Update

chess.md

@@ -92,7 +92,7 @@ So secondly we need to implement a so called **search** algorithm -- typically s
 
 Exhaustively searching the tree to great depths is not possible even with most powerful hardware due to astronomical numbers of possible move combinations, so the engine has to limit the depth quite greatly and use various [hacks](hacking.md), [approximations](approximation.md), [heuristics](heuristic.md) etc.. Normally it will search all moves to a small depth (e.g. 2 or 3 half moves or *plys*) and then extend the search for interesting moves such as exchanges or checks. Maybe the greatest danger of searching algorithms is so called **horizon effect** which has to be addressed somehow (e.g. by detecting quiet positions, so called *quiescence*). If not addressed, the horizon effect will make an engine misevaluate certain moves by stopping the evaluation at certain depth even if the played out situation would continue and lead to a vastly different result (imagine e.g. a queen taking a pawn which is guarded by another pawn; if the engine stops evaluating after the pawn take, it will think it's a won pawn, when in fact it's a lost queen). There are also many techniques for reducing the number of searched tree nodes and speeding up the search, for example pruning methods such as **alpha-beta** (which subsequently works best with correctly ordering moves to search), or **transposition tables** (remembering already evaluated position so that they don't have to be evaluated again when encountered by a different path in the tree).
 
-**Alternative approaches**: most engines work as described above (search plus evaluation function) with some minor or bigger modifications. The simplest possible stupid AI can just make random moves, which will of course be an extremely weak opponent (though even weaker can be made, but these will actually require more complex code as to play worse than random moves requires some understanding and searching for the worst moves) -- one might perhaps try to just program a few simple rules to make it a bit less stupid and possibly a simple training opponent for complete beginners: the AI may for example pick a few "good looking" candidate moves that are "usually OK" (pushing a pawn, taking a higher value piece, castling, ...) and aren't a complete insanity, then pick one at random only from those (this randomness can further be improved and gradually controlled by scoring the moves somehow and adding a more or less random value from some range to each score, then picking the moves with highest score). One could also try to just program in a few generic rules such as: checkmate if you can, otherwise take an unprotected piece, otherwise protect your own unprotected piece etc. -- this could produce some beginner level bot. Another idea might be a "Chinese room" bot that doesn't really understand chess but has a huge database of games (which it may even be fetching from some Internet database) and then just looking up what moves good players make in positions that arise on the board, however a database of all positions will never exist, so in case the position is not found there has to be some fallback (e.g. play random move, or somehow find the "most similar position" and use that, ...). As another approach one may try to use some **non neural network [machine learnening](machine_learning.md)**, for example [genetic programming](genetic_programming.md), to train the evaluation function, which will then be used in the tree search. Another idea that's being tried (e.g. in the Maia engine) is **pure neural net AI** (or another form of machine learning) which doesn't use any tree search -- not using search at all has long been thought to be impossible as analyzing a chess position completely statically without any "looking ahead" is extremely difficult, however new neural networks have shown to be extremely good at this kind of thing and pure NN AIs can now play on a master level (a human grandmaster playing ultra bullet is also just a no-calculation, pure pattern recognition play). Next, **[Monte Carlo](monte_carlo.md) tree search** (MCTS) is an alternative way of searching the game tree which may even work without any evaluation function: in it one makes many random playouts (complete games until the end making only random moves) for each checked move and based on the number of wins/losses/draws in those playouts statistically a value is assigned to the move -- the idea is that a move that most often leads to a win is likely the best. Another Monte Carlo approach may just make random playouts, stop at random depth and then use normal static evaluation function (horizon effect is a danger but hopefully its significance should get minimized in the averaging). However MCTS is pretty tricky to do well. MCTS is used e.g. in Komodo Dragon, the engine that's currently among the best. Another approach may lie in somehow using several methods and [heuristics](heuristic.md) to vote on which move would be best.
+**Alternative approaches**: most engines work as described above (search plus evaluation function) with some minor or bigger modifications. The simplest possible stupid AI can just make random moves, which will of course be an extremely weak opponent (though even weaker can be made, but these will actually require more complex code as to play worse than random moves requires some understanding and searching for the worst moves) -- one might perhaps try to just program a few simple rules to make it a bit less stupid and possibly a simple training opponent for complete beginners: the AI may for example pick a few "good looking" candidate moves that are "usually OK" (pushing a pawn, taking a higher value piece, castling, ...) and aren't a complete insanity, then pick one at random only from those (this randomness can further be improved and gradually controlled by scoring the moves somehow and adding a more or less random value from some range to each score, then picking the moves with highest score). One could also try to just program in a few generic rules such as: checkmate if you can, otherwise take an unprotected piece, otherwise protect your own unprotected piece etc. -- this could produce some beginner level bot. Another idea might be a "Chinese room" bot that doesn't really understand chess but has a huge database of games (which it may even be fetching from some Internet database) and then just looking up what moves good players make in positions that arise on the board, however a database of all positions will never exist, so in case the position is not found there has to be some fallback (e.g. play random move, or somehow find the "most similar position" and use that, ...). As another approach one may try to use some **non neural network [machine learning](machine_learning.md)**, for example [genetic programming](genetic_programming.md), to train the evaluation function, which will then be used in the tree search. Another idea that's being tried (e.g. in the Maia engine) is **pure neural net AI** (or another form of machine learning) which doesn't use any tree search -- not using search at all has long been thought to be impossible as analyzing a chess position completely statically without any "looking ahead" is extremely difficult, however new neural networks have shown to be extremely good at this kind of thing and pure NN AIs can now play on a master level (a human grandmaster playing ultra bullet is also just a no-calculation, pure pattern recognition play). Next, **[Monte Carlo](monte_carlo.md) tree search** (MCTS) is an alternative way of searching the game tree which may even work without any evaluation function: in it one makes many random playouts (complete games until the end making only random moves) for each checked move and based on the number of wins/losses/draws in those playouts statistically a value is assigned to the move -- the idea is that a move that most often leads to a win is likely the best. Another Monte Carlo approach may just make random playouts, stop at random depth and then use normal static evaluation function (horizon effect is a danger but hopefully its significance should get minimized in the averaging). However MCTS is pretty tricky to do well. MCTS is used e.g. in Komodo Dragon, the engine that's currently among the best. Another approach may lie in somehow using several methods and [heuristics](heuristic.md) to vote on which move would be best.
 
 Many other aspects come into the AI design such as opening books (databases of best opening moves), endgame tablebases (precomputed databases of winning moves in simple endgames), clock management, pondering (thinking on opponent's move), learning from played games etc. For details see the above linked chess programming wiki.
 
@@ -300,4 +300,4 @@ Chess is only mildly [bloated](bloat.md) but what if we try to unbloat it comple
 - [Catan](catan.md)
 - [Deep Blue](deep_blue.md)
 - [stockfish](stockfish.md)
-- [anal bead](anal_bead.md)
+- [anal bead](anal_bead.md)