Expected Utility


Utility refers to the quality or state of usefulness or being useful. Expected utility is the mathematical description of preferences of people when betting as regards to any uncertain events like the game of poker and it accounts for the size of the payout, the probability of the occurrence, aversion to risk and different types of utility of the same type of payout to people with different preferences. In layman's language, it means that as the required use of money changes, expectations or the outcomes of the game will also change.

Most of the poker players take only Expected Value along with implied odds into consideration while trying to take correct decisions. More importance is given to Expected Value due to the assumption underlying Expected Value concept and that is "Every dollar has the same value". This assumption, though true sometimes, is not true all the time. Assume that a person has a billion dollars in his bank account and you offer him a bet of billion dollars on flip of a coin. In this scenario, some people may take the bet but majority will not. This is due to the utility or the usefulness or happiness that a second billion may bring or not bring. If you have one billion in your bank account, the second billion may not bring that much happiness as say a palatial house and that happiness is not same if you lose everything in the event of bet going wrong. The reason why this happens is that the utility of money gets changed depending on availability of money.

Different level of income is associated with a level of utility and this does not necessarily increase in a uniform fashion. In the above example, for many the second billion is not worth much as compared to the first. This Utility is called Diminishing Marginal Utility and those falling in this category are generally averse to risk. But you may find some people who may take the bet as the second billion is worth the same to them as the first billion and they fall into "risk-neutral" category.

You may come across another type of people who may not take the billion dollar bet at 50% odds, but surely go for it if the probability of winning is raised to 55%. Suppose, the same billion dollar bet is offered with a winning chance of 45%. These people will still go for it simply for the reason that the marginal utility they derive from the second billion surpasses the utility derived from first billion. They may require exactly $2 billion in order to save themselves from bankruptcy. Such people fall in the category of risk-loving people and are more likely to turn into compulsive gamblers as they like to place bet with negative expected value.

Use of Expected Utility in Poker

Expected utility helps a poker player by categorizing his opponent. Whether the opponent is risk-loving, risk-averse or risk neutral may help a poker player to place his bets. Also, depending upon his own category, a poker player can play at the table. Some players, while moving up the limits, play scared and the reason behind this is the amount of money at the table does not match with their utility curve. They are risk-averse and they should not play with a limit which is more then their expectation. Conversely, if the pot at the table decreases, the player may turn risk-loving.

Another important aspect to remember in context of Expected Utility in poker is not to assume that risk-loving player is loose and risk-averse player is tight. A poker player might be playing tight as that may be the only option against a particular type of opponent. Also, a strong poker player in a game of No-Limit may play between loose and tight by not turning down the bet and by not laying a slight edge. This is because he falls in risk-neutral category. This condition which makes him vary is due to the responses of his opponents.

Thus, it is pertinent that the poker player plays risk-neutral and is able to read his opponent correctly. Just because the opponent is playing tight, the player should not guess that the opponent is averse to risk. He should avoid bluffing his opponent in such scenario. The most advantageous strategy is to determine quickly whether the opponent is really averse to risk or he is playing tight to fool other players and take advantage. All said and done, Expected Utility can be used as a poker strategy to gain upper hand and win hands down.


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