Friday, February 12, 2010

Quantum Poker

"No way, I can't believe you made a straight flush! This game must be rigged!"

"You hit a two-outer, that's nuts, that never happens."

"I flopped a full house, but the other guy flopped quads!"

Seldom does a day go by where I don't hear the lament of some poor poker-playing soul who seems to be devoid of luck, who literally has the deck stacked against him. A crazy thing happens, and he simply can't get over the fact that not only was he unlucky, he was statistically very very unlucky. It happens again and again, and some players eventually come to believe that everything about the game is rigged in some way or another. This is especially true in online poker, where bad beats come thick and fast, and it often seems incredibly unlikely that the things happening are random. Is poker as random as it is advertised? Or is there some devious master plan that is simultaneously screwing over most players while benefiting a select few?

I have a favorite analogy to describe how the apparently skewed results poker players see every time they walk into a card room derive from a misunderstanding those players have of statistics combined with the sheer volume of statistical trials a poker table or room produces. For me, the statistical voodoo found in poker rooms is a fairly accurate model for some aspects of quantum mechanics.

How, you may ask, could a room full of large, macroscopic things such as cards, people, tables etc, have anything to do with quantum mechanics, which deals almost exclusively with the microscopic and smaller? Statistically, quantum mechanics describes random chance's effects on particles, as well as the effect of a massive number of trials for any given event occurring. There is, for example, an event known as quantum tunneling, where a particle can mysteriously move from one point to another in space, even if there is something blocking that route. The likelihood of this happening is ridiculously, monumentally small, yet we observe it over and over again. The reason is that, though the chance of any individual particle tunneling through an impassable wall at a given moment is incredibly unlikely, if you put a bajillion(or so) particles next to the wall and give it enough time, that incredibly, monumentally unlikely occurrence is almost a certainty to occur. It's a good thing this is true, because quantum tunneling enables, among other things, the nuclear reactions that occur in the sun to happen, which is very important to a poker player's continued existence and profit margin.

So, the poker part of this whole mess: If you have 85 tables in the Borgata poker room, each dealing something along the lines of 25 hands an hour, with each one of those hands being played by 10 people or so, it suddenly becomes very likely that "something weird" will occur, on a fairly regular basis.

The odds of flopping a royal flush are 1 in 610,756 hands(trust me). 85 tables *25 hands per hour * 10 players per hand = 21,250 hands played in total per hour in the Borgata. 600,000/20,000 gives a rough estimate that, on average, one person will flop a royal flush in the Borgata poker room every 30 hours or so. Suddenly, that incredibly unlikely event is happening almost once a day! Factor in the range of things that are considered unlikely(four-of-a-kind, a runner-runner draw(meaning hitting 2 perfect cards on the turn and river to win a hand), set over set, four-of-a-kind running into a straight flush, etc) and you can see how very very unlikely things will be almost commonplace in a busy enough poker room.

So every time something incredibly, unbelievably unlucky happens to ME, I remind myself that, if it weren't for random, unlikely events occurring, the universe wouldn't work. So I've got that going for me. Which is nice.

2 comments:

  1. PS. Quantum tunneling happens because of a particle's "probability wave" which describes any particle's possible locations as a function of probability. This relates to the Heisenberg uncertainty principle: You can measure a particle's velocity or a particle's location, but not both to any degree of accuracy. You can, however, map out a "probability wave" of the places where the particle is most likely to be. An electron is overwhelmingly likely to be orbiting around the nucleus of an atom, but it doesn't HAVE to be. It could be a little to the left, it could be on the other side of our theoretical impassable wall, it could be on the moon, etc etc. So for tunnelling, the probability wave for a particle lies mostly on one side of the wall, yet there is a little spike on the other, which is all our quantum escape artist needs to get across the wall.

    PPS. If any of my physics is incorrect here, forgive me, it's been awhile. Feel free to correct me in the comments. The point of the post holds true as far as I know.

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  2. Ha, I just wrote a book called Quantum Poker and saw this post when I was searching it. It is true that Quantum mechanics and poker are similar, especially with the uncertainty about opponent's hole cards.

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