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 PahTum

Discuss about Pah Tum games or find new opponents. Waiting for an opponent to make a move in a game, why not try some Solitary Pah Tum

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24. augustus 2005, 03:03:42
AbigailII 
Onderwerp: Re: my opinion
Aangepast door AbigailII (24. augustus 2005, 03:04:05)
Nothingness: I think white has a huge advantage - with perfect play, white cannot lose. Here's a proof.

Suppose a game is won for black (the second player) - that is, there is a strategy for black that always wins, regardless of how white plays. Then white starts by playing a random stone (this is never a disadvantage), and then adopting the strategy that wins the game for the second player. If that strategy requires placing a stone where white already had played a stone - white plays the stone at a random position. But that means white wins, contradicting the hypothesus that the game would be won for black. Ergo, there is no winning strategy for black if white doesn't make a mistake.

This 'proof' works for any game where placed stones don't move, and don't influence placement of other stones, and where having a stone at a certain position is never a hindrance. Examples outside PahTum include Five in Line, and Hex.

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