Make Informed Decisions With Bayes’ Formula – Borgata Online

Using Bayesian Thinking to Elevate Your Online Poker Game

Poker is a game of incomplete information, but it’s not merely a guessing game. Today’s poker professionals rely on advanced math-based strategies like GTO (game theory optimal) to bridge the information gap and make informed decisions . These strategies often involve the use of poker solvers and flop charts, as calculating the odds of hands in poker can be too complex for many players to do on their own. Consequently, some players might not fully grasp their actions beyond following the directives of their poker tools.

In contrast, Bayesian thinking presents an alternative rooted in rigorous mathematics — yet it’s easier to understand intuitively. Although it’s not exclusive to poker — Alan Turing famously used it to decipher the German Enigma code during World War II — it proves to be highly effective in the game. Read on to learn how to apply Bayes’ theorem when playing online poker.

Bayes’ Probability Rule

Bayesian thinking centers around making the most accurate predictions by calculating poker odds and probabilities, then updating these probabilities as new information surfaces. The core mathematical concept is Bayes’ Theorem. This probability rule, developed by 18th-century English philosopher and mathematician Thomas Bayes, states: “The probability of an event occurring (A), given that another event has occurred (B), is equivalent to the probability of event B occurring given that event A has occurred, divided by the total probability of all possible outcomes.”

While this might sound complicated, it becomes clearer when put into simpler terms. The best way to understand how to apply Bayes’ theorem is through a practical example. Let’s dive in.

You’re engaged in a heads-up cash game at your local casino against a familiar opponent named Ben. You hold a bluff catcher (top pair with a weak kicker), and Ben just bet on the river. After hours of play, you’ve noticed that he value-bets on the river approximately 60% of the time and bluffs around 40%. take your time in bisaya Additionally, you’ve picked up on a reliable tell: after betting for value, he tends to double-check his hole cards, while when he bluffs, he usually lays his cards on the table.

In this instance, he lays his cards down while you’re contemplating your next move. Should you call or fold?

Clearly, if Ben’s tell were accurate every single time, you’d confidently call his bluff. Unfortunately, there’s still a 20% chance he could be bluffing even when he checks his hole cards. It’s a reliable tell with 80% accuracy, but not foolproof.

So, what should you do? Here’s where Bayes’ formula comes into play pinay teen 2023.

How to Play Poker with Bayes’ Theorem

Bayes’ formula can be articulated in various forms, but for our poker context, the simplest and most effective way is to lay out the information in a table.

Value Betting	Bluffing	Total
Double-checks cards	48	56
Lays cards down	12	32
TOTALS	60	40

In this table, the bottom row shows your prior probabilities for Ben’s value betting or bluffing. myla pablo boyfriend This reflects what you know about his frequencies before factoring in his tells into the calculation.

In the value betting column, you can see that he double-checks his cards 48% of the time when value betting (80% of 60 is 48), and he lays them down 20% of the time when value betting (20% of 60 is 12). Correspondingly, he lays his cards down 32% of the time when bluffing (80% of 40 is 32), and he double-checks 8% of the time when bluffing (20% of 40 is 8) etravel gov ph registration.

Now, it’s time to combine the two types of incomplete information with the prior probability and determine if Ben is bluffing or not. Here’s how it works.

Recall that Ben laid his cards down after betting. The second row demonstrates that he does this 44 times in 100 hands, and he’s bluffing 32 out of those 44, which means he’s bluffing 73% of the time. This indicates that the likelihood of Ben bluffing is significantly greater than the 40% prior probability suggests, thereby swaying your decision towards calling.

Putting Bayes’ Formula to Work

This example is quite simple and doesn’t account for nuances like bet size and pot size, but it fundamentally illustrates how Bayesian thinking operates, and you can adapt it to various scenarios. If Ben takes a vacation and returns a significantly tighter player (90% value bets and 10% bluffs) while maintaining the same tells, he bets into you on the river and lays his cards on the table. While your instinct should be to fold, remember that his bluff tell is accurate 80% of the time. Should you call? If you insert the figures into the table, you’ll note that he’s bluffing only 31% of the time and value betting 69%, leading you to fold, despite the 80% accuracy of the tell.

This might seem counterintuitive, yet that’s the essence of Bayes’ formula. The more you apply it, the more you’ll uncover the flaws in your opponents’ bluffs. You can also utilize it to address more intricate questions, such as how to minimize your variance, determining whether an opponent raising from the cutoff is aggressive or conservative, or whether their unusually high win rate stems from skill or sheer luck. While these topics are beyond this blog’s scope, for those eager to dive deeper, books like “The Mathematics of Poker” by Bill Chen and Jerrod Ankenman can provide additional insights.

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