THE STYLE OF PLAYING AND THE PROSPECT THEORY

It is notorious that there are four ways of playing poker hands:

• tight
• loose
• aggressive
• passive.

A tight poker player tends to play only strong hands and then he usually folds.

A loose poker player tends to play any hand.

An aggressive poker player tends to bet or raise any hand.

A passive poker player rarely bets or raises.

These attitudes can be combined in four styles:

• tight-aggressive
• tight-passive
• loose-aggressive
• loose-passive.

A poker player usually does not maintain the same style for all the duration of a tournament, but his style changes according to the tournament evolution. The overall style can be represented by a state diagram (Figure 1).

Figure 1

The transactions from a state to another occurs because of the tournament events. For example, a bad beat can induce a poker player who is normally tight-passive to assume a loose-aggressive style (and sometimes to play recklessly obvious weak hands -> tilt). Framing influences the decision process of the poker player; it consists in:

• the number of players
• the entity of the stacks
• the level of the blinds
• the position with respect to the button
• the chronology of the past hands.

In particular framing influences the risk aversion of the player. In economics, the risk aversion characterizes a broker who usually prefers a sure income against a random one. More generally, the behavior of a broker can be:

• risk-aversion
• risk-neutrality
• risk-propensity.

In economics, the classical decision theory is based on the expected utility model: this model was former used in the theory of games (Theory of games and economic behavior, Von Neumann & Morgenstern, 1947) and it assumes that a decider is a rational individual who selects the optimal choice.

This theory is based on the hypothesis that the broker computes a weighted average of the utilities of the possible events, using as weights the single event probabilities. According to this method the decider must be able to determine the utilities of the different decision aftermaths.

As example, let suppose he must decide between two jobs:

• he determines several significant results (for example: income, personal interest, and so on)
• he associates an utility to a result
• he estimates the probability that the result is achieved
• he sums the weighted utilities
• he choose the job which reaches the highest value.

The weakness of this approach consists in not considering the limits of the decider:

• his consciousness about utility
• his cognitive system
• his processing capability
• the context which can influence the decision.

The prospect theory (Kahneman e Tversky, 1979) is instead a descriptive theory, whose aim is to give an explanation to the fact that choices systematically deviate from the forecast of the classical theory and a decider frequently violates the basic axioms of the expected utility model.

This theory is based on the idea that individuals interprets and evaluates the choices in terms of difference from a reference point and their behavior depends on the way the problem is presented.

In particular the two authors focus on two important connected psychological phenomena:

• framing: the frame that is the context in which the individual makes his choice; it has a decisive influence on the decision itself. In particular, the way in which the problem is presented influences the way the individual fix the point of reference (“status quo”) which uses to evaluate the possible effects of his decision.
• loss aversion: for most of the individuals the motivation to avoid a loss is stronger than the motivation to realize a gain. This general psychological principle is probably connected with the survival instinct and makes the decider to select different decisions if the same problem is represented in terms of loss instead of gain. Individuals tends to avoid any risk when the prospect is a gain while they tends to accept the risk when the prospect is a loss.

For example, imagine that USA must decide about a Asian pandemic that will produce 600 victims. There are two alternative plans. Two formulation of the same problem are possible.

Formulation1.

• If plan A is chosen, 200 people will be saved.
• If plan B is chosen, there is 1/3 probability that they all be saved and 2/3 probability that they all will die.

Experimental result: the 72% of the individuals chooses plan A.

Formulation1.

• If plan A is chosen, 400 people will die.
• If plan B is chosen, there is 1/3 probability that nobody will die and 2/3 probability that 600 people will die.

Experimental result: the 78% of the individuals choose plan B.

The feeling that an choice corresponds to a gain or a loss is a function of a reference point which varies because of the problem presentation. The shift of the reference point can bring to different decision if it transforms a gain in a loss or the other way round.

The utility function of Von Neumann and Morgenstern is substituted by the value function which has the following features (Figure 2):

• it is dependent from the size of the gain or loss
• it is concave in the gain range (risk aversion)
• it is convex in the loss range (risk propensity)
• it is much steeper in the loss range

Figure 2

Figure 2

The emotional state of the poker player can be:

• loss feeling
• gain feeling.

The state diagram of the style of playing is influenced by the state diagram of the emotional state (Figure 3).

Figure 3

To be continued…