Game Theory in Playing Poker Hand
Poker hands is a common entertainment game played by many, usually accompanied with some amount of bets. As one becomes experienced in poker hands, it is important to consider the number of strategies available and how to utilize them properly.
The article discusses a variety of opening range the poker players should know. In some situations, it is simply a guaranteed win. In others, it is more beneficial to directly fold. However, it reduces a player’s benefits when he/she always chooses strategies (either bet for value or bluff) according to the opening range as I will discuss below.
Similar to the football scenario where one player should randomizes his strategy (for example, only kicking left one third of time event though he/she is more apt at kicking left as a right – leg kicker) in order to prevent his adversary form knowing which side to defend, in Pokers’ game, you should also randomize the number of times where you bluff or bet for value. When one bluffs all the time, the opponent would surely know to always call. Similarly, when one bets for actual value all the time, the opponent knows to fold early, which prevents the individual from making as much profit as he could if he chooses the right strategies (a combination of bluff and bet for value).
Before applying Game Theory to this situation, first, we need to set up some assumptions to simplify the payoff values. That is, we consider it a win when your opponent calls at your value bet and a lose when your opponent calls at your bluffing.
Now, in order to calculate how often we should bluff / bet for value, we consider the expected payoff/ expected value of different scenarios. Assume that now there’s 300 dollars in the pool (you put in $100 already), you are your opponent would each put in $200 to call, there are only the two of you left in this round.
Scenario one: you are bluffing 100% of time
Your opponent will call 100% of time – your payoff is -300, your opponent payoff is +700.
Scenario two: you are betting for value 100% of time
your opponent will fold 100% of time – your payoff is the 200, but nothing additional.
Scenario three: you are betting for value 50% of time, bluffing 50% of time
Assuming your opponent will call 100% of time (a huge assumption, but for the sake of simplifying situation) – your payoff is 400 when you are betting for value and -300 when you are bluffing
Expected payoff = 0.5 (400) + (0.5) (-300) = 50
Scenario four: you are betting for value 2/3 of time, bluffing 1/3 of time
Assume your opponent will call 100% of time – your payoff is 400 when you are betting for value and -300 when you are bluffing
expected payoff = 0.67 (400) + (0.33)(-300) = 169
These are only several of the many scenarios that can happen. As we see here, using both bluffs and bets for value will increase your chance of a higher payoff. Although the situation could be vastly different in, for example, a five-players poker game, combining both strategies is definitely a smarter choice than solely using one throughout.
Source:
https://www.pokernews.com/poker-range-charts