Tuesday, October 6, 2009

Klondike Solitaire - is it beatable ?

I am one of those people who can play klondike (sometimes also just called solitaire) for hours and hours. And I was always looking for the best strategy to play. When searching on the internet I noticed that there is next to no websites on strategy and zero information on the expected value (EV) of this game.
One of the few pages with some insight on this topic is OddThinking but this is a slightly different game than the one I am interested in. I prefer the vegas style game where you can only move through the deck exactly once and any card that has been moved up has to stay up.
As stated before I could not find an analysis of this game online which is strange because this game can even be played in some online casinos for real money. So I build myself a simulator to play it automatically. Here are my first results:
My best strategy so far is able to move up about 9.3 cards in average. Which would result in a house edge of 7%. I am confident that it still can be improved.
A Monte Carlo run of 1000 plays per deck (meaning a certain deck or single game is played 1000 times with totally random moves) is able to score a average of 14.5 cards. Of course this value can never be reached by any "real" strategy it will only give a upper threshold.
A "real" strategy has to make a decision on the next move by the information which is currently available (we call this a information set). Since Klondike is a game of imperfect information (because some cards are still hidden) there might be different games which have the same information set. All visible cards are exactly the same but the hidden cards are distributed differently. Our strategy always has to make the same move which of course will result in different results on each unique game. Monte Carlo will choose different moves each time and will ignore the information set. That is the reason why a strategy will never beat the Monte Carlo approach (if the game has imperfect information).

More to follow.....

Tuesday, September 30, 2008

Miniconomy - economic browser game

Well the blog is also about pc games. So here is the latest browser game i am testing

An economic browser game. It doesn't have the nicest graghics around but it seems fairly complex. Every movement costs gas and everytime you search your land for resources the condition if it gets worse.
You can choose to dig for resources or create a more advanced product. You may even found your own bank or try to get elected as mayor. Even a life in crime is possible. It is totally up to you....Now see you in miniconomy....You can find my shop in Centropolis.

Wednesday, August 27, 2008

Professional Go player defeated by computer

Some time ago I wrote about checkers being completly solved. And i was happy to say that Go is still something everyone can win against a computer opponent. About 2 weeks ago I was proven wrong :-(
A supercomputer matched a professional Go player. Kim MyungWan, an 8 dan pro (9 is the maximum) was defeated by the program MoGo running on an IBM Power 575 Hydro-Cluster system. This supercomputer (located at Amsterdam, Netherlands) has a peak speed of 60 Teraflop per second. So it is save to say that the average player will not face such a opponent every other day but we all know how fast the computational speed is increasing.
Go still is one of the hardest games for a computer and it seems like only speed and mass (storage that is) enables such a system to beat a human player. It is still a long way to go for all working on artificial intelligence (AI) to make a computer "think".
On the other hand the human brain is nothing else.....and even if we are slow at math and things like that the human brain is working incredible fast because there is so much going on at the same time. And we a freaking good at guessing ;-)
Many of us would struggle to solve a quadratic equation. Still each and everyone is able to catch a ball or at least to teach it by predicting its flight curve. That is just the same and you even do it without pen and paper or even a calculator. Never correct but always close enough to survive. So keep making mistakes but enjoy your games and life.....

Monday, July 28, 2008

Improve your chess with Chess Tactics Server

Here is another way besides the personal chess trainer to improve your chess skills. The Chess Tactics Server offers 23803 different chess problems of different difficulty. And the number is growing.
You can choose to solve the puzzles as a guest or create a account. If you get a totally free account (you only need to choose a nick and enter a email address) you can trace your rating development. Also if you get a account you will always get problems that match your rating.
The problems are not always typical puzzles where you have to find a mate in X. There are also lots of exercises where you just have to realiz the best move is to take back a figure.
The only thing I don't like about the site is that each puzzle has to be solved with very little time. So it is a good way to improve your blitz chess. You should make sure to redo puzzles you didn't solve on the first attempt. Solving same on later tries will not affect your rating on the site but will help you to improve your chess skills. Remember most of the time chess is just detection patterns and move accourdingly. Chess Tactics Server will help you in doing so.
Now have fun solving problems and dream of chess patterns all day and night :-)