Marco Naccarato Blog: Counterintuitive

A little over a month ago, here on the Pokerdicas Forum, the user danielpxm82 created a topic questioning the percentages that appear in the video on TV poker broadcasts. To clarify his doubt, he posted an excerpt from the movie 21 (original title: 21, from 2008). The movie is set in Las Vegas and mainly at the Planet Hollywood casino, and tells the story of a group of MIT (Massachusetts Institute of Technology) students who developed a card counting system to gain an advantage at the city's blackjack tables. Playing as a team, they manage to win some money, but they face several problems as the story unfolds. So far, nothing special, it's a great afternoon session, but the scene that danielpxm82 highlighted and posted on the PD Forum, which generated a lot of exchange of ideas among users, provides a good discussion if we draw a parallel with poker.

The problem presented in the video is the Monty Hall Paradox, which became very well-known in the 1970s due to the television show that popularized it (Monty Hall, in fact, is the name of the host). Many PhDs in mathematics from various American universities turned their noses up at the unconventional answer to the problem. Well, let's see why. The problem is simple: you are on a television game show and the host shows you three doors, saying that behind one of them there is a brand new car, and a goat in each of the other two doors. He then asks you to choose one of the doors, and if you guess the car, the prize is yours.

It turns out that after your first choice, the host opens one of the unchosen doors and reveals a goat. Of course, the host knows in advance where the car is, and to give the show a dramatic tone, he asks if you want to change doors.

Apparently, if there are only two doors left, one with a car and the other with a ruminant, the chance of winning the prize is 50%, but that's not quite true, because the answer that gives you the highest probability of winning is counterintuitive. Switching the doors increases your chance of winning to 2/3, because the fact that there is a door revealed does not change your chance, but making the switch does. When you chose the door, the chance of having chosen a goat is 2/3, and when you make the switch, the chance of getting the caranga increases to 2/3, as shown in the video. If you want to try it in practice, ask a friend to separate two spades and one diamond, place them face down, and simulate the problem a few times, at least ten times keeping your initial choice, and then another ten making the switch, and check the results.

We now know that the best choice is the one that increases the probability of winning, that is, as in poker, the best play is the one that respects mathematics, and brings a better expectation of winning. This parallel makes the Monty Hall paradox quite interesting in itself, but it raises very interesting questions for poker.

Often, in the felt, we are deceived by the apparent ease of a logic that does not always represent reality, and we will be faced with choices that seem to be rational and based on absolute truths, but we will fall flat on our faces, as we have to look at the situation from various points of view, and sometimes, essentially in a counter-intuitive way.

Well, in 2010 I was in Las Vegas, playing in the evening tournament at the aforementioned Planet Hollywood Casino poker room. At the table there was a mix of good players and recreational players, but one of them, a tough-looking Indian, was sparing no chips in the many hands he played. One of these hands caught my attention, because of the unusual line the Indian used. After a player limped in early position, he opened a 3xBB raise in MP, and received three calls, including the original limper, SB and BB.

Even though I was out of the hand, I watched the action, and we saw the devil's flop, 666. Everyone checked, the Indian put in half the pot, the blinds folded and the action returned to the player in EP, who insta-called. On the turn, a 3, EP checked and the Indian checked-behind. On the river another 3, making a full house on the board, and after the third check by the player in EP, the Indian went all-in. Minutes later, he decided to call and showed 99, while the Indian threatened to muck, but showed A6 and took the pot.

In the Indian's view, limping in early position could indicate a low-value pair, and it was probably unlikely that at least one of the callers didn't have a pair in his hand, which is why he bet on the flop with the nuts. On the river, with a board like that, I have no doubt that he took advantage of the situation to extract as many chips as possible from his opponent. You would certainly conclude that the Indian was playing with the board, or at best, that he had a full with a pair in his hand. In the EP player's view, it would be unlikely that someone would bet like that with four of a kind or a bigger full in their hand, which made the Indian's bet look more like a bluff than value.

This is an extreme example, and it is worth mentioning that it was a turbo tournament, and that the Indian was very aggressive at the table, but it shows that unconventional lines of play change the dynamics of the game (pushing the blinds from UTG is a good example of an unconventional play that has become common in poker). According to the rules, the Indian should have cooked his opponent until he improved his hand, and only then bet for value on the river, but by creating reasonable doubt he took his opponent off the table. Sometimes the opponent seems to want to take you out of the hand, which seems logical, but in fact he is betting to take all your chips. This hand reminds me of the final hand of the 1998 WSOP Main Event, not so much because of the betting line, because after all Scotty Nguyen only called until the turn, but because of the shove at the end of the hand with a little chatter, to confuse the opponent, inducing him to make a mistake.

Another example is the Ultimatum Game, which is nothing more than a practical application of the famous Game Theory (a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to improve their return). In the Ultimatum Game, a banker offers a prize to player A, say 100 chips. This player must divide, at his discretion, a percentage of the chips and offer it to player B. If player B does not accept the offer (he can only say yes or no, without any kind of bargaining), the banker does not pay either of them. Namely, the bank does this only once, that is, the players will not have a new round of offering and accepting, so that mathematically player B should accept any amount, as winning a chip is better than none, but studies have shown that in practice, 2/3 of the people in the role of player A, made 50/50 divisions or close to that, and players who offered less than 20% of the winnings, lost the prize, as it seems illogical and even unfair, generating a result with an emotional outcome.

In all these examples, whether in the Monty Hall paradox, the Indian hand at Planet Hollywood or the Ultimatum Game, we learn that the search for any player who decides to commit to learning poker, whether recreationally or professionally, always comes up against a method of playing with positive expectations and an understanding of the emotional and psychological aspects that involve the game, and although there is luck and bad luck involved in every hand, poker is an excellent mental game, where your level of play will only improve when you realize that the quality of your choices at the table are more important than winning or losing the hand.

For a more detailed explanation of the Monty Hall paradox, access this Wikipedia link. The topic mentioned, for those who want to follow, is here, with the results of the discussion of the Monty Hall problem and hand percentages. And finally, to learn more about Game Theory, access this link and research even more, because after all, well-played poker is the result of a lot of practice, but also of dedication and research.

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].