Marco Naccarato Blog: Probability

Galileo Galilei, yes, Galileo himself, mathematician, physicist, astronomer and philosopher, in addition to all the legacy he left for humanity, solved in his “Considerations on the Game of Dice” a simple but curious problem. In the 17th century, some players questioned Galilei about the imbalance of the results 9 and 10 when rolling three dice, since the possible combinations for each were six options:

Result 9: 126, 135, 144, 225, 234 and 333
Result 10: 136, 145, 226, 235, 244 and 334

Through practice, the players had realized that the sum of 10 occurred more often than the sum of 9, even though the combinations were apparently the same. This seemed like an unsolvable problem, and practice defied logic, because the more they played, the more apparent the advantage of the sum of 10 became. Galileo noticed that there were more inversions, or different ways of obtaining each of these combinations, verifying that the total number of combinations for the sum of 10 was 27, while for the sum of 9 it was 25 inversions. For example, to obtain the sum of 10 with the faces 1, 3 and 6, there were six possibilities (136, 163, 316, 361, 613 and 631), and not just one combination, as the players imagined. Clicking here, a link to an appendix that explains the problem well.

Once again, a counter-intuitive solution, a theme explored in my last article here at PD. Situations where apparent logic does not reflect reality are more frequent than one might imagine, and are one of the foundations of the so-called deception game, a fundamental tool in poker, which basically consists of inducing the opponent into error.

However, the focus of this article is different. Note that even though these 17th century players had experience and knowledge of the game of dice, they took the balance of results for granted and were logical, which was not allowing them to reach a more refined reasoning, as they were conditioned in their understanding. In poker, the learning curve, perhaps as in any human activity, is quite steep at the beginning, but players constantly reach a point where their knowledge about the game and the relationships they are able to establish seem to reach a reasonable ceiling of understanding, and that is where the problem lies, when the ability to analyze poker becomes conditioned.

This invariably happens when the player misunderstands the mathematical side of the game and ends up overvaluing or misunderstanding the odds of winning a hand. You've probably seen several examples of this, when, even though you have a much higher chance of winning than your opponent, the combination of cards on the board doesn't help, and your opponent, who doesn't even know poker theory, wins the hand.

Well, you must have been really pissed off about this, and even felt wronged, but after all, that is exactly the main point of this discussion, because the fact that you are a favorite in a hand does not mean that you will win it. Probability is just a theoretical representation that demonstrates the incidence of a certain occurrence. It does not do “justice” nor does it make you deserving of winning a hand, it’s that simple. The fact is that many players, guided by logical and mathematical play, do not accept defeats caused by situations where the opponent is an underdog and ends up winning. Relying solely and exclusively on mathematics gives a false sense of mastery of the game and ends up basing your conclusions on how to play, without taking into account the emotional and situational aspects present at every moment in each decision and hand played.

Enough whining, either you choose to use probability in your favor and risk putting chips on the player who is looking for the flush until the river, or you control the pot to lose less if he hits, because you know what his playing pattern is like. The curious thing is to see the mathematical/logical player complaining about the shuffle in a feverish state of emotional loss of control, when supposedly his strong point would be precisely having emotional control. It makes no sense to apply a mathematical approach to non-theoretical players and gamblers, and if you frequently commit a large part, if not all, of your stack in a hand because you have a good pair or similar, it is good to observe your game and try different ways of playing that hand, identifying where your leaks are and looking for a method of counterplay for this type of opponent.

Without realizing their own mistakes, many poker players look for an external reason to justify their defeats, attributing the bitter negative result to bad luck or the supposed incorrect way their opponent played. But don't worry, this is a natural human defense mechanism. It's just not worth it to always do this, because getting angry is normal, but trying poker with this understanding only brings harm to yourself and will cause your playing method to stagnate, leaving you conditioned. If you lost due to bad luck but played well, there is no apparent reason to worry. Although it often sucks and a given opportunity is unique (let's say you are on the bubble of the WSOP ME final table), exalting and praising bad luck only means that your view is similar to the understanding of poker as a game of chance.

Professional players and those who study the game work out their winning expectancy over a sufficient period of time to have an accurate sample size, so they can analyze their mistakes and fix them. Ask any good poker player if he checks, or knows how often his pocket jacks have been busted to account for his terrible bad luck? I bet he's trying to figure out a better way to play AA than to worry about it.

In conclusion, leave aside the apparent fairness of the odds for a moment, and start working on your head to be able to handle the shock when the going gets tough, and learn to lose, as this will give you the tools to avoid tilting along the way.

Marco Naccarato is a businessman, designer, poker player and author of the book Floating in Vegas, which deals with small stakes in Las Vegas casinos (available for sale at www.floatinginvegas.com.br). Naccarato debuted his column on Leo Bello's Aprendendo Poker website in February, and can be found on the PD Forum under the nickname Carcamano, and every 15 days in the articles section of the PokerDicas portal. To contact the author, send an email to [email protected].