The theory behind the 'cold poker master.'
Jeopardy is a human problem "solved" by a machine, but poker is a machine problem at the outset. Winning, or maximizing one's winning potential, is a matter of analyzing a card game as a succession of states, wherein each state offers players probabilities of certain events happening or not happening that can then be maximized in the interests of winning. Poker is a natural computer science problem, but, fortunately, computers are rarely allowed at the table.As noted in the intro to a 2011 post, the ability to make decisions under conditions of incomplete information is a talent that can be developed:
Yet, sometimes they are. Meet Lengpudashi, a poker bot developed by researchers at Carnegie Mellon University whose name translates to "cold poker master." Which is perfect. In a recent set of exhibition matches on China's Hainan island, Lengpudashi won $792,327 in poker chips over the course of five days and 36,000 hands. Its opposition was Team Dragon, a group of human engineers and computer scientists led by Yue Du, an amateur poker player and venture capitalist who took home a 2016 World Series of Poker golden bracelet (the first Chinese player to do so).
Lengpudashi's win meant an IRL $290,000 in prize money, which will be reinvested in Strategic Machine, an AI company founded by CMU researchers Tuomas Sandholm and Noam Brown. An earlier poker bot developed by the duo won $1,766,250 in chips earlier this year in an epic 20-day match against five of the world's top poker players.
However natural it may seem as an AI problem, poker isn't Go. Poker introduces the problem of incomplete information. A machine playing Go or chess can observe a board and know immediately the complete state of the game. Like a human poker player, however, the poker bot only knows what it sees. The best it can do is count cards—based on what's on the table and in my hand, what cards are left in the deck? This set of remaining cards only constrains possibilities. Luck makes the final call. Luck, after all, is just what we don't know.
More technically, poker is an example of an information-imperfect game. Sandholm and Brown go deeper in a paper presented earlier this year at the AAAI-17 Workshop on Computer Poker and Imperfect Information Games in San Francisco. The technique described in the paper for such problems is a variation of what's known as "endgame solving."
In a information-complete game like checkers or chess (or Go), the computer's strategy is to decompose the larger game into a bunch of smaller games. Iteratively solve those problems and you should wind up with a solution to the whole problem. This is endgame solving as it's usually understood. Checkers was definitively solved in this fashion.
"In imperfect-information games, endgame solving is drastically more challenging," Sandholm and Brown write. "In perfect-information games it is possible to solve just a part of the game in isolation, but this is not generally possible in imperfect-information games." Imperfect-information games have to be solved as whole entities, not through decomposition.
This is a problem with large games, like No-Limit Texas Hold'em. No-Limit Texas Hold'em has 10 165 nodes that have to be computed in order to be "solved."...MORE
Why Analysts Should Keep it Simple (BAC)
I just read half of a manager's lengthy defense of a position in Bank of America that sounds to be seriously underwater.And from a 2007 post on carbon markets:
After a few thousand words I asked myself if this was the highest use of my time and got a ringing "No" for an answer.
I've never cared for the 37-page investment thesis approach to investing.
Instead, I've hung around people who are very quick on their feet and who make decisions-based-on-imperfect-information all day long and I've sort of acquired the trait....
...Here's economist John Kay in the Financial Times last year:
...The first problem was the lawyers, whose instinct is to write rules to cover every possible contingency. But no one can anticipate every possible contingency. Some economists believe in, and lawyers aspire to, a world in which contracts and property rights are completely specified. But business must face imperfect information today and inescapable uncertainty tomorrow. The genius of the market system is that it responds flexibly, if imperfectly, to a future that will not have been predicted. That is why clear and transparent regulation is hard to achieve in a market economy....
