive expectancy but what would you do if there was less $ in the pot?

To figure out the expected value we look at probability times payout. Therefore:

This means that on average we expect to make 0.11 each time we find ourselves in this situation and call. Expected value is one of the most important ideas to understand when it comes to evaluating decisions.

Stay tuned for future poker quiz posts.

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  • Ross

    Nice post!