The Appeal To Probability Fallacy in Poker
Nine out of ten readers enjoyed this article on The Appeal To Probability Fallacy, so you will too. Blind Spot
The Appeal To Probability Fallacy in Poker
Nine out of ten readers enjoyed this article on The Appeal To Probability Fallacy, so you will too.
Blind Spot
In 2009, the statistician, data-journalist author and poker player Nate Silver was named one of the world's 100 most influential people by Time Magazine after his election forecasting model correctly predicted the 2008 U.S. presidential election outcomes in 49 of the 50 states.
His subsequent models predicted the outcome of the 2012 and 2020 presidential elections with high accuracy too. However, in 2016, the model predicted a Hillary Clinton win, giving the former Secretary of State and First Lady a 71% chance of victory. Most major forecasters predicted Clinton to win a far higher percentage of the time but that didn’t stop people from criticizing Silver’s model.
In an interview with the Harvard Gazette in March 2017, Silver explained how the result did not represent a failure of data analytics, but rather a failure by people, especially those working for media outlets, to properly understand probability:
“I think people shouldn’t have been so surprised. The polls pointed toward a competitive race. The national polls in particular were very close to where the race ended up… However, I think people thought ‘Well, Clinton’s ahead in most of the polls in most states, and I remember that seems similar to Obama four years ago, and therefore I’m very confident that she’ll win.’ That’s ad hoc and not a very rigorous thought process… I think it [shows that] there were blind spots in people’s thinking.”
Another word for a blind spot in this context is cognitive bias but which specific cognitive bias was most at play here? I suspect that it was ‘the appeal to probability fallacy’. When something is likely or unlikely to happen, humans often jump to the conclusion that it will definitely or definitely not happen. When one thing followed another thing before, humans often assume that history must repeat itself. Inevitability is assigned to a set of circumstances which is undetermined. That which is uncertain becomes apodictic. Nine out of ten readers enjoyed this article, so you will too. This saves mental energy but it obviously leads to some extremely flawed reasoning.
Cash Games At The Norwegian Championships
In recent years, the Irish Poker Open has made a new home for itself in the Royal Dublin Society (RDS) but for a time, it’s venue was the Citywest Hotel on the outskirts of Dublin where it joined forces with the Norwegian Poker Championships to form a 17-day poker extravaganza. The daily tournaments were all well-attended but, outside of the two main events, the unique selling point of this festival was the cash games.
In fact, the action on the cash tables was so loose and so wild that even grizzled tourney donks like myself would dust off their mediocre 200 big blind games and splash around. Straddles would be posted. Shots would be imbibed. Tiny percentages of the Norwegian Wealth Fund would be punted and Irish players would basically do whatever it took to keep the blonde-haired, blue-eyed, chisel-jawed degenerates of Scandinavia happy
My modus operandi would be to show up for the afternoon tournament, re-enter it if necessary, play the evening turbo, re-enter that if necessary and then hop into the €2/€5 action. 2016 was a particularly good year. I won back-to-back tournaments on consecutive days and I was running hot in the cash games.
The Hallowed Hatrick
I have a very vivid memory of my journey to Citywest on the morning of March 20th 2016. It was pissing rain and I got soaking wet whilst walking along Dublin’s Grand Canal on my way to the tram stop. I recall how the curmudgeon/masochist in me was especially strong because I was not willing to treat myself to a taxi ride on the day after I won the €350 8-Max tournament and two days after I won the €150 Shootout. As a result, I arrived to the venue completely sodden.
Undaunted and indomitable, I used the hand-dryer in the restroom to exsiccate my shirt, jacket and shoes. Unflinching and steadfast, I exited the restroom and bee-lined for the registration desk. I was on a mission. I wanted the poker tournament three-peat and I knew how to give myself the best chance. I was going to play the smallest runner field possible.
After ponying up the money to the €150 Open Face Chinese Poker 4-Max, I took my seat on a table with event organiser Frode Fagerli and Norwegian poker legend Thor Hansen. While I dreamt of the hallowed hat-trick, they would give me a rude awakening, schooling me at a game in which I only had moderate proficiency. They would eventually come first and second while I would be the first player eliminated. I scuttled from the tournament area and towards the cash game tables with my tail between my legs and my feet firmly back on terra firma. To the extent that I had indulged a bit of whimsy, succumbing briefly to the appeal to probability fallacy, that was nothing compared to what I was about to witness.
A Busted Flush Draw
Sitting in a lively €2/€5 game, the straddles were on and a good start meant that I was sitting behind a stack of about €1800, having bought in for €1000. In the spirit of the game, I had been VPIPing almost half of the hands and while two big pots had come my way thanks to making a couple of big hands, I had also lost back a chunk bluffing. In that spot, I was chasing the nut straight, found myself on the river with 6-high and felt like it was a good spot to bluff. I fired out a pot bet of €350, my opponent snap-called and I snap-mucked, laughing at how he had caught me with my hand in the cookie jar.
A few orbits and a couple of compulsory Jaeger-bombs later, I got embroiled in a hand that I will never forget. I posted the straddle, the player in the Hijack made it €40 to go, the button called and I called with A♦️J♦️. With just north of €125 in the pot, the three of us saw a flop of T♠️9♦️3♦️. I checked, the hijack checked and the button casually threw out two €25 chips.
I raised to €200, the hijack folded and the button called. With €525 in the middle, the turn came the 6♣️. I bet €350 and the button called. The pot was €1225 and the river came the K♥️. I figured my line made sense for a set and Queen-Jack so I decided to go for it. Picking up a stack of €100 chips, I looked at the dealer and announced ‘All-in’. No sooner had the words passed my lips when my opponent yelled ‘Call’.
I winced, scrunching up my face in disappointment. ‘Nice hand’, I said and I rolled over my busted flush draw. “No way”, he yelled, “you are not gonna believe how much I just owned you!” “Oh really?”, I enquired, “what do you have… like a nine?” Lifting his cards off the felt, he started snapping them off each other. “Pocket fives?”, I asked sheepishly. He shook his head. “I knew you were bluffing. I knew it. I was 100% sure.” “Yeah, and you were right”, I said half-magnanimously, half just wanting this excruciating interaction to end. To my utter shock, he stood up and threw over the J♥️8♥️ for his own missed draw. “When you bluffed before, you got insta-called and you insta-mucked”, he said. “Lucky for me I didn’t do that this time”, I replied cheekily as I dragged in the €3600 pot.
The Appeal to Probability
Humans are pattern-seeking creatures who have a propensity to look for shortcuts in thinking. Poker players are particularly sensitive in this regard, seeking out heuristics that will help them figure out guideposts or rules to simplify problem-solving in what is an immensely complex game. They constantly interpret their opponents’ betting tendencies, searching for consistencies that can be predicted and exploited. They also process physical information, storing their findings up for a future ‘read’. These shortcuts help to streamline decision-making but sometimes a shortcut is the longest distance between two points. Sometimes, appealing to probability will get you lost.
My Norwegian opponent banked on me mucking all my bluffs because the one previous time that I was caught bluffing, I mucked it. To his credit, he was observant and had picked up a data-point. To his discredit, he made far too big a presumption based on that one data point. One swallow does not a Summer make. One muck does not a mucker make.
Nate Silver said “I don’t think people have a good intuitive sense for how to translate polls to probabilities.” Plain and simple, most people struggle with probabilistic thinking. They get comfort from viewing the world as a predictable, less chaotic and more determined thing. That leads to flawed logic which, in turn, leads to mistakes.
By becoming adept at identifying the Appeal to Probability Fallacy and resisting its allure, people will equip themselves to engage in more rational discussions and make better decisions. Spotting this fallacy starts with a healthy dose of skepticism. Whenever someone says “most likely”, “rarely” or “usually”, pause to consider whether a probability is masquerading as a certainty, a statistical likelihood is being presented as a guarantee.
Play Smarter, Not Just Harder
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