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Pentago Is a First-Player Win
First time accepted submitter jwpeterson writes "Like chess and go, pentago is a two player, deterministic, perfect knowledge, zero sum game: there is no random or hidden state, and the goal of the two players is to make the other player lose (or at least tie). Unlike chess and go, pentago is small enough for a computer to play perfectly: with symmetries removed, there are a mere 3,009,081,623,421,558 (3e15) possible positions. Thus, with the help of several hours on 98304 threads of Edison, a Cray supercomputer at NERSC, pentago is now strongly solved. 'Strongly' means that perfect play is efficiently computable for any position. For example, the first player wins."
Out of curiousity, does anybody know what the number for chess that compares to the 3e15 number for pentago is? In other words, how much "bigger" is chess?
After playing in chess tournaments for 20 years, I have strongly solved that chess is a forced win for any player facing me.
Assuming the game goes for at least 30 moves, and that each player has roughly 10 options per move you get 10^(2*30). 10 options times 30 moves * 2 (there are two players, so two moves per "move").
No, tic-tac-toe is always a tie.
"[Regarding the 'cloud,'] ownership was what made America different than Russia." -- Woz
All these posts have the caveat of "with perfect play"
Human play is about creating mental shortcuts that create useful heuristics for "winningness", and developing those shortcuts is most of the fun to be had.
If you are always losing as the second person in tic-tac-toe, you might want to lay off the drugs or stop posting on Slashdot as your IQ is too low.
Can't the editors write a headline that meets the basic rules of grammar? How about "In the game of Pentago the first player can always win", or "Pentago is strongly solved".
No cause with out those grammar mistakes their would be 30 pricent fuer com-mints on /.
It all starts at 0
If Matthew Broderick had played pentago, the computer would have concluded the first country launching a nuclear missile always wins the war.
Il came close
No, now that Pentago is solved, we're reduced to online games of Pedant.
HINT: Last player always wins.
I thought it meant, the game of Pentago is a really awesome first person shooter. or other game from the first person perspective. You know, the opposite of "Pentago Is a First-Player FAIL"
Again Go proves superior: Memorizing Go openings is a start. Learning why they work the way they do is required.
In Go, your opening is strong for a reason. Somebody plops a stone in the middle of it, or does an approach out of turn, you have an advantage or at least are no worse off than if you played a standard opening. Fast players just play standard openings and get into midgame--Koreans like to do this. The Japanese like to analyze their opponent, the board, and form a long-term strategy based on standard openings, often not even following the standard more than 2 or 3 moves. Standard openings like Ni Ren Sei and San Ren Sei are only a few moves (Ni Ren Sei is black on two adjacent corners, white on two adjacent corners, black's move--which is usually approach, or strengthen, sometimes split).
In Go, your opponent can do more than just move a piece toward you in a bumbling and foolish manner. He can jump right into the middle of your opening and screw it up. Mid-level players do this a lot: a slightly stronger opponent will disrupt a weaker opponent because he can make a position off the disruption, and the weaker opponent does not know why he is playing the Low Chinese other than because it is a correct opening--and thus makes a really screwy position responding poorly.
Go is about concepts. Memorizing Joseki is often advertised as a good way to start; it is a poor way to continue. Joseki study is done to learn why: to learn about variations, about how a joseki is strong, about why a korean Jung-Sek is formed differently from a similar looking Japanese Joseki--what was the goal?
Life and Death is often by rote... for the simple shapes. Vulnerable points. Recognizing the shapes before they come.
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Connect Four was the same way. Whoever went first wins. Didn't take a supercomputer to figure that out, either. Once you did figure that out, though, it pretty much made playing that game pointless. Up in the back of the closet it went. Something tells me Pentago will be joining it, soon.